Combining Multiple Images with Enfuse 4.2

This manual is for Enfuse version ⟨4.2⟩, a tool to merge different exposures of the same scene to produce an image that looks much like a tone-mapped image.

Frontmatter A Notation

This manual uses some typographic conventions to clarify the subject. The markup of the ready-to-print version differs from the web markup.

Chapter 1 Overview

Enfuse merges overlapping images using the Mertens-KautzVan Reeth exposure fusion algorithm.¹ This is a quick way for example to blend differently exposed images into a nice output image, without producing intermediate high-dynamic range (HDR) images that are then tone-mapped to a viewable image. This simplified process often works much better than tone-mapping algorithms.

Enfuse can also be used to build extended depth-of-field (DoF) images by blending a focus stack.

The idea is that pixels in the input images are weighted according to qualities such as, for example, proper exposure, good local contrast, or high saturation. These weights determine how much a given pixel will contribute to the final image.

A Burt-Adelson multi-resolution spline blender² is used to combine the images according to the weights. The multi-resolution blending ensures that transitions between regions where different images contribute are difficult to spot.

For the concept of pixel weighting, and details on the different weighting functions, see Chapter 5.

Adjust how much importance is given to each criterion by setting the weight parameters on the command line. For example, if you set

Enfuse will favor well-exposed pixels over highly-saturated pixels when blending the source images. The effect of these parameters on the final result will not always be clear in advance. The quality of the result is subject to your artistic interpretation. Playing with the weights may or may not give a more pleasing result. The authors encourage the users to experiment, perhaps using down-sized or cropped images for speed.

Enfuse expects but does not require each input image to have an alpha channel. By setting the alpha values of pixels to zero, users can manually remove those pixels from consideration when blending. If an input image lacks an alpha channel, Enfuse will issue a warning and continue assuming all pixels should contribute to the final output. Any alpha value other than zero is interpreted as “this pixel should contribute to the final image”.

The input images are processed in the order they appear on the command line. Multi-layer images are processed from the first layer to the last before Enfuse considers the next image on the command line. Consult Section 4.5 on how to change the images’ order within multi-layer image files.

Tom Mertens, Jan Kautz, and Frank van Reeth, “Exposure Fusion”, Proceedings of the 15^th Pacific Conference on Computer Graphics and Applications 2007, pages 382–390.

Peter J. Burt and Edward H. Adelson, “A Multiresolution Spline With Application to Image Mosaics”, ACM Transactions on Graphics, Vol. 2, No. 4, October 1983, pages 217–236.

Chapter 2 Known Limitations

Enfuse has its limitations. Some of them are inherent to the programs proper others are “imported” by using libraries as for example VIGRA. Here are some of the known ones.

Chapter 3 Photographic Workflow^c

3.1 Standard, All-In-One Workflow

Figure 3.1 shows where Enfuse and Enblend sit in the tool chain of the standard workflow.

3.2 External Masks

In the usual workflow Enfuse and Enblend generate the blending and fusing masks according to the command-line options and the input images including their associated alpha-channels, and then they immediately use these masks for multi-resolution blending or multi-resolution fusing the output image.

Sometimes more control over the masks is wanted. To this end, both applications provide the option pair --load-masks and --save-masks. See Chapter 4, for detailed explanations of both options. With the help of these options the processing can be broken up into two phases:

In between these two steps the user may apply whatever transformation to the mask files, as long as their geometries and offsets remain the same. Thus the “Combine Images” box of Figure 3.1 becomes three activities as is depicted in Figure 3.2.

To further optimize this kind of workflow, both Enfuse and Enblend stop after mask generation if option --save-masks is given, but no output file is specified with the --output option. This way the time for pyramid generation, blending, fusing, and writing the final image to disk is saved, as well as no output image gets generated.

3.3 Interacting with Enfuse^c

This section explains how to find out about the inner workings of your version of Enfuse without looking at the source code. And it states how to interact with Enfuse besides passing command-line options and image filenames.

3.3.1 Finding Out Details About enfuse

An enfuse binary can come in several configurations. The exact name of the binary may vary and it may or may not reflect the “kind of enfuse”. Therefore, enfuse offers several options that allow the user to query exactly…

Exact Version Number

Example 3.3.1 shows a possible output of ‘enfuse --version’. The version number at the beginning of the text tells about the exact version of the binary. It is the number that can be compared with the version number of this document, which by the way is ⟨4.2⟩. Our slightly cranky markup (see also Notation) dispels copy-paste errors.

The version indicator consist of a two (major and minor version) or three (major and minor version plus patch-level) numbers separated by dots and an optional hexadecimal identifier. Binaries from the “Development Branch” are assigned two-part version numbers, whereas a three-part version number is reserved for the “Stable Branch” of development. Officially released versions lack the hexadecimal identifier.

Matching the version codes is the only reliably way to pair a given binary with its manual page (“manual page for enblend 4.2-1e4d237daabf”) and its documentation. This document mentions the version code for example on its Title and the Abstract.

The twelve-digit hexadecimal ID-CODE is automatically generated by our source-code versioning system, Mercurial. Use the ID-CODE to look up the version on the web in our public source code repository or, if you have cloned the project to your own workspace, with the command

Compiled-In Features

Adding option --verbose to --version will reproduce the information described in the previous section plus a list of “extra features”. Any unavailable feature in the particular binary queried returns

whereas available features answer “yes” followed by a detailed report on the feature and its connection to some library or specific hardware. Example 3.3.2 shows such a report. Remember that your binary may include more or less of the features displayed there.

The ‘--version --verbose’ combo is one of the first things test if enfuse “suddenly” behaves strangely.

Supported Images Formats

Enfuse can read and write a fixed set of image formats if it was compiled to support them. For example the EXR-format requires special support libraries. Use option --show-image-formats to find out

All others are optional. In particular the high-dynamic range (HDR) format OpenEXR only gets compiled if several non-standard libraries are available.

The provided per-channel depths range from just one, namely “8 bits unsigned integral” (uint8) up to seven:

Name Of Builder

During building each enfuse is automatically signed to give the users an extra level of confidence that it was constructed by someone that they can trust to get it right. Access this signature with ‘--show-signature’ and enfuse will print something like

Compiler And Libraries Used To Build

Sometimes enfuse refuses to start or runs into trouble because the libraries supplied to it do not match the ones it was compiled with. Option --show-software-components can be helpful to diagnose the problem in such cases, because it shows the version information of Enfuse’s most important libraries as they have identified themselves during compile-time.

Furthermore the report reveals the compiler used to build enfuse along with the most important compiler extensions like, for example, OpenMP. Example 3.3.3 shows such a report.

3.3.2 Console Messages

Enfuse is meant to read multiple images, “montage” them together, and finally write a single output image. So, any console messages either serve the entertainment desire of the user or indicate problems.

When enfuse is instructed to only show information about its configuration (see Section 4.2.6) the text goes to Standard Output. enfuse sends error and warning messages to Standard Error. The messages follow a fixed format.

In very unfortunate circumstances Enfuse quits because of a problem, but does not show any message. The output file then either does not exist or it is broken. One known reason are out-of-memory situations, where the process needs additional memory, but cannot allocate it and while terminating needs even more memory so that the operating system wipes it out completely wherever it then happens to be in its execution path.

3.3.3 Environment Variables

A small set of environment variables influences the execution of enfuse. All of them depend on enfuse having been compiled with certain features. The hint “(direct)” indicates genuine variables in enfuse, whereas “(implicit)” denotes variables that control libraries that are linked with enfuse.

Chapter 4 Invocation

INPUT images are either specified literally or via so-called response files (see Section 4.4). The latter are an alternative to specifying image filenames on the command line. If omitted, the name of the output IMAGE defaults to ⟨a.tif⟩.

4.1 Input Image Requirements

Moreover, there are some good practices, which are not enforced by the application, but almost certainly deliver superior results.

4.2 Command-Line Options

does and sort them alphabetically within their groups. For an alphabetic list of all options consult the Option Index.

enfuse accepts arguments to any option in uppercase as well as in lowercase letters. For example, ‘deflate’, ‘Deflate’ and ‘DEFLATE’ as arguments to the --compression option described below all instruct enfuse to use the Deflate compression scheme. This manual denotes all arguments in lowercase for consistency.

4.2.1 Common Options^c

Common options control some overall features of Enfuse. They are called “common” because they are used most often. However, in fact, Enfuse and Enblend do have these options in common.

4.2.2 Advanced Options^c

Advanced options control e.g. the channel depth, color model, and the cropping of the output image.

4.2.3 Fusion Options

Fusion options define the proportion to which each input image’s pixel contributes to the output image.

4.2.4 Expert Options

4.2.5 Expert Fusion Options

Expert fusion options control details of contrast-weight algorithms and they set ultimate cutoffs for entropy and exposure fusion.

4.2.6 Information Options^c

As Dr. Daniel Jackson correctly noted, actually, it is not a pyramid: “Ziggaurat, it’s a Ziggaurat.”

4.3 Option Delimiters^c

Enfuse and Enblend allow the arguments supplied to the programs’ options to be separated by different separators. The online documentation and this manual, however, exclusively use the colon ‘:’ in every syntax definition and in all examples.

4.3.1 Numeric Arguments

Valid delimiters are the semicolon ‘;’, the colon ‘:’, and the slash ‘/’. All delimiters may be mixed within any option that takes numeric arguments.

4.3.2 Filename Arguments

Here, the accepted delimiters are comma ‘,’, semicolon ‘;’, and colon ‘:’. Again, all delimiters may be mixed within any option that has filename arguments.

