G’MIC 1.7.1: When the flowers are blooming, image filters abound!

Disclaimer: This article is a duplicate of this post, originally published on the Pixls.us website, by the same authors.

Then we shall all burn together by Philipp Haegi.

 A new version 1.7.1Spring 2016” of G’MIC (GREYC’s Magic for Image Computing),
the open-source framework for image processing, has been released recently (26 April 2016). This is a great opportunity to summarize some of the latest advances and features over the last 5 months.

G’MIC: A brief overview

G’MIC is an open-source project started in August 2008. It has been developed in the IMAGE team of the GREYC laboratory from the CNRS (one of the major French public research institutes). This team is made up of researchers and teachers specializing in the algorithms and mathematics of image processing. G’MIC is released under the free software licence CeCILL (GPL-compatible) for various platforms (Linux, Mac and Windows). It provides a set of various user interfaces for the manipulation of generic image data, that is images or image sequences of multispectral data being 2D or 3D, and with high-bit precision (up to 32bits floats per channel). Of course, it manages “classical” color images as well.

logo_gmic

Logo and (new) mascot of the G’MIC project, the open-source framework for image processing.

Note that the project just got a redesign of its mascot Gmicky, drawn by David Revoy, a French illustrator well-known to free graphics lovers for being responsible for the great libre webcomics Pepper&CarottG’MIC is probably best known for it’s GIMP plug-in, first released in 2009. Today, this popular GIMP extension proposes more than 460 customizable filters and effects to apply on your images.

gmic_gimp171_s

Overview of the G’MIC plug-in for GIMP.

But G’MIC is not a plug-in for GIMP only. It also offers a command-line interface, that can be used in addition with the CLI tools from ImageMagick or GraphicsMagick (this is undoubtly the most powerful and flexible interface of the framework). G’MIC also has a web service G’MIC Online to apply effects on your images directly from a web browser. Other G’MIC-based interfaces also exist (ZArt, a plug-in for Krita, filters for Photoflow…). All these interfaces are based on the generic C++ libraries CImg and libgmic which are portable, thread-safe and multi-threaded (through the use of OpenMP). Today, G’MIC has more than 900 functions to process images, all being fully configurable, for a library of only approximately 150 kloc of source code. It’s features cover a wide spectrum of the image processing field, with algorithms for geometric and color manipulations, image filtering (denoising/sharpening with spectral, variational or patch-based approaches…), motion estimation and registration, drawing of graphic primitives (up to 3d vector objects), edge detection, object segmentation, artistic rendering, etc. This is a versatile tool, useful to visualize and explore complex image data, as well as elaborate custom image processing pipelines (see these slides to get more information about the motivations and goals of the G’MIC project).

A selection of some new filters and effects

Here we look at the descriptions of some of the most significant filters recently added. We illustrate their usage from the G’MIC plug-in for GIMP. All of these filters are of course available from other interfaces as well (in particular within the CLI tool gmic).

Painterly rendering of photographs

The filter Artistic / Brushify tries to transform an image into a painting. Here, the idea is to simulate the process of painting with brushes on a white canvas. One provides a template image and the algorithm first analyzes the image geometry (local contrasts and orientations of the contours), then attempt to reproduce the image with a single brush that will be locally rotated and scaled accordingly to the contour geometry. By simulating enough of brushstrokes, one gets a “painted” version of the template image, which is more or less close to the original one, depending on the brush shape, its size, the number of allowed orientations, etc. All these settings being customizable by the user as parameters of the algorithm: This filter allows thus to render a wide variety of painting effects.

gmic_brushify

Overview of the filter “Brushify” in the G’MIC plug-in GIMP. The brush that will be used by the algorithmis visible on the top left.

The animation below illustrates the diversity of results one can get with this filter, applied on the same input picture of a lion. Various brush shapes and geometries have been supplied to the algorithm. Brushify is computationally expensive so its implementation is parallelized (each core gives several brushstrokes simultaneously).

brushify2

A few examples of renderings obtained with “Brushify” from the same template image, but with different brushes and parameters.

Note that it’s particularly fun to invoke this filter from the command line interface (using the option -brushify available in gmic) to process a sequence of video frames (see this example of “ brushified “ video):

Reconstructing missing data from sparse samples

G’MIC gets a new algorithm to reconstruct missing data in images. This is a classical problem in image processing, often named “Image Inpainting“, and G’MIC already had a lot of useful filters to solve this problem. Here, the newly added interpolation method assumes only a sparse set of image data is known, for instance a few scattered pixels over the image (instead of continuous chuncks of image data). The analysis and the reconstruction of the global image geometry is then particularly tough.

The new option -solidify in G’MIC allows the reconstruction of dense image data from such a sparse sampling, based on a multi-scale diffusion PDE’s-based technique. The figure below illustrates the ability of the algorithm with an example of image reconstruction. We start from an input image of a waterdrop, and we keep only 2.7% of the image data (a very little amount of data!). The algorithm is able to reconstruct a whole image that looks like the input, even if all the small details have not been fully reconstructed (of course!). The more samples we have, the finer details we can recover.

waterdrop2

Reconstruction of an image from a sparse sampling.

As this reconstruction technique is quite generic, several new G’MIC filters takes advantage of it:

  • Filter Repair / Solidify applies the algorithm in a direct manner, by reconstructing transparent areas from the interpolation of opaque regions. The animation below shows how this filter can be used to create an artistic blur on the image borders.
gmic_sol

Overview of the “Solidify” filter, in the G’MIC plug-in for GIMP.

From an artistic point of view, there are many possibilities offered by this filters. For instance, it becomes really easy to generate color gradients with complex shapes, as shown with the two examples below (also in this video that details the whole process).

gmic_solidify2

Using the “Solidify” filter of G’MIC to easily create color gradients with complex shapes (input images on the left, filter results on the right).