4.4 Response Files^c

A response file contains names of images or other response filenames. Introduce response file names at the command line or in a response file with an ⟨@⟩ character.

Enfuse and Enblend process the list INPUT strictly from left to right, expanding response files in depth-first order. Multi-layer files are processed from first layer to the last. The following examples only show Enblend, but Enfuse works exactly the same.

4.4.1 Response File Format

Response files contain one filename per line. Blank lines or lines beginning with a ⟨#⟩ sign are ignored; the latter can serve as comments. Filenames that begin with a ⟨@⟩ character denote other response files. Table 4.5 states a formal grammar of response files in EBNF.

In a response file relative filenames are used relative the response file itself, not relative to the current-working directory of the application.

If Enfuse or Enblend do not recognize a response file, they will skip the file and issue a warning. To force a file being recognized as a response file add one of the following syntactic comments to the first line of the file.

4.4.2 Syntactic Comments

Comments that follow the format described in Table 4.6 are treated as instructions how to interpret the rest of the response file. A syntactic comment is effective immediately and its effect persists to the end of the response file, unless another syntactic comment undoes it.

4.4.3 Globbing Algorithms

control the algorithm that Enfuse or Enblend use to glob filenames in response files.

All versions of Enfuse and Enblend support at least two algorithms: literal, which is the default, and wildcard. See Table 4.7 for a list of all possible globbing algorithms. To find out about the algorithms in your version of Enfuse or Enblend use option --show-globbing-algorithms.

Example 4.4.6 gives an example of how to control filename-globbing in a response file.

4.4.4 Default Layer Selection

The key layer-selector provides the same functionality as does the command-line option --layer-selector, but on a per response-file basis. See Section 4.2.1.

This syntactic comment affects the layer selection of all images listed after it including those in included response files until another layer-selector overrides it.

4.5 Layer Selection^c

Some image formats, like for example TIFF, allow for storing more than one image in a single file, where all the contained images can have different sizes, number of channels, resolutions, compression schemes, etc. The file there acts as a container for an ordered set of images.

In the TIFF-documentation these are known as “multi-page” files and because the image data in a TIFF-file is associated with a “directory”, the files sometimes are also called “multi-directory” files. In this manual, multiple images in a file are called “layers”.

The main advantage of multi-layer files over a set of single-layer ones is a cleaner work area with less image-files and thus an easier handling of the intermediate products which get created when generating a panorama or fused image, and in particularly with regard to panoramas of fused images.

The difficulty in working with layers is their lack of a possibly mnemonic naming scheme. They do not have telling names like taoth-vaclarush or valos-cor, but only numbers.

4.5.1 Layer Selection Syntax

To give the user the same flexibility in specifying and ordering images as with single-layer images, both Enfuse and Enblend offer a special syntax to select layers in multi-page files by appending a layer-specification to the image file name. Table 4.8 defines the grammar of layer-specifications.

Selecting a tuple of layers with a layer-specification overrides the active layer selection algorithm. See also option --layer-selector and Section 4.4. Layer selection works at the command-line as well as in Response Files; see Section 4.4.

The simplest layer-specification are the layer-indexes. The first layer gets index 1, the second layer 2, and so on. Zero never is a valid index! For convenience indexing backwards² is also possible. This means by prefixing an index with a minus-sign (‘-’) counting will start with the last layer of the associated multi-page image, such that the last layer always has index -1, the next to last index -2 and so on. Out-of-range indexes are silently ignored whether forward or backward.

The single layer of a single-layer file always can be accessed either with index ‘1’ or ‘-1’.

Select a contiguous range of indexes with the range operator ‘⟨..⟩’, where the range-bounds are forward or backward indices. Leaving out a bound or substituting the open-range indicator ‘⟨_⟩’ means a maximal range into the respective direction.

Layer specifications ignore white space, but usual shells do not. This means that at the command-line

works, whereas spaced-out out phrase ‘multi-layer.tif [2 : ]’ must be quoted

Quoting will also be required if Enfuse’s delimiters have special meanings to the shell.

4.5.2 Tools for Multi-Page Files

Here are some tools that are particularly useful when working with multi-page files. For more helpful utilities check out Appendix A.

Please bear in mind that some image-processing tools – none of the above though – do not handle multi-page files correctly, where the most unfruitful ones only take care of the first layer and silently ignore any further layers.

Samantha Carter: “There has to be a way to reverse the process. The answer has to be here.”

Chapter 5 Weighting Functions

As has been noted in the introductory Overview, Enfuse supports four different types of weighting. The following sections describe the concept of weighting and all weighting functions in detail.

5.1 Weighting Pixels

Image fusion maps each pixel P(i, x, y) of every input image i to a single pixel Q(x, y) in the output image:

where x runs from 1 to the width of the images, y from 1 to the height, and i from 1 to the number n of input images.

Here we have abbreviated P(i, x, y) to P for simplicity. The user defines the constants w_exp, w_sat, w_cont, and w_ent with the options --exposure-weight, --saturation-weight, --contrast-weight, and --entropy-weight respectively. The functions f_exp, f_sat, f_cont, and f_ent along with the window sizes r_cont and r_ent are explained in the next sections.

5.1.1 Weighted Average

By default, Enfuse uses a weighted average, where each pixel contributes as much as its weight demands. Of course the weights can be extreme, favoring only a few pixels or even only one pixel in the input stack. Extremes are not typical, however.

Equal weights are another extreme that turns (5.1) into an arithmetic average. This is why we sometimes speak of the “averaging property” of this weighting algorithm, like smoothing out noise.

5.1.2 Disabling Averaging: Option ‘--hard-mask’

The weighted average computation as described above has proven to be widely successful with the exception of one special case: focus stacking, where the averaging noticeably softens the final image.

Use ‘--hard-mask’ to switch Enfuse into a different weighting mode, where the pixel with the highest weight wins, this is, gets weight one, and all other pixels get the weight of zero. With option --hard-mask (5.1) becomes

Note that this “averaging” scheme lacks the nice noise-reduction property of the weighted average (5.1), because only a single input pixel contributes to the output.

5.1.3 Single Criterion Fusing

Enfuse allows the user to weight each pixel of an input image by up to four different criteria (see e.g. Chapter 1). However, it does not force the user to do so. For some applications and more often simply to gain further insight into the weighting and fusing process, looking at only a single criterion is the preferred way to work.

The version of Enfuse for which this documentation was prepared, uses the default weights as stated in Table 5.1. Notice that by default more than one weight is larger than zero, which means they are active.

instructs Enfuse to consider only the exposure weight. Combine this with option --save-masks and it will become clearer how Enfuse computes the exposure weight for the set of images.

Another problem that can be inspected by fusing with just a single active criterion and saving the masks is if the weights of one criterion completely overpower all others.

5.2 Exposure Weighting

Exposure weighting prefers pixels with a luminance Y close to the user-chosen optimum value (option --exposure-optimum, default: ⟨0.5⟩) of the normalized, real-valued luminance interval (0, 1).

RGB-pixels get converted to luminance before using the grayscale projector given by ‘--gray-projector’, which defaults to average. Grayscale pixels simply are identified with luminance.

In the normalized luminance interval 0.0 represents pure black and 1.0 represents pure white independently of the data type of the input image. This is, for a JPEG image the luminance 255 maps to 1.0 in the normalized interval and for a 32 bit TIFF picture the highest luminance value 4294967295 also maps to 1.0. The middle of the luminance interval, 0.5, is where a neutral gray tone ends up with every camera that had no exposure correction dialed in, for example the image of any gray-card or white-card.

The exposure weighting algorithm only looks at a single pixel at a time; the pixel’s neighborhood is not taken into account.

5.2.1 Built-In Functions

whose maximum position Y_opt and width are controlled by the command line options --exposure-optimum and --exposure-width respectively, where Y_opt defaults to ⟨0.5⟩ and width defaults to ⟨0.2⟩. Figure 5.1 shows some Gaussians.

The options --exposure-optimum and --exposure-width serve to fine-tune the final result without changing the set of input images. Option --exposure-optimum sets the point of optimum exposure. Increasing the optimum makes Enfuse prefer lighter pixels, rendering the final image lighter, and vice versa. Option --exposure-width defines the width of acceptable exposures. Small values of width penalize exposures that deviate from optimum more, and vice versa.

In Enfuse version 4.2 several new exposure weight functions have been added. Select them with option --exposure-weight-function. For the following presentation we refer to the linear luminance transform

behave like 1 − z² around the optimum. However for large |z| the Gaussian weight rolls off like exp(−z²/2) and the Lorentzian only as z⁻².

Both, the Gaussian and the Lorentzian are easy to use, because they do not go exactly to zero. Thus, Enfuse can select “better” pixels even far away from the chosen optimum.

behave like 1 − z² around the optimum, like Gaussian and Lorentzian. However for large |z| they both are exactly zero. The difference is how they decrease just before they reach zero. Half-Sine behaves like z − z′ and Full-Sine like (z − z″)², where z′ and z″ are the respective zeros.

is the only predefined function that behaves like 1 − z⁴ around the optimum.

The weight functions Half-Sine, Full-Sine, and Bi-Square are more difficult to use, because they yield exactly zero if the normalized luminance of a pixel is far enough away from the optimum. This can lead to pathologies if the luminances of the same pixel position in all N input images are assigned a weight of zero. For all-zero weights Enfuse falls back to weighing equally. This is, each pixel gets a weight of 1/N, which may or may not be the desired result. However, if the width is chosen so large that the weight never vanishes or the input images span a large enough range of luminances for each and every pixel, the problem is circumnavigated.