  • Filter Artistic / Smooth abstract uses same idea as the one with the waterdrop image: it purposely sub-samples the image in a sparse way, by choosing keypoints mainly on the image edges, then use the reconstruction algorithm to get the image back. With a low number of samples, the filter can only render a piecewise smooth image, i.e. a smooth abstraction of the input image.
smooth_abstract

Overview of the “Smooth abstract” filter in the G’MIC plug-in for GIMP.

  • Filter Rendering / Gradient [random] is able to synthetize random colored backgrounds. Here again, the filter initializes a set of colors keypoints randomly chosen over the image, then interpolate them with the new reconstruction algorithm. We end up with a psychedelic background composed of randomly oriented color gradients.
gradient_random

Overview of the “Gradient [random]” filter in the G’MIC plug-in for GIMP.

  • Simulation of analog films : the new reconstruction algorithm also allowed a major improvement for all the analog film emulation filters that have been present in G’MIC for years. The section Film emulation/ proposes a wide variety of filters for this purpose. Their goal is to apply color transformations to simulate the look of a picture shot by an analogue camera with a certain kind of film. Below, you can see for instance a few of the 300 colorimetric transformations that are available in G’MIC.
gmic_clut1

A few of the 300+ color transformations available in G’MIC.

From an algorithmic point of view, such a color mapping is extremely simple to implement : for each of the 300+ presets, G’MIC actually has an HaldCLUT, that is a function defining for each possible color (R,G,B) (of the original image), a new color (R’,G’,B’) color to set instead. As this function is not necessarily analytic, a HaldCLUT is stored in a discrete manner as a lookup table that gives the result of the mapping for all possible colors of the RGB cube (that is 2^24 = 16777216 values if we work with a 8bits precision per color component). This HaldCLUT-based color mapping is illustrated below for all values of the RGB color cube.

gmic_clut0

Principle of an HaldCLUT-based colorimetric transformation.

This is a large amount of data: even by subsampling the RGB space (e.g. with 6 bits per component) and compressing the corresponding HaldCLUT file, you ends up with approximately 200 and 300 kB for each mapping file. Multiply this number by 300+ (the number of available mappings in G’MIC), and you get a total of 85MB of data, to store all these color transformations. Definitely not convenient to spread and package!

The idea was then to develop a new lossy compression technique focused on HaldCLUT files, that is volumetric discretised vector-valued functions which are piecewise smooth by nature. And that what has been done in G’MIC, thanks to the new sparse reconstruction algorithm. Indeed, the reconstruction technique also works with 3D image data (such as a HaldCLUT!), so one simply has to extract a sufficient number of significant keypoints in the RGB cube and interpolate them afterwards to allow the reconstruction of a whole HaldCLUT (taking care to have a reconstruction error small enough to be sure that the color mapping we get with the compressed HaldCLUT is indistinguishable from the non-compressed one).

gmic_clut2

How the decompression of an HaldCLUT now works in G’MIC, from a set of colored keypoints located in the RGB cube.

Thus, G’MIC doesn’t need to store all the color data from a HaldCLUT, but only a sparse sampling of it (i.e. a sequence of { rgb_keypoint, new_rgb_color }). Depending on the geometric complexity of the HaldCLUTs to encode, more or less keypoints are necessary (roughly from 30 to 2000). As a result, the storage of the 300+ HaldCLUTs in G’MIC requires now only 850 KiB of data (instead of 85 MiB), that is a compression gain of 99% ! That makes the whole HaldCLUT data storable in a single file that is easy to ship with the G’MIC package. Now, a user can then apply all the G’MIC color transformations while being offline (previously, each HaldCLUT had to be downloaded separately from the G’MIC server when requested).

It looks like this new reconstruction algorithm from sparse samples is really great, and no doubts it will be used in other filters in the future.

Make textures tileable

Filter Arrays & tiles / Make seamless [patch-based] tries to transform an input texture to make it tileable, so that it can be duplicated as tiles along the horizontal and vertical axes without visible seams on the borders of adjacent tiles. Note that this is something that can be extremely hard to achieve, if the input texture has few auto-similarity or glaring luminosity changes spatially. That is the case for instance with the “Salmon” texture shown below as four adjacent tiles (configuration 2×2) with a lighting that goes from dark (on the left) to bright (on the right). Here, the algorithm modifies the texture so that the tiling shows no seams, but where the aspect of the original texture is preserved as much as possible (only the texture borders are modified).

seamless1

Overview of the “Make Seamless” filter in the G’MIC plug-in for GIMP.

We can imagine some great uses of this filter, for instance in video games, where texture tiling is common to render large virtual worlds.

seamless2

Result of the “Make seamless” filter of G’MIC to make a texture tileable.

Image decomposition into several levels of details

A “new” filter Details / Split details [wavelets] has been added to decompose an image into several levels of details. It is based on the so-called “à trous” wavelet decomposition. For those who already know the popular Wavelet Decompose plug-in for GIMP, there won’t be so much novelty here, as it is mainly the same kind of decomposition technique that has been implemented. Having it directly in G’MIC is still a great news: it offers now a preview of the different scales that will be computed, and the implementation is parallelized to take advantage of multiple cores.

gmic_wavelets

Overview of the wavelet-based image decomposition filter, in the G’MIC plug-in for GIMP.

The filter outputs several layers, so that each layer contains the details of the image at a given scale. All those layers blended together gives the original image back. Thus, one can work on those output layers separately and modify the image details only for a given scale. There are a lot of applications for this kind of image decomposition, one of the most spectacular being the ability to retouch the skin in portraits : the flaws of the skin are indeed often present in layers with middle-sized scales, while the natural skin texture (the pores) are present in the fine details. By selectively removing the flaws while keeping the pores, the skin aspect stays natural after the retouch (see this wonderful link for a detailed tutorial about skin retouching techniques, with GIMP).

skin

Using the wavelet decomposition filter in G’MIC for removing visible skin flaws on a portrait.