Another way of cutting off underexposed or overexposed pixels is to use option --exposure-cutoff, which has the additional benefit of allowing to choose upper and lower cutoff separately.

Figure 5.6 compares all available exposure weight functions for the same parameters, namely their defaults. They all intersect at w = 1/2 independently of optimum or width, making it simple to just try them out without fundamentally changing brightness.

5.2.2 User-Defined Exposure Weighting Functions

5.2.3 User-Defined, Dynamically-Linked Exposure Weighting Functions

On operating systems, where dynamic linking (or synonymously: dynamic loading) of code is possible, for Enfuse executables compiled with dynamic-linking support (see Section 3.3.1 on how to check this feature), Enfuse can work with user-defined exposure weighting functions, passed with the long form of option --exposure-weight-function, load the exposure weight function identified by SYMBOL from SHARED-OBJECT and optionally pass some ARGUMENTs:

Prerequisites

To use a home-grown exposure-weight function several prerequisites must be met. On the software side

Coding Guidelines

Example 5.2.7 shows the C++-code of a suitable extension. If Enfuse has been compiled with support for user-defined weight functions, the examples presented here should have been duplicated in directory /usr/share/doc/enblend-enfuse/examples/enfuse along with a GNU-Makefile called Makefile.userweight.

As the extension language is C++, we can write templated families of functions, like Example 5.2.8 demonstrates.

The last example, 5.2.9, shows a weight function that accesses an extra ARGUMENT passed in with --exposure-weight-function. A class like VariablePower allows full control over the exponent at the command line including fractional exponents thereby generalizing both of the previous examples.

Performance Considerations

Exposure weighting objects are created and destroyed only O(1) times. Thus, method initialize could be used to perform all kinds of computationally expensive tasks. In contrast, methods normalize and weight are called for every pixel in each of the input images. Therefore, if performance of the weight function is a problem, these two functions are the prime candidates for optimization.

Compiling, Linking, and Loading

5.3 Saturation Weighting

Saturation weighting prefers pixels with a high saturation, where the saturation S_HSL is computed in HSL color space. For an introduction to the HSL color space, please consult Wikipedia.

Taking the largest and smallest components of the RGB-value (R, G, B) in the normalized RGB-cube

The saturation weighting algorithm only looks at a single pixel at a time. The neighborhood of the pixel is not taken into account.

Obviously, saturation weighting can only be defined for RGB-images, not for grayscale ones. If you need something similar, check out Section 5.5 on Entropy Weighting, which works for both RGB and grayscale pictures.

5.4 Local Contrast Weighting

Local contrast weighting favors pixels inside a high contrast neighborhood. The notion of “high contrast” is defined either by two different criteria or by a blend of both:

Enfuse converts every RGB image to grayscale before it determines its contrast. Option --gray-projector controls the projector function. Depending on the subject, one of several grayscale projectors may yield the best black-and-white contrast for image fusion.

5.4.1 Standard Deviation

The pixel under consideration C sits exactly in the center of a square, the so-called local analysis window. It always has an uneven edge length. The user sets the size with option --contrast-window-size. Figure 5.7 shows two windows with different sizes.

During the analysis, Enfuse scans the local analysis window across all rows and all columns¹ of each of the input images to compute the contrast weight of every pixel.

Statistical Moments

It associates a probability p with each of the n different possible outcomes ω of the random variable X.

Based on w, we define the expectation value or “First Moment” of the random variable X:

Using the definition of the expectation value, we define the variance, or “Second Moment” as

Obviously, the variance of X is the expectation value of the squared deviation from the expectation value of X itself. Note that the variance’s dimension is X’s dimension squared; the standard deviation rectifies the dimension to make it comparable with X itself again.

Estimators

In Enfuse, we assume that X follows a uniform probability function w(x) = const. That is, all pixel values in the local analysis window are considered to be equally probable. Thus, the expectation value and the variance can be estimated from the pixel values like this

In other words: the expectation value is the arithmetic mean of the lightness of all pixels in the local analysis window. Analogously, the variance becomes

5.4.2 Laplacian of Gaussian

The Laplacian-of-Gaussian (LoG) is an operator to detect edges in an image. Sometimes the LoG-operator is also called Marr-Hildreth operator. A Laplacian-of-Gaussian operator, vigra::laplacianOfGaussian is part of the package VIGRA that Enfuse is built upon and is used for edge detection if option --contrast-edge-scale is non-zero and --contrast-min-curvature equal to or less than zero.

The parameter σ, the argument of option --contrast-edge-scale, is the length scale on which edges are detected by g(x, y). We apply the Laplacian operator in Cartesian coordinates

to g(x, y), to arrive at a continuous representation of the two-dimensional filter kernel

Enfuse uses a discrete approximation of k in the convolution with the image. The operator is radially symmetric with respect to the origin, which is why we can easily plot it in Figure 5.8, setting R = √x² + y².

Sometimes the LoG is plagued by noise in the input images. After all, it is a numerical approximation of the second derivative and deriving always “roughens” a function. The (normalized) mask files relentlessly disclose such problems. Use option --contrast-min-curvature with a negative argument CURVATURE to suppress all edges with a curvature below −CURVATURE (which is a positive value). Check the effects with the mask files and particularly the hard-mask files (⟨hardmask-%n.tif⟩) if using option --hard-mask.

To indicate the CURVATURE in relative terms, which is particularly comprehensible for humans, append a percent sign (‘%’). Try minimum curvatures starting from −0.5% to −3%.

5.4.3 Blend Standard Deviation and Laplacian-of-Gaussian

Enfuse can team the standard deviation computation and Laplacian of Gaussian to deliver the best of both methods. Use a positive argument CURVATURE with option --contrast-min-curvature to combine both algorithms. In this mode of operation Enfuse computes the SDev-weight and the LoG-weight, then uses the LoG to decide whether to go with that value or prefer the SDev data. If the LoG is greater than CURVATURE Enfuse uses the weight delivered by the LoG, otherwise the SDev-weight is rescaled such that its maximum is equal to CURVATURE, and the scaled SDev is used as weight.

This technique merges the two edge detection methods where they are best. The LoG excels with clear edges and cannot be fooled by strong but smooth gradients. However, it is bad at detecting faint edges and it is susceptible to noise. The SDev on the other hand shines with even the most marginal edges, and resists noise quite well. Its weakness is that is is easily deceived by strong and smooth gradients. Tuning CURVATURE the user can pick the best threshold for a given set of images.

5.4.4 Scaling and Choice of Mode

Experience has shown that neither the parameters EDGESCALE and CURVATURE nor the mode of operation (SDev-only, LoG-only, or a blend of both) scales to different image sizes. In practice, this means that if you start with a set of reduced size images, say 2808 × 1872 pixels, carefully optimize EDGESCALE, CURVATURE and so on, and find LoG-only the best mode, and then switch to the original resolution of 5616 × 3744 pixels, multiplying (or dividing) the parameters by four and sticking to LoG-only might not result in the best fused image. For best quality, perform the parameter optimization and the search for the most appropriate mode at the final resolution.

5.5 Local Entropy Weighting

Let S be an n-ary source. Watching the output of S an observer on average gains the information

per emitted message, where we assume the knowledge of the probability function p(S). The expectation value H_a(n) is called entropy of the source S. Entropy measures our uncertainty if we are to guess which message gets chosen by the source in the future. The unit of the entropy depends on the choice of the constant a > 1. Obviously

holds for all b > 1. We use a = 2 for entropy weighting and set the entropy of the “impossible message” to zero according to

Enfuse computes a pixel’s entropy by considering the pixel itself and its surrounding pixels quite similar to Local-Contrast Weighting (5.4). The size of the window is set by ‘--entropy-window-size’. Choosing the right size is difficult, because there is a serious tradeoff between the locality of the data and the size of the sample used to compute H. A large window results in a large sample size and therefore in a reliable entropy, but considering pixels far away from the center degrades H into a non-local measure. For small windows the opposite holds true.

Another difficulty arises from the use of entropy as a weighting function in dark parts of an image, that is, in areas where the signal-to-noise ratio is low. Without any precautions, high noise is taken to be high entropy, which might not be desired. Use option --entropy-cutoff to control the black level when computing the entropy.

On the other extreme side of lightness, very light parts of an image, the sensor might already have overflown without the signal reaching 1.0 in the normalized luminance interval. For these pixels the entropy is zero and Enfuse can be told of the threshold by properly setting the second argument of ‘--entropy-cutoff’.

In the current implementation a floor(contrast-window-size / 2)-wide border around the images remains unprocessed and gets a weight of zero.

Chapter 6 Color Spaces And Color Profiles^c

This chapter explains the connection of pixel data types, ICC-color profiles, blend color spaces in Enfuse or Enblend.

Here, we collectively speak of blending and do not distinguish fusing, for the basic operations are the same. Furthermore, we assume the multi-resolution spline algorithm has calculated a set of weights w_i for i = 1, 2, … and ∑w_i = 1 for each pixel that must be blended from the participating input pixels P_i, i = 1, 2, ….

In the simplest, non-trivial case we have to blend a pair of grayscale input pixels. Given their luminances L₁, L₂ and their weighting factor 0 ≤ w ≤ 1, what luminance L is their “weighted average”? This is the heart of Enfuse’s and Enblend’s pyramidal blending operations! We are in particular interested in a weighted average that appears visually correct, this is, our eyes and brains consider L convincing or at the very least credible.

The details of blending pixels and in particular color pixels is quite intricate, which is why we start this chapter with a mathematical introduction.