Image denoising based on “Patch-PCA”

G’MIC is also well known to offer a wide range of algorithms for image denoising and smoothing (currently more than a dozen). And he got one more ! Filter Repair / Smooth [patch-pca] proposed a new image denoising algorithm that is both efficient and computationally intensive (despite its multi-threaded implementation, you probably should avoid it on a machine with less than 8 cores…). In return, it sometimes does magic to suppress noise while preserving small details.

patchpca

Result of the new patch-based denoising algorithm added to G’MIC.

The “Droste” effect

The Droste effect (also known as “mise en abyme“ in art) is the effect of a picture appearing within itself recursively. To achieve this, a new filter Deformations / Continuous droste has been added into G’MIC. It’s actually a complete rewrite of the popular Mathmap’s Droste filter that has existed for years. Mathmap was a very popular plug-in for GIMP, but it seems to be not maintained anymore. The Droste effect was one of its most iconic and complex filter. Martin “Souphead”, one former user of Mathmap then took the bull by the horns and converted the complex code of this filter specifically into a G’MIC script, resulting in a parallelized implementation of the filter.

droste0

Overview of the converted “Droste” filter, in the G’MIC plug-in for GIMP.

This filter allows all artistic delusions. For instance, it becomes trivial to create the result below in a few steps: create a selection around the clock, move it on a transparent background, run the Droste filter, et voilà!.

droste2

A simple example of what the G’MIC “Droste” filter can do.

Equirectangular to nadir-zenith transformation

The filter Deformations / Equirectangular to nadir-zenith is another filter converted from Mathmap to G’MIC. It is specifically used for the processing of panoramas: it reconstructs both the Zenith and the
Nadir regions of a panorama so that they can be easily modified (for instance to reconstruct missing parts), before being reprojected back into the input panorama.

zenith1

Overview of the “Deformations / Equirectangular to nadir-zenith” filter in the G’MIC plug-in for GIMP.

Morgan Hardwood has wrote a quite detailled tutorial, on pixls.us, about the reconstruction of missing parts in the Zenith/Nadir of an equirectangular panorama. Check it out!

Other various improvements

Finally, here are other highlights about the G’MIC project:

  • Filter Rendering / Kitaoka Spin Illusion is another Mathmap filter converted to G’MIC by Martin “Souphead”. It generates a certain kind of optical illusions as shown below (close your eyes if you are epileptic!)
spin2

Result of the “Kitaoka Spin Illusion” filter.

  • Filter Colors / Color blindness transforms the colors of an image to simulate different types of color blindness. This can be very helpful to check the accessibility of a web site or a graphical document for colorblind people. The color transformations used here are the same as defined on Coblis, a website that proposes to apply this kind of simulation online. The G’MIC filter gives strictly identical results, but it ease the batch processing of several images at once.
gmic_cb

Overview of the colorblindness simulation filter, in the G’MIC plug-in for GIMP.

  • Since a few years now, G’MIC has its own parser of mathematical expression, a really convenient module to perform complex calculations when applying image filters This core feature gets new functionalities: the ability to manage variables that can be complex, vector or matrix-valued, but also the creation of user-defined mathematical functions. For instance, the classical rendering of the Mandelbrot fractal set (done by estimating the divergence of a sequence of complex numbers) can be implemented like this, directly on the command line:
    $ gmic 512,512,1,1,"c = 2.4*[x/w,y/h] - [1.8,1.2]; z = [0,0]; for (iter = 0, cabs(z)
gmic_mand

Using the G’MIC math evaluator to implement the rendering of the Mandelbrot set, directly from the command line!_

This clearly enlarge the math evaluator ability, as you are not limited to scalar variables anymore. You can now create complex filters which are able to solve linear systems or compute eigenvalues/eigenvectors, and this, for each pixel of an input image. It’s a bit like having a micro-(micro!)-Octave inside G’MIC. Note that the Brushify filter described earlier uses these new features extensively. It’s also interesting to know that the G’MIC math expression evaluator has its own JIT compiler to achieve a fast evaluation of expressions when applied on thousands of image values simultaneously.

  • Another great contribution has been proposed by Tobias Fleischer, with the creation of a new API to invoke the functions of the libgmic library (which is the library containing all the G’MIC features, initially available through a C++ API only). As the C ABI is standardized (unlike C++), this basically means G’MIC can be interfaced more easily with languages other than C++. In the future, we can imagine the development of G’MIC APIs for languages such as Python for instance. Tobias is currently using this new C API to develop G’MIC-based plug-ins compatible with the OpenFX standard. Those plug-ins should be usable indifferently in video editing software such as After effects, Sony Vegas Pro or Natron. This is still an on-going work though.
gmic_natron

Overview of some G’MIC-based OpenFX plug-ins, running under Natron.

gmic_blender2

Overview of a dedicated G’MIC script running within the Blender VSE.

  • You can find out G’MIC filters also in the opensource nonlinear video editor Flowblade, thanks to the hard work of Janne Liljeblad (Flowblade project leader). Here again, the goal is to allow the application of G’MIC effects and filters directly on image sequences, mainly for artistic purposes (as shown in this video or this one).
gmic_flowblade

Overview of a G’MIC filter applied under Flowblade, a nonlinear video editor.

What’s next ?

As you see, the G’MIC project is doing well, with an active development and cool new features added months after months. You can find and use interfaces to G’MIC in more and more opensource software, as GIMPKritaBlenderPhotoflowFlowbladeVeejayEKD and Natron in a near future (at least we hope so!).

At the same time, we can see more and more external resources available for G’MIC : tutorials, blog articles (hereherehere,…), or demonstration videos (herehereherehere,…). This shows the project becoming more useful to users of opensource software for graphics and photography.

The development of version 1.7.2 already hit the ground running, so stay tuned and visit the official G’MIC forum on pixls.us to get more info about the project developement and get answers to your questions. Meanwhile, feel the power of free software for image processing!

Image processing made easier with a powerful math expression evaluator.

Warning: This post contains personal thoughts about my research work in image processing. I’ll discuss about some of the issues I’m facing as an active developer of two open-source image processing frameworks (namely CImg and G’MIC). So keep in mind this will be a bit self-centered. There are high chances you find all this really boring if you are not a developer of image processing software yourself (and even if so). Anyhow, feel free to give your impressions after the reading!

1. Context and issues

In imaging science, image processing is processing of images using mathematical operations by using any form of signal processing for which the input is an image, such as a photograph or video frame.

That’s what Wikipedia says about  image processing. Selecting and ordering those mathematical operations is what actually defines algorithms, and implementing ready-to-use and interesting image processing algorithms is actually one of my goals, as well as making them available for interested users afterwards.

After all those years (>10) as a researcher in the image processing field (and like most of my colleagues), I can say I’ve already implemented a lot of these different algorithms. Mostly in C++ as far as I’m concerned. To be more precise, an important part of my work is even to design (and hopefully publish) my own image processing methods. Most of the time of course, my trials end up with clunky, ineffective and slow operators which give nothing interesting else than knowing the approach is not good enough to be followed. Someone who says everything he tries works right the first time is a liar. Step by step, I try to refine/optimize my prototypes or sometimes even take a completely different direction. Quickly, you realize that it is crucial in this job not to waste time when doing algorithm prototyping because the rate of success is in fact very low.

2644977732_bd871a2e5c_m

Don’t waste your time, in any occasion! (photo by (OvO), under CC-by-nc-sa.)

That’s actually one of the reason why I’ve started the G’MIC project. It was primarily designed as a helper to create and run custom image processing pipelines quickly (from the shell, basically). It saves me time, everyday. But the world of image processing algorithms is broad and sometimes you need to experiment with very low-level routines working at a pixel scale, trying such weird and unexpected stuffs that none of the “usual” image processing algorithms you already have in your toolbox can be of use as it is. Or it is used in a so diverted way that it gets hard to even think about using it adequately. In a word, your pixel-level algorithm won’t be expressed as a simple pipeline (or graph if you want to call it so) of macro-scale image processing operators. That’s the case for instance with most of the well known patch-based image processing algorithms (e.g. Non-Local-Means, or PatchMatch and plenty of variants), where each pixel value of the resulting image is computed from (a lot of) other pixel values whose spatial locations are sometimes not evenly distributed (but not random as well!).

Until now, when I was trying to implement this kind of algorithms, I was resigned to go back coding them in C++: It is one language I feel comfortable with, and I’m sure it will run fast enough most of the time. Indeed, computation time is often a bottleneck in image processing. Some of my colleagues are using scripting languages as Matlab or Python for algorithm prototyping. But they often need some tricks to avoid writing explicit code loops, or need to write at least some fast C/C++ modules that will be compiled and run from those higher-level interfaces, to ensure they get something fast enough (even for prototyping, I’m definitely not talking about optimized production code here!).

dec20-leadtime

But, I’m not really satisfied with my C++ solution: Generally, I end up with several small pieces of C++ sources I need to compile and maintain. I can hardly re-use them in a bigger pipeline, or redistribute them as clean packages without a lot of extra work. Because they are just intended to be prototypes: They often have only basic command-line interfaces and thus cannot be directly integrated into bigger and user-friendly image processing frameworks. Making a prototype algorithm really usable by others requires at least to wrap it as a plug-in/module for [..copy the name of your favorite image processing tool or language here..]. This generally represents a lot of boring coding workthat may even require more time and efforts than writing the algorithm itself!  And I don’t talk about maintenance. If you’ve ever tried to maintain a 10-year old C++ prototype code, lost in one of your sub-sub-sub-sub folder in your $HOME, you know what I mean. I’d definitely prefer a simpler solution that let me spend more time on writing the algorithm itself than packaging it or making it usable. After all, the primary purpose of my work is to create cool algorithms, not really coding user interfaces for them. On the other way, I am a scientist and I’m also happy to share my discoveries with users (and possibly get feedback from them!). How to make those prototyped algorithms finally usable without spending too much time on making them usable ? 🙂

Ideally, I’d like something that could nicely integrate into G’MIC (my favorite framework for doing image processing stuffs, of course 🙂 ). Even if at the end, those algorithms run a bit slower than they are in C++. One could suggest to make them as Octave or Scilab scripts/modules. But I’m the developer of G’MIC, so of course, I’d prefer a solution that help to extend my own project.

So finally, how could I code prototypes for new algorithms working at a pixel-level and make them readily available in G’MIC ? This question has worried me for a long time.

2. Algorithm code viewed as a complex math expression

In G’MIC, the closest thing to what I was looking for, is the command

-fill 'expression'

This command fills each pixel of a given image with the value evaluated from a “mathematical expression”. A mathematical expression being a quite vague concept, it appears you can already write some complex formulas. For instance, typing this on the command line:

$ gmic 400,400,1,3 -fill "X=x-w/2; Y=y-h/2; R=sqrt(X^2+Y^2); a=atan2(Y,X); if(R<=180,255*abs(cos(c+200*(x/w-0.5)*(y/h-0.5))),850*(a%(0.1*(c+1))))"

creates this weird-looking 400×400 color image (I advise you to put sunglasses):

"Image

Fig.1. One synthetic color image obtained by one application of the G’MIC command -fill.

Of course, the specified expression can refer to pixels of an existing input image. And so, it can modify the pixels of an image as well, as in the following example:

$ gmic leno.png -fill "(abs(i(x+1,y)-i(x-1,y)))^0.25"

which computes gamma-corrected differences of neighboring pixels along the X-axis, as shown below:

gmic_leno1

Fig.2.1. Original image leno.png

gmic_leno2

Fig.2.2. Result of the -fill command described above.

(As an aside, let me tell you I’ve recently received e-mails and messages from people who claim that using the image of our beloved Lena to illustrate an article or a blog post is “sexist” (someone even used the term “pornographic”…). I invite you reading the Lena story page if you don’t know why we commonly use this image. As I don’t want to hurt the over-sensibility of these people, I’ll be using a slight variation I’ve made by mixing a photograph of the blessed Jay Leno with the usual image of Lena. Let me call this the Leno image and everyone will be happy (but seriously, get a life!)).