6.1 Mathematical Preliminaries

Let us first address grayscale images because they only require us to talk about luminances. For a linear representation of luminances, we just blend for a given t with

where the luminances L_i, i = 1, 2, range from zero to their data-type dependent maximum value L_max, thereby defining a “luminance interval”. We can always map this interval to (0, 1) by dividing the luminances by the maximum, which is why we call the latter “normalized luminance interval”:

Sometimes images are gamma-encoded with exponent γ and the blended luminance becomes

which couples t and L′ in a non-linear way. See also Eric Brasseur’s explanation of the gamma error in picture scaling.

The usual color-input images fed into Enfuse are RGB-encoded, which means each pixel comes as a triple of values (r, g, b)^T that represent the red, green, and blue parts. We apply the normalization (6.2) to each of the three primary colors and arrive at an “RGB-cube” with unit edge length. The vectors of primary colors span the cube

For each point inside – familiarly called pixel – the generalization of (6.3) holds

Blending the pixels of color images is more complicated than blending plain luminances. Although we can write down the naïve blending equation, (6.1), again for RGB-coded pixels

6.2 Floating-Point Images

Floating-point images (EXR, floating-point TIFF, or VIFF) get a special treatment. Their values L are first converted by the Log-transform.

which is undone by the inverse transform after blending. Here, log(x) with a lower-case initial denotes the natural logarithmic function (i.e. to base e). Figure 6.1 shows the forward transform in the range from −20 to 100. Around L = 0 function Log(L) has the series expansion

In the current version of Enfuse and Enblend it is strongly recommended to use blending inside the RGB-cube whenever the input data is in floating-point format; this is the default, too.

6.3 Color Profiles

ICC-color profiles completely absorb gamma encodings (6.4) and ICC profile aware software like Enfuse and Enblend decode and encode images automatically respecting the gamma curves. Moreover color profiles define what is the darkest representable black, so called black-point

In Case 1. the applications blend grayscale images in the normalized luminance interval and color images inside the sRGB-cube. To override the default sRGB-profile select the desired profile with option --fallback-profile.

In Case 2. the images first are by default transformed to CIELUV color space – respecting the input color profile – then they are blended or fused, and finally the data get transformed back to RGB color space defined by the profile of the input images. Consequently, the input profile is assigned to the output image. Enforce a different blending color space than CIELUV with option --blend-colorspace.

Mixing different ICC profiles or alternating between images with profiles and without them generates warnings as it generally leads to unpredictable results.

Floating-Point images are an exception to the above rules. They are always blended in the RGB cube by default. The next section describes their treatment in detail.

6.4 Blending Color Spaces

Enfuse and Enblend offer to work inside the RGB-cube (6.5) or in several perceptually uniform color spaces. To override the default select a particular blending color space with option --blend-colorspace. Here are the four available color spaces.

Surprisingly often blending “inside the RGB-cube” works, although perceptually uniform color spaces, which represent luminance, saturation, and hue are preferable for blending and fusing operations.

6.5 Practical Considerations

Fusing with a Hard Mask is different, because exactly one weight factor is unity and all the others are zero. There is nothing to blend – just to copy.

Chapter 7 Understanding Masks^c

A binary mask indicates for every pixel of an image if this pixel must be considered in further processing, or ignored. For a weight mask, the value of the mask determines how much the pixel contributes, zero again meaning “no contribution”.

Masks arise in two places: as part of the input files and as separate files, showing the actual pixel weights prior to image blending or fusion. We shall explore both occurrences in the next sections.

7.1 Masks In Input Files

Each of the input files for Enfuse and Enblend can contain its own mask. Both applications interpret them as binary masks no matter how many bits per image pixel they contain.

Use ImageMagick’s identify (see Example 7.1.10) or, for TIFF files only, tiffinfo (see Example 7.1.11) to inquire quickly whether a file contains a mask. Appendix A shows where to find these programs on the web.

The “Matte” part of the image class and the “Extra Samples” line tell us that the file features a mask. Also, many interactive image manipulation programs show the mask as a separate channel, sometimes called “alpha”. There, the white (high mask value) parts of the mask enable pixels and black (low mask value) parts suppress them.

Enfuse and Enblend only consider pixels that have an associated mask value other than zero. If an input image does not have an alpha channel, Enblend warns and assumes a mask of all non-zero values, that is, it will use every pixel of the input image for fusion.

Sometimes it is helpful to manually modify a mask before fusion. For example to suppress unwanted objects (insects and cars come into mind) that moved across the scene during the exposures. If the masks of all input images are black at a certain position, the output image will have a hole in that position.

7.2 Weight Mask Files

Chapter 8 Applications of Enfuse

This section describes some of the novel possibilities that Enfuse offers the photographer. In contrast to the previous chapters, it centers around the effects on the final image.

8.1 What Makes Images Fusable?

Images should align well to be suitable for fusion. However, there is no hard mathematical rule what “well” means. The alignment requirements for 16 MPixel images to yield a sharp 4" × 6" print at 300 dpi or even for web presentation are relatively low, whereas the alignment of 8 MPixel images for a 12" × 18" print ought to be tight.

If the input images need to be aligned, Hugin (see also Appendix A.2) is the tool of choice. It produces images exactly in the format that Enfuse expects.

Sometimes images naturally align extremely well so that no re-alignment is required. An image series with preprogrammed exposure steps taken in rapid succession where the camera is mounted on a heavy tripod and a humongous ball head, mirror lockup, and a cable release are used, comes to mind.

8.2 Repetition – Noise Reduction

With the default settings, Enfuse computes a weighted average of the input pixels. For a series of images, repeated with identical settings, this results in a reduction of (photon shot) noise. In other words, the dynamic range increases slightly, because the higher signal-to-noise ratio makes darker shades usable. Furthermore, smooth or glossy surfaces get a “cleaner” look, and edges become visually sharper. The nitty-gritty reportage look that sometimes stems from a high sensitivity setting disappears.

Averaged images, and therefore low-noise images, are the base for a multitude of techniques like, for example, differences. The most prominent method in this class is dark-frame subtraction.

Enfuse sets defaults for the exposure-weight to ⟨1.0⟩, for saturation-weight to ⟨0.2⟩ and for all other weights to zero, a good combination for noise reduction. Eliminating the saturation component with --saturation-weight=0.0 sometimes can be worth the extra run.

8.3 Exposure Series – Dynamic Range Increase

An exposure series is a set of images taken with identical parameters except for the exposure time. Some cameras even provide special functions to automate recording exposure series. See the instruction manual of your model for details. Also check out the features that Magic Lantern offers to shoot HDR-series and to extend the dynamic range right in the camera.

Enfuse’s defaults for exposure weight, ⟨1.0⟩ and saturation weight, ⟨0.2⟩ are well suited for fusion of color images. Remember that saturation weighting only works for RGB data. Option --saturation-weight helps to control burnt-out highlights, as these are heavily desaturated. Alternatively, use option --exposure-cutoff to suppress noise or blown-out highlights without altering the overall brightness too much. If no image suffers from troublesome highlights, the relative saturation weight can be reduced and even be set to zero.

For black and white images ‘--entropy-weight’ can be an alternative to ‘--saturation-weight’ because it suppresses overexposed pixels, as these contain little information. However, entropy weighting is not limited to gray-scale data; it has been successfully applied to RGB images, too. Note that entropy weighting considers each color channel of an RGB image separately and chooses the channel with the minimum entropy as representative for the whole pixel.

Enfuse offers the photographer tremendous flexibility in fusing differently exposed images. Whether you combine only two pictures or a series of 21, Enfuse imposes no limits on you. Accordingly, the photographic effects achieved range from subtle to surreal, like the late 1980s “Max Headroom” TV-Series, to really unreal. Like some time ago in the chemical days of photography, when a new developer opened unseen possibilities for artists, exposure fusion extends a photographer’s expressive space in the digital age. Whether the results look good or bad, whether the images are dull or exciting, is entirely up the artist.

In the next sections we give assistance to starters, and rectify several misconceptions about Enfuse.

8.3.1 Tips For Beginners

8.3.2 Common Misconceptions

8.4 Flash Exposure Series – Directed Lighting

8.5 Polarization Series – Saturation Enhancement

In the current implementation of Enfuse, it is not possible in general to fuse a polarization series. Naïvely (ab)using ‘--saturation-weight’ will not work.

8.6 Focus Stacks – Depth-of-Field Increase

A focus stack is a series of images where the distance of the focal plane from the sensor varies. Sloppily speaking, the images were focused at different distances. Fusing such a stack increases the depth-of-field (DoF) beyond the physical limits of diffraction.

8.6.1 Why create focus stacks?

the photographer controls the depth-of-field with the aperture. Smaller apertures – this is larger aperture numbers – increase the DoF and vice versa. However, smaller apertures increase diffraction which in turn renders the image unsharp. So, there is an optimum aperture where the photographer gets maximum DoF. Sadly, for some purposes like macro shots it is not enough. One way out is to combine the sharp parts of images focused at different distances, thereby artificially increasing the total DoF. This is exactly what Enfuse can do.

All lenses have a so called “sweet spot” aperture, where their resolution is best. Taking pictures at this aperture, the photographer squeezes the maximum quality out of the lens. But: the “sweet spot” aperture often is only one or two stops away from wide open. Wouldn’t it be great to be able combine these best-possible images to form one high-quality, sufficient-DoF image? Welcome to Enfuse’s local-contrast selection abilities.