So, as you can imagine, the command -fill already allows me to do a lof of complex and exotic things on images at a pixel level. Technically speaking, it uses the embedded math parser I’ve written for the CImg Library, a C++ open-source image processing library I’ve been developing since 1999 (and on which G’MIC is based). This math parser is quite small (around 1500 lines of C++ code) and quite fast as well, when it is applied on a whole image. That’s mainly because:

1. It uses parallelization (thanks to the use of OpenMP directives) to evaluate expressions on blocs of image pixels in a multi-threaded way.

2. Before being evaluated, the given math expression is pre-compiled on-the-fly by CImg, into a sequence of bytecodes. Then, the evaluation procedure (which is done for the whole image, pixel by pixel) requires only that bytecode sequence to be interpreted, which is way faster than parsing the input mathematical expression itself.

Anyway, I thought the complexity of the pixel-level algorithms I’d like to implement was really higher than just the evaluation of a mathematical formula. But wait… What is missing actually ? Not much more than loops and updatable variables… I already had variables (though non-updatable) and conditionals. Only loops were really missing. That looks like something I could try adding during my summer holidays, isn’t it ? 😉 So, that is where my efforts were focused on during these last weeks: I’ve added new functions to the CImg math parser that allow users to write their own loops in mathematical expressions, namely the functions dowhile(expr,_cond)whiledo(cond,expr) and for(init,cond,expr_end,_expr_body). Of course, it made me also review and re-implement large parts of the math parser code, and I took this opportunity to optimize the whole thing. A new version of the math parser has been made available for the release of G’MIC 1.6.5.2 at the end of August. I’m still working on this expression evaluator in CImg and new improvements and optimizations are ready for the upcoming version 1.6.6.0 of G’MIC (soon to be released).

3. A toy example: Julia fractals

So, what can we do now with these new math features in G’MIC ? Let me illustrate this with a toy example. The following custom G’MIC command renders a Julia fractal. To test it, you just have to copy/paste the following lines in a regular text file user.gmic:

julia_expr :
  1024,1024
  -fill "
    zr = -1.2 + 2.4*x/w;
    zi = -1.2 + 2.4*y/h;
    for (iter = 0, zr^2+zi^2<=4 && iter<256, ++iter,
      t = zr^2 - zi^2 + 0.4;
      (zi *= 2*zr) += 0.2;
      zr = t
    );
    iter"
  -map 7

and invoke the new command -juliar_expr it defines by typing this in the terminal:

$ gmic user.gmic -julia_expr

Then, you’ll get this 1024×1024 color image:

Rendering of the Julia fractal set only from filling an image with a math expression.

Fig.3. Rendering of a Julia fractal only by filling an image with a complex math expression, containing an iteration loop.

As you see, this custom user command -julia_expr is very short and is mainly based on the invokation of the -fill command of G’MIC. But the coolest thing of all happens when we look at the rendering time of that function. The timing measure has been performed on an ASUS laptop with a dual-core HT i7 2Ghz. This is what I get:

Edit : This post has been edited, on 09/20/2015 to reflect the new timings due to math parser optimization done after the initial post of this article.

$ gmic user.gmic -tic -julia -toc
[gmic]-0./ Start G'MIC interpreter.
[gmic]-0./ Input custom command file 'user.gmic' (added 1 command, total 6195).
[gmic]-0./ Initialize timer.
[gmic]-0./julia/ Input black image at position 0 (1 image 1024x1024x1x1).
[gmic]-1./julia/ Fill image [0] with expression ' zr = -1.2 + 2.4*x/w; zi = -1.2 + 2.4*(...)( zi *= 2*zr) += 0.2; zr = t ); iter '.
[gmic]-1./julia/ Map cube color LUT on image [0], with dirichlet boundary conditions.
[gmic]-1./ Elapsed time : 0.631 s.

Less than 0.7 second to fill a 1024×1024 image where each of the 1,048,576 pixels may require up to 256 iterations of a computation loop ? Definitely not bad for a prototyped code written in 5 minutes and which does not require compilation to run! Note that all my CPUs have been active during the computation. Trying the same G’MIC code on my machine at work (a powerful 4x 3-core HT Xeon 2.6Ghz) makes the same render in 0.176 second only!

But of course, one could say:

Why not using the native G’MIC command -mandelbrot instead (here, native means hard-coded as a C++ function) ? It is probably way faster!

Let me compare my previous code with the following G’MIC invokation (which renders exactly the same image):

$ gmic 1024,1024 -tic -mandelbrot -1.2,-1.2,1.2,1.2,256,1,0.4,0.2 -map 7 -toc
[gmic]-0./ Start G'MIC interpreter.
[gmic]-0./ Input black image at position 0 (1 image 1024x1024x1x1).
[gmic]-1./ Initialize timer.
[gmic]-1./ Draw julia fractal on image [0], from complex area (-1.2,-1.2)-(1.2,1.2) with c0 = (0.4,0.2) and 256 iterations.
[gmic]-1./ Map cube color LUT on image [0], with dirichlet boundary conditions.
[gmic]-1./ Elapsed time : 0.055 s.

That’s 12 times faster, than the previous command -julia_expr run on my laptop, indeed! A bit reassuring to know that C++ compiled into assembly code is faster than CImg home-made bytecode compiled on the fly 😉

But the point is: Suppose now I want to slightly modify the rendering of the fractal, i.e. I don’t want to display the maximum iteration anymore for each pixel (variable iter), but the latest value of the variable zi before the divergence test occurs. Look how simple this is to create a slightly modified command -julia_expr2 that does exactly what I want to do. I have the full control on what the function does at a pixel level:

julia_expr2 :
  1024,1024
  -fill "
    zr = -1.2 + 2.4*x/w;
    zi = -1.2 + 2.4*y/h;
    for (iter = 0, zr^2+zi^2<=4 && iter<256, ++iter,
      t = zr^2 - zi^2 + 0.4;
      (zi *= 2*zr) += 0.2;
      zr = t
    );
    zi"
  -normalize 0,255 -map 7

and this modified algorithm renders the image below (still in 0.7 second of course):

Fig.4. Slightly modified version of the Julia fractal by displaying another variable zi in the rendering algorithm.