8.6.2 Preparing Focus Stacks

We are going to combine images with limited DoF to increase their in-focus parts. The whole process is about image sharpness. Therefore, the input images must align very well, not just well, but very well. For optimum results the maximum control point distance in Hugin should not exceed 0.3–0.5 pixels to ensure perfect blending.

As in all image fusion operations it is preferable to use 16 bit linear (i.e. gamma = 1) images throughout, but 8 bit gamma-encoded images will do. Naturally, high signal-to-noise (SNR) ratio input data always is welcome.

8.6.3 Local Contrast Based Fusing

If you want to see some entertaining progress messages – local-contrast weighting takes a while –, also pass the --verbose option for an entertaining progress report.

8.6.4 Basic Focus Stacking

For a large class of image stacks Enfuse’s default algorithm, as selected in 8.6.3, to determine the sharpness produces nice results. The algorithm uses a moving square window, the so-called contrast window. It computes the standard deviation of the pixels inside of the window. The program then selects the window’s center pixel of the image in the stack where the standard deviation is largest, that is, the local contrast reaches the maximum.

However, the algorithm fails to deliver good masks for images which exhibit high contrast edges on the scale of the contrast window size. The typical artifacts that show up are

where the distance of the seams from the middle of the edge is comparable to the contrast window size.

If your results do not show any of these artifacts, stick with the basic algorithm. Advanced focus stacking, as described in the next sections, delivers superior results in case of artifacts, though requires manually tuning several parameters.

8.6.5 Advanced Focus Stacking

If your fused image shows any of the defects described in the previous section, you can try a more difficult-to-use algorithm that effectively works around the seam artifacts. It is described in the next section.

Detailed Look at the Problem

Let us use an example to illustrate the problem of relating the sharpness with the local contrast variations. Say we use a 5 × 5 contrast window. Moreover, let sharp_edge and smooth_edge be two specific configurations:

where ‘;’ separates the rows and ‘,’ separates the columns. This is in fact Octave syntax. Figure 8.1 and 8.2 show plots of the matrices sharp_edge and smooth_edge.

Our intuition lets us “see” an extremely sharp edge in the first matrix, whereas the second one describes an extraordinarily smooth diagonal intensity ramp. Which one will be selected? Well, sharp_edge has a standard deviation of 88.07 and smooth_edge has 88.41. Thus, smooth_edge wins, contradicting our intuition, and even worse, our intention! Sadly, configurations like smooth_edge occur more often with high-quality, good bokeh lenses. In fact, they are the very manifestation of “good bokeh”. Therefore, Laplacian edge detection plays an important role when working with high-quality lenses.

Laplacian Edge Detection

Enfuse provides a Laplacian-based algorithm that can help in situations where weighting based on the standard deviation fails. It is activated with a positive value for SCALE in --contrast-edge-scale=SCALE. The Laplacian will detect two-dimensional curvature on the scale of SCALE. Here and in the following we simply speak of “curvature” where we mean “magnitude of curvature”. That is, we shall not distinguish between convex and concave edges. Enfuse always use the magnitude of curvature for weighting.

Typically, SCALE ranges between 0.1 pixels and 0.5 pixels, where 0.3 pixels are a reasonable starting point. To find the best value for SCALE though, usually some experimentation will be necessary. Use ‘--save-masks’ to get all soft-mask (default: ⟨softmask-%n.tif⟩) and hard-mask files (default: ⟨hardmask-%n.tif⟩). Check how different scales affect the artifacts. Also see Chapter 7.

Local Contrast Enhancement

Sometimes Enfuse misses smoother edges with ‘--contrast-edge-scale’ and a little local contrast enhancement (LCE) helps. Set --contrast-edge-scale=SCALE:LCE-SCALE:LCE-FACTOR, where LCE-SCALE and LCE-FACTOR work like the unsharp mask filters in various image manipulation programs. Start with LCE-SCALE ten times the value of SCALE and a LCE-FACTOR of 2–5.

LCE-SCALE can be specified as a percentage of SCALE. LCE-FACTOR also can be specified as a percentage. Examples:

Suppressing Noise or Recognizing Faint Edges

The Laplacian-based algorithm is much better at resisting the seam problem than the local-contrast algorithm, but it has two shortcomings:

The argument to --contrast-min-curvature=CURVATURE either is an absolute lightness value, e.g. 0…255 for 8 bit data and 0…65535 for 16 bit data, or, when given with a ‘%’-sign it is a relative lightness value ranging from 0% to 100%.

To suppress unreal edges or counter excessive noise, use the --contrast-min-curvature option with a negative curvature measure CURVATURE. This forces all curvatures less than −CURVATURE to zero.

A positive curvature measure CURVATURE makes Enfuse merge the LoG data with the local-contrast data. Every curvature larger than or equal to CURVATURE is left unchanged, and every curvature less than CURVATURE gets replaced with the rescaled local-contrast data, such that the largest local contrast is just below CURVATURE. This combines the best parts of both techniques and ensures a precise edge detection over the whole range of edge curvatures.

Focus Stacking Decision Tree

Figure 8.3 helps the user to arrive at a well-fused focus stack with as few steps as possible.

Always start with the default, contrast weighting with a local contrast window. Only if seams appear as described in Section 8.6.5 switch to Laplacian-of-Gaussian contrast detection.

If some seams remain even in LoG-mode, decrease the sensitivity of the edge detection with a positive --contrast-min-curvature. A too high value of --contrast-min-curvature suppresses fine detail though. Part of the detail can be brought back with pre-sharpening, that is, 8.6.5 or combining LoG with local-contrast-window mode by using a negative --contrast-min-curvature.

Carefully examining the masks (option --save-masks) that Enfuse uses helps to judge the effects of the parameters.

8.6.6 Tips For Focus Stacking Experts

We have collected some advice with which even focus-stacking adepts can benefit.

cr2hdr is part of Magic Lantern’s source distribution.

Appendix A Helpful Programs And Libraries^c

Several programs and libraries have proven helpful when working with Enfuse or Enblend.

A.1 Raw Image Conversion

A.2 Image Alignment and Rendering

A.3 Image Manipulation

A.4 High Dynamic Range

A.5 Major Libraries

A.6 Meta-Data Handling

A.7 Camera Firmware Extension

Appendix B Bug Reports^c

Bug reports play an important role in making Enfuse and Enblend reliable and enjoyable.

When you encounter a problem, the first thing to do is to see if it is already known. To this end, visit the package’s LaunchPad bug ⟨database⟩. Search it for your particular problem. If it is not known, please report it.

In order for a bug report to serve its purpose, you must include the information that makes it possible to fix the bug.

B.1 Have You Really Found a Bug?

B.2 How to Report Bugs

The fundamental principle of reporting bugs usefully is this: report all the facts. If you are not sure whether to state a fact or leave it out, state it. Often people omit facts because they think they know what causes the problem and they conclude that some details do not matter. Play it safe and give a specific, complete example.

Keep in mind that the purpose of a bug report is to enable someone to fix the bug if it is not known. Always write your bug reports on the assumption that the bug is not known.

Try to make your bug report self-contained. If we have to ask you for more information, it is best if you include all the previous information in your response, as well as the information that was missing.

B.3 Sending Patches for Enfuse or Enblend

If you would like to write bug fixes or improvements for Enfuse or Enblend, that is very helpful. When you send your changes, please follow these guidelines to avoid causing extra work for us in studying the patches. If you do not follow these guidelines, your information might still be useful, but using it will take extra work.

Appendix C Authors^c

Thanks to Simon Andriot and Pablo Joubert for suggesting the Mertens-Kautz-Van Reeth technique and the name “Enfuse”.

Appendix D The GNU Free Documentation License^c

Syntactic Comment Index

enblend-response-file, 4.4.1
enfuse-response-file, 4.4.1
filename-globbing, 4.4.3
glob, 4.4.3

globbing, 4.4.3
layer-selector, 4.4.4
response-file, 4.4.1

Program/Application Index

CinePaint, A.3
Cinepaint, 4.2.2
Darktable, A.1
Gimp, 3.1, 4.2.2, 4.2.5, A.3
GraphicsMagick, A.3
Hugin, 3.1, 4.5.2, 8.1, A.2, B.2
ImageFuser, B.2
ImageMagick, 4.2.5, 4.2.5, A.3
LittleCMS, A.6
Magic Lantern, A.7
Mercurial, 3.3.1
PanoTools, 3.1, A.2
RawTherapee, A.1
UFRaw, A.1
align_image_stack (Hugin), A.2
convert (ImageMagick), 4.5.2, A.3
convert, 4.2.5
dcraw, 3.1, A.1
display (ImageMagick), 4.5.2
display (ImageMagick), A.3

exiftool, A.6
exrdisplay (OpenEXR), A.4
fulla (Hugin), A.2
gm (GraphicsMagick), A.3
gmic, A.3
identify (ImageMagick), 7.1, A.3
montage (ImageMagick), A.3
nona (Hugin), 4.2.2, 4.5.2, 7.1, A.2
PFSTools, A.4
PTmender (PanoTools), A.2
PTOptimizer (PanoTools), A.2
tiffcp (LibTIFF), 4.5.2
tiffinfo (libtiff), 7.1
tiffinfo (LibTIFF), 4.5.2
tiffinfo (libtiff), A.5
tiffsplit (LibTIFF), 4.5.2
tificc (LittleCMS), A.6
ufraw-batch, A.1
ufraw, 3.1, A.1

If a program belongs to a larger package, it has its association mentioned in parenthesis.