Without these new loop features introduced in the math parser, I would have been forced to do one of these two things in G’MIC, to get the same result:

  1. Either, add some new options to the native command -mandelbrot to allow this new type of visualization. This basically means: Writing new pieces of C++ code, compiling a new version of G’MIC with these added features, package it and release it to make this available for everyone. Even if I already have some decent release scripts, this implies a lot of extra-work and packaging time. This is not like the user can get the new feature in a few minutes (if you’ve already used the filter update mechanism present in the G’MIC plug-in for GIMP, you know what I mean). And I don’t speak about all the possibilities I couldn’t think of (but the user will obviously need one day 🙂 ), when adding such new display options to a native command like -mandebrot
  2. Or, write a new G’MIC custom script able to compute the same kind of result. This would be indeed the best way to make it available for other people quickly. But here, as the algorithm is very specific and works at a pixel level, doing it as a pipeline of macro-operators is quite a pain. It means I would have to use 3 nested -repeat...-done loops (which are basically the loops commands used in G’MIC pipelines) and it would probably take ages to render, as a G’MIC pipeline is always purely interpreted without any pre-compilation steps. Even by using multi-threading, it would have been a nightmare to compute here.

In fact, the quite long math expression we are using in command -julia_expr2 defines one complex algorithm as a whole, and we know it will be pre-compiled into a sequence of bytecodes by CImg before being evaluated for each of the 1024×1024=1,048,576 pixels that compose the image. Of course, we are not as fast as a native C++ implementation of the same command, but at the same time, we gain so much flexibility and genericity in the stuffs we can do now, that this disadvantage is easily forgiven. And the processing time stays reasonable. For fast algorithm prototyping, this feature seems to be incredibly nice! I won’t be forced to unsheathe my C ++ compiler every time I want to experiment some very specific image processing algorithms working at the pixel level.

4. A more serious example: the “Non-Local Means”

The Non-Local-Means is a quite famous patch-based denoising/smoothing algorithm in image processing, introduced in 2005 by A. Buades (beware, his home page contains images of Lena, please do not click if you are too sensitive!). I won’t enter in all the implementation details, as several different methods has been proposed in the literature just for implementing it. But one of the most simple (and slowest) technique requires 4 nested loops per image pixel. What a good opportunity to try writing this “slow” algorithm using the G’MIC -fill function! It took me less than 10 minutes, to be honest:

nlmeans_expr : -check "${1=10}>0 && isint(${2=3}) && $2>0 && isint(${3=1}) && $3>0"
  -fill "
    const sigma = $1;  # Denoising strength.
    const hl = $2;     # Lookup half-size.
    const hp = $3;     # Patch half-size.
    value = 0;
    sum_weights = 0;
    for (q = -hl, q<=hl, ++q,
      for (p = -hl, p<=hl, ++p,
        diff = 0;
        for (s = -hp, s<=hp, ++s,
          for (r = -hp, r<=hp, ++r,
            diff += (i(x+p+r,y+q+s) - i(x+r,y+s))^2
          )
        );
        weight = exp(-diff/(2*sigma)^2);
        value += weight*i(x+p,y+q);
        sum_weights += weight
      )
    );
    value/(1e-5 + sum_weights)
  "

Now, let’s test it on a noisy version of the Leno image:

$ gmic user.gmic leno.png -noise 20 -c 0,255 -tic --nlmeans_expr 35,3,1 -toc
[gmic]-0./ Start G'MIC interpreter.
[gmic]-0./ Input custom command file 'user.gmic'(added 1 command, total 6195).
[gmic]-0./ Input file 'leno.png' at position 0 (1 image 512x512x1x3).
[gmic]-1./ Add gaussian noise to image [0], with standard deviation 20.
[gmic]-1./ Cut image [0] in range [0,255].
[gmic]-1./ Initialize timer.
[gmic]-1./nlmeans_expr/ Set local variable sigma='35'.
[gmic]-1./nlmeans_expr/ Set local variable hl='3'.
[gmic]-1./nlmeans_expr/ Set local variable hp='1'.
[gmic]-1./nlmeans_expr/ Fill image [0] with expression ' value=0; sum_weights=0; for(q = -3,q<(...)ight ) ); value/(1e-5 + sum_weights) '.
[gmic]-2./ Elapsed time : 3.156 s.

which results on these two images displayed on the screen, the noisy version (left), and the denoised one using the Non-Local-Means algorithm (right). Of course, the timing may differ from one machine to another. I guess my 3 seconds run here is seemly (tested on my powerful PC at the lab). It still takes less than 20 seconds on my laptop. A crop of the results are presented below. The initial Leno image is a 512×512 RGB image, and the timing has been measured for processing the whole image, of course.

gmic_leno3

Fig.5.1. Crop of a noisy version of the Leno image, degraded with gaussian noise, std=20.

gmic_leno4

Fig.5.2. Denoised version using the NL-means algorithm (custom command -nlmeans_expr).

Here again, you could argue that the native G’MIC command -denoise does the same thing and is faster to run. It is, definitely. Jérome Boulanger (one very active G’MIC contributor) has written a nice custom command -nlmeans that implements the NL-means with a smarter algorithm (avoiding the need for 4 nested loops per pixel) which runs even faster (and it is already available in the plug-in for GIMP). But that’s not the point. What I show here is I’m now able to do some (relatively fast) prototyping of algorithms working at a pixel level in G’MIC, without having to write and compile C++ code. But the best of all is about integration: if the algorithm appears to be interesting/effective enough, I can add it to the G’MIC standard library in a few minutes, and quickly create a filter for the GIMP plug-in as well. Let say it right away, probably 5 minutes after I’ve finished writing the first version of the algorithm, the plug-in users should be able to get it and use it on their own images (and give positive/negative feedback to help for future improvements). That’s what I call a smooth, quick and painless integration! And that is exactly the kind of algorithms I couldn’t implement before as custom G’MIC commands running at a decent speed.