Option Index

--blend-colorspace, 4.2.2
--ciecam, 4.2.2
--compression, 4.2.1
--contrast-edge-scale, 4.2.5
--contrast-min-curvature, 4.2.5
--contrast-weight, 4.2.3
--contrast-window-size, 4.2.5
--depth, 4.2.2
--entropy-cutoff, 4.2.5
--entropy-weight, 4.2.3
--entropy-window-size, 4.2.5
--exposure-cutoff, 4.2.5, 5.2.1
--exposure-optimum, 4.2.3, 5.2, 5.2.1, 5.2.3
--exposure-weight-function, 4.2.5, 5.2.1, 5.2.3
--exposure-weight, 4.2.3
--exposure-width, 4.2.3, 5.2.1, 5.2.3
--fallback-profile, 4.2.4
--gray-projector, 4.2.5, 5.2
--hard-mask, 4.2.3, 5.1.2, 8.6.6
--help, 4.2.6
--layer-selector, 4.2.4
--levels, 4.2.1
--load-masks, 3.2, 4.2.4
--no-ciecam, 4.2.2

--no-parameter, 4.2.4
--output, 3.2, 4.2.1
--parameter, 4.2.4
--saturation-weight, 4.2.3
--save-masks, 3.2, 4.2.4
--show-globbing-algorithms, 4.2.6
--show-image-formats, 3.3.1, 4.2.6
--show-signature, 3.3.1, 4.2.6
--show-software-components, 3.3.1, 4.2.6, 5.2.3
--soft-mask, 4.2.3
--verbose, 3.3.1, 4.2.1
--version, 3.3.1, 3.3.1, 4.2.6
--wrap, 4.2.2
-c (long: --ciecam), 4.2.2
-d (long: --depth), 4.2.2
-f, 4.2.2
-g, 4.2.2
-h (long: --help), 4.2.6
-l (long: --levels), 4.2.1
-o (long: --output), 4.2.1
-V (long: --version), 4.2.6
-v (long: --verbose), 4.2.1
-w (long: --wrap), 4.2.2

General Index

360^∘
- horizontal panorama, see panorama, 360^∘
- vertical panorama, see panorama, 360^∘
# (response file comment), 4.4.1
@ (response file prefix), 4.4
Adelson, Edward H., 1
active criteria, see criteria, active
advanced focus stacking, see focus stacking, advanced
- recognizing faint edges, 8.6.5
- suppressing noise, 8.6.5
advanced options, 4.2.2
affine transformation, see transformation, affine
algorithm, see globbing algorithm
- globbing, 4.2.6
algorithms
- globbing, 4.4.3
alignment
- photometric, 3.1
alpha, 7.1
alpha channel
- associated, 4.2.2
anti-value gray projector, see gray projector, anti-value
aperture
- sweet spot, 8.6.1
applications of Enfuse, 8
arithmetic JPEG compression, see compression
associated alpha channel, see alpha channel, associated
authors, C
average
- disabling, 5.1.2
- weighted, 5.1.1
average gray projector, see gray projector, average
BigTIFF, 2
Born, Max, 4.2.2
Brasseur, Eric, 6.1
Burt, Peter J., 1
Burt-Adelson, 1
basic focus stacking, see focus stacking, basic
binary mask, see mask, binary
binary version, see software, version
bit depth, see bits per channel
bits per channel, 3.3.1, 4.2.2
black-and-white image, see image, black-and-white
black-point, 6.3
blend colorspace, see colorspace, blend
blending color space, see colorspace, for blending and fusing
blending exposures, 8.3.2
blending pixels, see pixels, blending
bracketing
- HDR, A.7
branches of Enfuse/Enblend
- development, 3.3.1
bug
- database at LaunchPad, B
- reports, B
  - how to, B.2
  - identification of bugs, B.1
  - sending patches, B.3
builder, 3.3.1
Carter, Samantha, 4.5.1
CIECAM02 colorspace, see colorspace, CIECAM02, see colorspace, CIECAM02
CIEL*a*b* colorspace, see colorspace, CIEL*a*b*
CIEL*u*v* colorspace, see colorspace, CIEL*u*v*, see colorspace, CIEL*u*v*
CILK_NWORKERS, see environment variable, CILK_NWORKERS
CoC, see circle-of-confusion
channel
- alpha, 1, 3.1, 3.3.1, 7.1
- depth, 4.2.2
- width, see channel, depth
channel-mixer gray projector, see gray projector, channel-mixer
circle-of-confusion, 8.6.1
code,
see also return code, 3.3.2
code repository, see public repository
coding guidelines, 5.2.3
color appearance model, 4.2.2
color cube
- RGB, 4.2.2, 6.3, 6.4
- sRGB, 6.3
- RGB, 4.2.2
color profile, 6, 6.3
color profiles
- math, 6.1
colorspace, 6
- CIECAM02, 4.2.2, 6.4
- CIEL*a*b*, 4.2.2
- CIEL*u*v*, 4.2.2, 6.4
- HSL, 5.3
- L*a*b*, 6.4
- blend, 4.2.2
- CIELUV, 4.2.2
- for blending and fusing, 6.4
- practical considerations, 6.5
command-line, 4
common options, 4.2.1
compiled-in features, see features
compiler, 3.3.1
compression, 4.2.1
- JPEG, 4.2.1
- JPEG of TIFF, 4.2.1
- LZW, 4.2.1
- arithmetic JPEG, 4.2.1
- deflate, 4.2.1
- packbits, 4.2.1
console messages, 3.3.2
contrast
- local enhancement, 4.2.5
- minimum curvature, 4.2.5
- window size, 4.2.5
contrast enhancement
- local, 8.6.5
contrast weight, see weight, local contrast
contrast weighting, see weighting, local contrast
contrast weighting using Laplacian-of-Gaussian, see weighting, contrast using Laplacian-of-Gaussian
contrast weighting using a blend of methods, see weighting, contrast using a blend of methods
contrast weighting using standard deviation, see weighting, contrast using standard deviation
conventions
- typographic, see notation
conversion
- RGB-L*a*b*, see RGB-L*a*b* conversion
- raw, 3.1
criteria
- active, 5.1.3
- overpowering one another, 5.1.3
cutoff
- exposure, see exposure, cutoff
cutoff entropy, see entropy, cutoff
D50 white-point, see white-point, D50, see white-point, D50
DoF, see depth-of-field, see depth-of-field
DYLD_FALLBACK_LIBRARY_PATH, see environment variable, DYLD_FALLBACK_LIBRARY_PATH
DYLD_LIBRARY_PATH, see environment variable, DYLD_LIBRARY_PATH
dark frame, 8.6.6
decision tree
- focus stacking, 8.6.5
default layer selection, 4.4.4
default output filename, see filename, output, default
default weights, see weights, default
deflate compression, see compression
delimiters,
see also options, delimiters, 4.3
depth-of-field, 1, 8.6, 8.6.1
depth-of-focus increase, 8.6
detailed configuration, 3.3.1
development branch, see branches, development, see branches, development
digital blending, 8.3.2
disabling average, see average, disabling
dlopen
- Linux, 5.2.3
- OS X, 5.2.3
double precision float (IEEE754), see IEEE754, double precision float
dual-ISO, A.7
dynamic library, 4.2.5, 5.2.3
dynamic linking, see linking, dynamic
dynamic linking support, 5.2.3
dynamic loading, see loading, dynamic
dynamic range increase, 8.3, 8.4
dynamic-library environment, 4.2.6
EXIF, A.6
EXR, A.4
EXR image, see image, EXR
edge detection
- Laplacian, 8.6.5
entropy, see weighting, local entropy
- cutoff, 4.2.5
- definition, 5.5
- window size, 4.2.5
entropy weight, see weight, entropy
entropy weighting, see weighting, local entropy
environment,
see also environment variable, 3.3.3
environment variable, 3.3.3, 3.3.3
- CILK_NWORKERS, 3.3.3
- DYLD_FALLBACK_LIBRARY_PATH, 5.2.3
- DYLD_LIBRARY_PATH, 5.2.3
- LD_LIBRARY_PATH, 5.2.3, 5.2.3
- OMP_DYNAMIC, 3.3.3
- OMP_NUM_THREADS, 3.3.3
- TMPDIR, 3.3.3
estimators, 5.4.1
expectation value, 5.4.1
expert focus stacking tips, see tips, focus stacking experts
expert fusion options, 4.2.5
expert options, 4.2.4
exposure
- cutoff, 4.2.5
- optimum, 4.2.3
- weight, 4.2.3
- width, 4.2.3
exposure fusion, see fusion, exposure
exposure series, see series, exposure
- common misconceptions, 8.3.2
- tips for beginners, 8.3.1
exposure weight
- function, see weight, function, exposure
- linear transform, 4.2.5
exposure weight function, 4.2.5
- FWHM, 4.2.5
- bi-square, 5.2.1
- bisquare, 5.2.1
- full-sine, 5.2.1
- fullsine, 5.2.1
- gauss, 5.2.1, 5.2.1
- half-sine, 5.2.1
- halfsine, 5.2.1
- lorentz, 5.2.1
- Gaussian, 5.2.1, 5.2.1
- Lorentz curve, 5.2.1
- Lorentzian, 5.2.1
- bi-square, 4.2.5
- bisquare, 4.2.5
- full width half maximum, 4.2.5
- full-sine, 4.2.5
- fullsine, 4.2.5
- gauss, 4.2.5
- gaussian, 4.2.5
- half-sine, 4.2.5
- halfsine, 4.2.5
- lorentz, 4.2.5
- lorentzian, 4.2.5
exposure weight functions, 5.2.1
exposure weighting, see weighting, exposure, see weighting, exposure
- functions, 5
external mask, 3.2
extra features, see features
extra samples, 7.1
FDL, see GNU Free Documentation License
FWHM, 4.2.3, see full width half maximum
fallback profile, see profile, fallback
features, 3.3.1
file
- Mach-O, 5.2.3
- multi-page, 4.5
- response, 4, 4.4
filename
- literal, 4
- output, 4.2.1
  - default, 4.2.1
filename template, see mask, filename template, see mask, filename template
first moment, see moment, first
flash exposure series, see series, flash exposure
floating-point TIFF image, see image, floating-point TIFF
floating-point TIFF mask, see mask, floating-point TIFF
floating-point VIFF image, see image, floating-point VIFF
floating-point image, see image, floating-point
focus stacking
- advanced, 8.6.5
- basic, 8.6.4
focus stacking decision tree, see decision tree, focus stacking
focus stacks, 8.6
- fusing, 8.6.3
- preparation, 8.6.2
- why to create them?, 8.6.1
format
- image, 4.2.6
format of response file, see response file format
full width half maximum, 4.2.5
fusing
- local-contrast-based, 8.6.3
- single criterion, 5.1.3
fusing pixels, see pixels, fusing
fusion
- exposure, 1
fusion options, 4.2.3
Ganos Lal, see Morgan le Fay
GNU FDL, see GNU Free Documentation License
GNU Free Documentation License, D
glob, 4.4.3
globbing algorithm, 4.4.3
- literal, 4.4.3, 4.4.3
- none, 4.4.3
- sh, 4.4.3
- shell, 4.4.3
- wildcard, 4.4.3, 4.4.3
globbing algorithms, see algorithm, globbing, 4.4.3
grammar
- response file, see response file, grammar
- syntactic comment, 4.4.2
gray projector, 4.2.5
- anti-value, 4.2.5
- average, 4.2.5
- channel-mixer, 4.2.5
- l-star, 4.2.5
- lightness, 4.2.5
- luminance, 4.2.5
- pl-star, 4.2.5
- value, 4.2.5
grayscale projector, see projector, grayscale
HDR, see high dynamic range, A.4
HDR-bracketing, see bracketing, HDR
HSL colorspace, see colorspace, HSL
half precision float (OpenEXR), see OpenEXR, half precision float
hard mask, see mask, hard
header files, 4.2.6
help, 4.2.6
helpful libraries, A.5
helpful programs, A,
see also Program/Application Index, D
- HDR, A.4
- camera firmware, A.7
- High Dynamic Range, A.4
- image alignment, A.2
- image manipulation, A.3
- image rendering, A.2
- libraries, A.5
- meta-data handling, A.6
- raw image conversion, A.1
high dynamic range, 1
hot pixels, 8.6.6
ICC, A.6
ICC profile, see profile, ICC, see profile, ICC
ICC profile black-point, see black-point
ICC profile white-point, see white-point
ICC profile, see profile, ICC
IEEE754
- double precision float, 4.2.2
- single precision float, 4.2.2
image
- EXR, 6.2
- black-and-white, 6.3
- directory, 4.5
- floating-point, 6.2
- floating-point TIFF, 6.2
- floating-point VIFF, 6.2
- frame, 4.5.2
image formats, 3.3.1, 3.3.1, see format, image
- JPEG, 3.3.1
- OpenEXR, 3.3.1
- PNG, 3.3.1
- TIFF, 3.3.1
image processing order, see order of image processing
image requirements, see requirements, image
images
- fusable, 8.1

information
- on software components, 4.2.6
information options, 4.2.6
input mask, see mask, input files
interaction with Enfuse, 3.3
invocation, 4
Jackson, Daniel, 8.6.6
Jackson, Daniel, 4.2.1, 4.2.4
JFIF, see JPEG
JPEG, A.5
JPEG compression, see compression
JPEG quality level, see compression
von Kármán, Theodore, 4.2.2
Kautz, Jan, 1
known limitations, 2
L*a*b* colorspace, see colorspace, L*a*b*
Laplacian edge detection, see edge detection, Laplacian
Laplacian-of-Gaussian, 4.2.5, 5.4.2
LaunchPad
- bug database, see bug, database at LaunchPad
LCE, see local contrast enhancement
LD_LIBRARY_PATH, see environment variable, LD_LIBRARY_PATH, see environment variable, LD_LIBRARY_PATH
LibJPEG, A.5
LibPNG, A.5
LibTiff, A.5
Lindbloom, Bruce, 6.1
LoadLibrary (Windows), 5.2.3
LoG, see Laplacian-of-Gaussian
LoG, see Laplacian-of-Gaussian
LZW compression, see compression
l-star gray projector, see gray projector, l-star
layer
- image, 4.5
- selection, 4.5
layer selection, 4.2.4
- all layers, 4.2.4
- default, 4.4.4
- first layer, 4.2.4
- largest-layer, 4.2.4
- last layer, 4.2.4
- no layer, 4.2.4
layer selection syntax, 4.5.1
lens distortion
- correction of, 3.1
level
- verbosity, 4.2.1
levels
- pyramid, 4.2.1
libraries, 3.3.1
library
- dynamic, see dynamic library, see dynamic library
light probe, 8.3.2
lightness gray projector, see gray projector, lightness
linking
- dynamic, 5.2.3
literal filename, see filename, literal
load mask, see mask, loading
loading
- dynamic, 5.2.3
local analysis window, see window, local-analysis
local contrast, see weighting, local contrast
local contrast enhancement, see contrast, local enhancement, see contrast enhancement, local
local contrast problem, 8.6.5
local contrast weight, see weight, local contrast
local contrast weighting, see weighting, local contrast
local entropy, see weighting, local entropy
local entropy weighting, see weighting, local entropy, 5.5
local-contrast-based fusing, 8.6.3
log-transform, see transform, log
luminance, 6
luminance gray projector, see gray projector, luminance
luminance interval, 6.1
- normalized, 5.2, 6.1, 6.1
- trivial, 4.2.2, 4.2.4
Math-O file, see file, Mach-O
Mertens, Tom, 1
Morgan le Fay, 8.6.6
mask, 7, 7.1
- binary, 7
- external, 3.2
- filename template, 4.2.4, 4.2.4
- floating-point TIFF, 4.2.4
- hard, 4.2.3
- input files, 7.1
- loading, 4.2.4
- save, 4.2.4
- soft, 4.2.3
- template character, 4.2.4
  - ‘%’, 4.2.4
  - ‘B’, 4.2.4
  - ‘b’, 4.2.4
  - ‘D’, 4.2.4
  - ‘d’, 4.2.4
  - ‘E’, 4.2.4
  - ‘e’, 4.2.4
  - ‘F’, 4.2.4
  - ‘f’, 4.2.4
  - ‘i’, 4.2.4
  - ‘n’, 4.2.4
  - ‘P’, 4.2.4
  - ‘p’, 4.2.4
- weight, 7, 7.2
matte, 7.1, 7.1
message
- category, 3.3.2
  - error, 3.3.2
  - info, 3.3.2
  - note, 3.3.2
  - timing, 3.3.2
  - warning, 3.3.2
- console, 3.3.2
- debug, 3.3.2
- foreign sources, 3.3.2
- “should never happen”, 3.3.2
mode of operation (SDev, LoG, …), 5.4.4
moment
- first, 5.4.1
- second, 5.4.1
multi-page file, see file, multi-page,
see also layer, 4.5
- tools, 4.5.2
multi-resolution spline, 1
name of builder, 3.3.1
natural sharp-unsharp transition, 8.6.6
noise reduction, 8.2
normalized luminance interval, see luminance interval, normalized
notation, Frontmatter A
O’Neill, Jack, 4.2.4
OMP_DYNAMIC, see environment variable, OMP_DYNAMIC
OMP_NUM_THREADS, see environment variable, OMP_NUM_THREADS
OpenEXR, A.4
- data format, 4.2.2
- half precision float, 4.2.2
OpenMP, 3.3.1, 3.3.3, 3.3.3
object
- shared, see shared object, see shared object
only save mask, see save mask only
optimum exposure, see exposure, optimum
option delimiters, see options, delimiters
options, 4.2
- advanced, 4.2.2
- common, 4.2.1
- delimiters, 4.3
  - filename arguments, 4.3.2
  - numeric arguments, 4.3.1
- expert, 4.2.4
- fusion, 4.2.3
- fusion for experts, 4.2.5
- information, 4.2.6
order
- of image processing, 4.4
output
- file compression, 4.2.1
output filename, see filename, output
- default, see filename, output, default
output image
- set size, 4.2.2
overpowering criteria, see criteria, overpowering
overview, 1
PNG, A.5
packbits compression, see compression
panorama
- 360^∘
  - horizontal, 4.2.2
  - vertical, 4.2.2
parallax error, 3.1
perceptual rendering intent, see rendering intent
performance considerations, 5.2.3
photographic workflow, 3
photometric alignment, see alignment, photometric
pixels
- blending, 6
- fusing, 6
- hot, 8.6.6
pl-star gray projector, see gray projector, pl-star
polarization series, see series, polarization
probability function, 5.4.1
problem reports, see bug reports
profile
- fallback, 4.2.4
- ICC, 3.3.1, 4.2.2, 6
projector
- grayscale, 5.2
projector to grayscale, see gray projector
public repository, 3.3.1
pyramid levels, see levels, pyramid
query
- compiler, 3.3.1
- features, 3.3.1
- image formats, 3.3.1
- libraries, 3.3.1
- name of builder, 3.3.1
query version, see version, query
Van Reeth, Frank, 1
RGB color cube, see color cube, RGB, see color cube, RGB, see color cube, RGB
RGB’-L*a*b* conversion, 4.2.5
RGB-cube, 4.2.4
RGB-L*a*b* conversion, 4.2.5
random variable, 5.4.1
raw conversion, see conversion, raw
rendering intent
- perceptual, 6.4
requantization, 4.2.2
requirements
- image, 4.1
response file, see file, response
- comment (‘#’), see ‘#’
- force recognition of, 4.4.1
- format, 4.4.1
- grammar, 4.4.1
- syntactic comment, 4.4.2
response file prefix
- ‘@’, see ‘@’
response files, 4.4
return code, 3.3.2
SNR, see signal-to-noise ratio
SourceForge, 1
saturation enhancement, 8.5
saturation weight, 4.2.3
saturation weighting, see weighting, saturation, see weighting, saturation
save mask, see mask, save
- only, 4.2.4
scaling of parameters, 5.4.4
second moment, see moment, second
sensor
- use clean, 8.6.6
series
- exposure, 8.3
- flash exposure, 8.4
- polarization, 8.5
- simple, 8.2
shared object, 4.2.5, 5.2.3
signal-to-noise ratio, 8.6.2
signature, 3.3.1, 4.2.6
signed binary, see signature
simple series, see series, simple
single criterion fusing, see fusing, single criterion
single precision float (IEEE754), see IEEE754, single precision float
size
- canvas, 4.2.2
soft mask, see mask, soft
software
- components, see information, on software components
- version, 4.2.6
software version, see version, software
source code repository, see public repository
spline, see multi-resolution spline
sRGB, 4.2.2
sRGB color cube, see color cube, sRGB
standard deviation, 5.4.1
standard workflow, see workflow, standard
statistical moments, 5.4.1
subtraction of dark frame, 8.6.6
sweet spot aperture, see aperture, sweet spot
syntactic comment
- grammar, 4.4.2
- response file, see response file, syntactic comment
syntax
- layer selection, 4.5.1
  - grammar, 4.5.1
TIFF, A.5
TMPDIR, see environment variable, TMPDIR
tips
- focus stacking experts, 8.6.6
transform
- floating-point images, 6.2
- log, 6.2, 6.2
transformation
- affine, 3.1
transition
- natural sharp-unsharp, 8.6.6
typographic conventions, see notation
unassociated alpha channel, see alpha channel, associated
understanding masks, 7
VIFF floating-point image, see image, floating-point VIFF
VR, see virtual reality
value gray projector, see gray projector, value
variable, see environment variable
variance, 5.4.1
verbosity level, see level, verbosity
version, see software, version
- query, 3.3.1
- software, 3.3.1
virtual reality, 4.2.2
weight
- entropy, 4.2.3
- exposure, see exposure, weight
- function
  - exposure, 4.2.5
- local contrast, 4.2.3
- mask, see mask, weight
- saturation, see saturation weight
weighted average, see average, weighted
weighting
- contrast using Laplacian-of-Gaussian, 5.4.2
- contrast using a blend of methods, 5.4.3
- contrast using standard deviation, 5.4.1
- entropy, 5.3
- exposure, 1, 5.2
  - built-in, 5.2.1
  - prerequisites, 5.2.3
  - user-defined, 5.2.2
    - dynamically-linked, 5.2.3
- general concept of, 5.1
- local contrast, 1, 5.4
- local entropy, 1, 5.5
  - window size, 5.5
- saturation, 1, 5.3
weighting factor, 6
weighting functions, 5
weights
- default, 5.1.3
white-point, 6.3
- D50, 6.4, 6.4
width of exposure weight curve, see exposure, width
window
- local-analysis, 5.4.1
window size
- contrast, see contrast, window size
- entropy, see entropy, window size
workflow, see photographic workflow
- Enblend, 3.1
- Enfuse, 3.1
- external mask, 3.2
- standard, 3.1
wrap around, 4.2.2