To me, it clearly opens exciting perspectives to quickly prototype and integrate new custom image processing algorithms into G’MIC in the future!

5. The Vector Painting filter

In fact, this has happened earlier than expected. I’ve been able to add one of my latest image filter (named Vector painting) in the G’MIC plug-in for GIMP recently. It has been somehow unexpected, because I was just doing some debugging for improving the CImg math expression evaluator. Briefly, suppose you want to determine for each pixel of an image, the discrete spatial orientation of the maximal value variation, with an angular precision of 45°: For each pixel centered in a 3×3 neighborhood, I want to estimate which pixel of the neighborhood has the highest difference with the center pixel (measured as the squared difference between the two pixel values). To make things simpler, I’ve considered doing this on the image luminance only instead of using all the RGB color channels. At the end, I transform each pixel value into a label (an integer in range [1,8]) that represents one of the possible 45°-orientations of the plane. That was typically the kind of problems that would require the use of custom loops working at a pixel level, so something I couldn’t do easily before the loop feature introduced in my math parser (or I would have done the prototype in C++).

The solution to this problem was surprisingly easy to write. Here again, it didn’t take much more than 5 minutes of work:

foo :
  -luminance
  -fill "dmax = -1; nmax = 0;
         for (n = 0, ++n<=8,
           p = arg(n,-1,0,1,-1,1,-1,0,1);
           q = arg(n,-1,-1,-1,0,0,1,1,1);
           d = (j(p,q,0,0,0,1)-i)^2;
           if(d>dmax,dmax = d; nmax = n,nmax)
         )"

And if we apply this new custom command -foo on our Leno image,

$ gmic user.gmic leno.png -foo

We get this result (after re-normalization of the label image in range [0,255]). Keep in mind that each pixel of the resulting image is an integer label originally in range [1,8]. And by the way, the computation time is ridiculous here (178ms for this 512×512 image).

gmic_vp_000001

Fig.6. Each pixel of the Leno image is replaced by a label saying about which of its 3×3 neighbors is the most different from the central pixel.

It actually looks a bit ugly. But that’s not surprising, as the original image contains noise and you’ll get a lot of small random variations in flat regions. As a result, the labels you get in those regions are noisy as well. Now, what happens when we blur the image before computing the labels? That should regularize the resulting image of labels as well. Indeed:

$ gmic user.gmic leno.png --blur 1% -foo

returns this:

gmic_vpb_000001

Fig.7. Each pixel of the blurred Leno image is replaced by a label saying about which of its 3×3 neighbors is the most different.

That’s interesting! Blurring the input image creates larger portions of constant labels, i.e. regions where the orientation of the maximal pixel variations is the same. And the original image contours keep appearing as natural frontiers of these labelled regions. Then, a natural idea would be to replace each connected region by the average color it overlays in the original color image. In G’MIC, this can be done easily with the command -blend shapeaverage.

$ gmic user.gmic leno.png --blur 1% -foo[-1] -blend shapeaverage

And what we get at the end is a nice piecewise constant abstraction of our initial image. Looks like a “vector painting”, no ? 😉

gmic_vp_res

Fig.8. Result of the “shape average” blending between the original Leno image, and its map of labels, as obtained with command -foo.

As you may imagine, changing the amplitude of the blurring makes the result more or less abstract. Having this, It didn’t take too much time to create a filter that could be run directly from the G’MIC plug-in interface for GIMP. That’s the exact code I wrote to integrate my initial algorithm prototype in G’MIC and make it usable by everyone. It was done in less than 5 minutes, really:

#@gimp Vector painting : gimp_vector_painting, gimp_vector_painting_preview(1)
#@gimp : Details = float(9,0,10)
#@gimp : sep = separator(), Preview type = choice("Full","Forward horizontal","Forward vertical","Backward horizontal","Backward vertical","Duplicate horizontal","Duplicate vertical")
#@gimp : sep = separator(), note = note("<small>Author: <i>David Tschumperl&#233;</i>.\nLatest update: <i>08/25/2015</i>.</small>")
gimp_vector_painting :
  -repeat $! -l[$>]
    --luminance -b[-1] {10-$1}%,1,1
    -f[-1] "dmax = -1; nmax = 0;
            for (n = 0, ++n<=8,
              p = arg(n,-1,0,1,-1,1,-1,0,1);
              q = arg(n,-1,-1,-1,0,0,1,1,1);
              d = (j(p,q,0,0,0,1)-i)^2;
              if (d>dmax, dmax = d; nmax = n,nmax)
            )"
    -blend shapeaverage
  -endl -done

gimp_vector_painting_preview :
  -gimp_split_preview "-gimp_vector_painting $*",$-1

Here is the resulting filter, as it can be seen in the G’MIC plug-in for GIMP (requires version 1.6.5.2+). Just after I’ve pushed it in the G’MIC standard library:

gmic_gimp_vp

Fig.9. The G’MIC plug-in for GIMP, running the “Vector Painting” filter.

Here again, that is how I conceive things should be done properly: 1. I create a quick algorithm prototype to transform an image into something else. 2. I decide that the algorithm is cool enough to be shared. 3. I add few lines to make it available immediately in the G’MIC image processing framework. What a gain of time compared to the time it would have taken by doing this in C++!