Date determined via file-system – potentially inaccurate.


Category	Description	Examples

Acronym	Common acronym	sRGB, OpenMP
Application	GUI or CLI application	Hugin, Enfuse
Command	Name of a binary in the running text	convert, enfuse
Common part	Chapter, section, or any other part that appears in both manuals	Response Files^c
Default	Value as compiled into the enfuse binary that belongs to this documentation	⟨1⟩, ⟨a.tif⟩
Environment variable	Variable passed to enfuse by the operating system	PATH, TMPDIR
Filename	Name of a file in the filesystem	a.tif
Filename extension	Name of a filename extension with or without dots	.png, tiff
Fix me!	Section that needs extending or at least some improvement	FIXExplainME
Literal text	Text that (only) makes sense when typed in exactly as shown	uint16
Option	Command-line option given to enfuse	--verbose
Optional part	Optional part of a syntax description in square brackets	--verbose [=LEVEL]
Placehoder	Meta-syntactic variable that stands in for the actual text	ICC-PROFILE
Proper name	Name of a person or algorithm	Dijkstra
Restricted note	Annotation that applies only to a particular program, configuration, or operating system	Enfuse.
Sample	Literal text in quotes	‘%’ or ‘--help’
Side note	Non-essential or “geeky” material	Gory details
White space	Indispensable white space	r␣g␣b


			Channel Bit-Depth

Format	Mask	Profile	Integral			Floating-Point

			uint8	uint16	uint32	float	double

JPEG	−	•	•	−	−	−	−
PNG	•	•	•	•	−	−	−
PNM	?	−	•	•	•	−	−
[V]TIFF	•	•	•	•	•	•	•


Level	Messages

0	only warnings and errors
1	reading and writing of images
2	mask generation, pyramid, and blending
3	reading of response files, color conversions
4	image sizes, bounding boxes and intersection sizes
5	Enblend only. detailed information on the optimizer runs
6	estimations of required memory in selected processing steps


Format	Interpretation

%%	Produces a literal ‘%’-sign.
%i	Expands to the index of the mask file starting at zero. ‘%i’ allows for setting a pad character or a width specification: % PAD WIDTH i PAD is either ‘0’ or any punctuation character; the default pad character is ‘0’. WIDTH is an integer specifying the minimum width of the number. The default is the smallest width given the number of input images, this is 1 for 2–9 images, 2 for 10–99 images, 3 for 100–999 images, and so on. Examples: ‘%i’, ‘%02i’, or ‘%_4i’.
%n	Expands to the number of the mask file starting at one. Otherwise it behaves identically to ‘%i’, including pad character and width specification.
%p	This is the full name (path, filename, and extension) of the input file associated with the mask. Example: If the input file is called /home/luser/snap/img.jpg, ‘%p’ expands to /home/luser/snap/img.jpg, or shorter: ‘%p’ ↦ /home/luser/snap/img.jpg.
%P	This is the full name of the output file.
%d	Is replaced with the directory part of the associated input file. Example (cont.): ‘%d’ ↦ /home/luser/snap.
%D	Is replaced with the directory part of the output file.
%b	Is replaced with the non-directory part (often called “basename”) of the associated input file. Example (cont.): ‘%b’ ↦ img.jpg.
%B	Is replaced with the non-directory part of the output file.
%f	Is replaced with the filename without path and extension of the associated input file. Example (cont.): ‘%f’ ↦ img.
%F	Is replaced with the filename without path and extension of the output file.
%e	Is replaced with the extension (including the leading dot) of the associated input file. Example (cont.): ‘%e’ ↦ .jpg.
%E	Is replaced with the extension of the output file.


Task	Cutoff Setting	Effect

Suppress some noise.	--exposure-cutoff=5%	The percentage makes the cutoff specification channel-width agnostic.
Shave off pure white pixels.	--exposure-cutoff=0:-1	This cutoff specification only works for integral pixels, but it will set the weight of the very brightest pixels to zero.
Shave off bright white pixels.	--exposure-cutoff=0:-1%	Here we exclude the brightest 1% of pixels form the exposure fusion no matter whether the image is encoded with integers or floating-point numbers.
Suppress some noise and shave off pure white pixels.	--exposure-cutoff=5%:-1	Combine the effects of lower and upper cutoff, while mixing relative and absolute specifications.

response-file	::=	line*
line	::=	(comment \| file-spec) [‘\r’] ‘\n’
comment	::=	space* ‘#’ text
file-spec	::=	space* ‘@ ’ filename space*
space	::=	‘␣’ \| ‘\t’

syntactic-comment	::=	space* ‘#’ space* key space* ‘:’ space* value
key	::=	(‘A’…‘Z’ \| ‘a’…‘z’ \| ‘-’)+

layer-specification	::=	‘[’ selection-tuple ‘]’
selection-tuple	::=	selection [ ‘:’ selection ]
selection	::=	{ singleton \| range }
range	::=	[ ‘reverse’ ] [ range-bound ] ‘..’ [ range-bound ]
range-bound	::=	singleton \| ‘_’
singleton	::=	index \| ‘-’ index


Criterion	Default Weight

Exposure	⟨1.0⟩
Saturation	⟨0.2⟩
Local Contrast	⟨0.0⟩
Local Entropy	⟨0.0⟩


Exposure Weight	WEIGHT-FUNC.	Equ.	Chart

Gaussian curve (default)	gauss, gaussian	4.3	5.1
Lorentz curve	lorentz, lorentzian	4.4	5.2
Upper half-wave of a sine	halfsine, half-sine	4.5	5.3
Full sine-wave shifted upwards by one	fullsine, full-sine	4.6	5.4
Quartic, or bi-square function	bisquare, bi-square	4.7	5.5