6. Comparison with ImageMagick’s -fx operator

While working on the improvement of my math expression evaluator in CImg, I’ve been wondering if what I was doing was not already existing in ImageMagick. Indeed, ImageMagick is one of the most well established open-source image processing framework, and I was almost sure they had already cope with the kind of questions I had for G’MIC. And of course, they had 🙂

So, they have a special operator -fx expression in convert that seems to be equivalent to what the G’MIC command -fill expression does. And yes, they probably had it for years, long before G’MIC even existed. But I admit I’ve almost completely stopped using ImageMagick tools when I’ve started developing my own C++ image processing library CImg, years ago. All the information you need to use this -fx operator in convert can be found on this documentation page, and even more examples on this page. Reading these pages was very instructive: I’ve noticed some interesting functions and notations they have in their own expression parser that I didn’t already have in mine (so, I’ve added some of them in my latest version of CImg!). Also I was particularly interested by this quote from their pages:

As people developed new types of image operations, they usually prototype it using a slow “-fx” operator first. When they have it worked out that ‘method’ is then converted into a new fast built-in operator in the ImageMagick Core library. Users are welcome to contribute their own “-fx” expressions (or other defined functions) that they feel would be a useful addition to IM, but which are not yet covered by other image operators, if they can be handled by one of the above generalized operators, it should be reasonably easy to add it.(…). What is really needed at this time is a FX expression compiler, that will pre-interpret the expression into a tighter and faster executable form. Someone was going to look into this but has since disappeared.

So it seems their -fx operator is quite slow as it re-parses the specified math expression for each image pixel. And when someone writes an interesting operator with -fx, they are willing to convert it into a C code and integrate this new built-in operator directly in the core ImageMagick library. It seems they don’t really mind adding new native hard-coded operators into IM, maybe even for very specific/unusual operators (at least they don’t mention it). That’s interesting, because that is precisely what I’m trying to avoid in G’MIC. My impression is that it’s often acceptable to be less efficient if the code we have to write for adding one feature is smaller, easier to maintain/upgrade and does not require releasing a new version to make this particular feature available. Personally, I’d always prefer to write a G’MIC custom command (so, a script that I can directly put in the G’MIC standard library) if possible, instead of adding the same feature as a new “native” built-in command (in C++). But maybe their -fx operator was that slow it was cumbersome to use in practice? I had to try!

And I’m a bit sorry to say this, but yes, it’s quite slow (and I have tested this on my pretty fast machine with 12 HT cores at 2.6Ghz). The ImageMagick -fx operator is able to use multiple cores which is clearly a good thing, but even with that, it is cumbersome to use on reasonably big images, with complex math expressions. In a sense, that reassures me about the usefulness of having developed my own math expression compiler in CImg. This pre-compilation step of the math expression into a shorter bytecode sequence seems then to be almost mandatory. I’ve done a quick timing comparison for some simple image effects that can be achieved similarly with both expression evaluators of G’MIC and ImageMagick. Most of the examples below have been actually taken from the -fx documentation pages. I’m dividing and multiplying my image values by 255 in the G’MIC examples below because ImageMagick formulas assume that RGB values of the pixels are defined in range [0,1]. These tests have been done with a high-resolution input image (of a motorbike) with size 3072×2048, in RGB mode. I’ve checked that both the ImageMagick and G’MIC invokations render the same images.

#
# Test1: Apply a sigmoid contrast function on the image colors.
#

$ time convert motorbike.jpg -fx "(1.0/(1.0+exp(10.0*(0.5-u)))-0.006693)*1.0092503" im_sigmo.jpg

real	0m9.033s
user	3m18.527s
sys	0m2.604s

$ time gmic -verbose - motorbike.jpg -/ 255 -fill "(1.0/(1.0+exp(10.0*(0.5-i)))-0.006693)*1.0092503" -* 255 -o gmic_sigmo.jpg,75

real    0m0.474s
user    0m3.183s
sys     0m0.111s
#
# Test2: Create a radial gradient from scratch.
#
$ time convert -size 3072x2048 canvas: -fx "Xi=i-w/2; Yj=j-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" im_radial.jpg

real	0m29.895s
user	8m11.320s
sys	2m59.184s

$ time gmic -verbose - 3072,2048 -fill "Xi=x-w/2; Yj=y-h/2; 1.2*(0.5-hypot(Xi,Yj)/70.0)+0.5" -cut 0,1 -* 255 -o gmic_radial.jpg

real    0m0.234s
user    0m0.990s
sys     0m0.045s

#
# Test3: Create a keftales pattern gradient from scratch.
#
$ time convert -size 3072x2048 xc: -channel G -fx  'sin((i-w/2)*(j-h/2)/w)/2+.5' im_gradient.jpg

real	0m2.951s
user	1m2.310s
sys	0m0.853s

$ time gmic -verbose - 3072,2048 -fill "sin((x-w/2)*(y-h/2)/w)/2+.5" -* 255 -o gmic_gradient.jpg

real    0m0.302s
user    0m1.164s
sys     0m0.061s
#
# Test4: Compute mirrored image along the X-axis.
#
$ time convert motorbike.jpg -fx 'p{w-i-1,j}' im_mirror.jpg 2>&1

real	0m4.409s
user	1m33.702s
sys	0m1.254s

$ time gmic -verbose - motorbike.jpg -fill "i(w-x-1,y)" -o gmic_mirror.jpg

real    0m0.495s
user    0m1.367s
sys     0m0.106s

The pre-compilation of the math expressions clearly makes a difference!

I would be really interested to compare the expression evaluators for more complex expressions, as the one I’ve used to compute Julia fractals with G’MIC for instance. I don’t have a deep knowledge of the ImageMagick syntax, so I don’t know what would be the equivalent command line. If you have any idea on how to do that, please let me know! I’d be interested also to get an idea on how Matlab is performing for the same kind of equations.

7. Conclusion and perspectives

What I conclude from all of this ? Well, I’m actually pretty excited by what the latest version of my expression evaluator integrated in G’MIC / CImg can finally do. It looks like it runs at a decent speed, at least compared to the one used in ImageMagick (which is definitely a reference project for image processing). I had also the idea of comparing it with GraphicsMagick, but I must admit I didn’t find the same -fx operator in it. And I didn’t find something similar (Maybe you could help teaching me how it works for GraphicsMagick?).

I’ve been already able to propose one (simple) artistic filter that I find interesting (Vector painting), and I’m very confident that these improvements of the math expression evaluator will open a lot of new possibilities for G’MIC. For allowing the design of new filters for everyone of course, but also to make my algorithm prototyping work easier and faster.

Could it be the beginning of a new boost for G’MIC? What do you think?