In your case I'd suggest to look into "colour entropy", something that I extensively used in my previous research to measure colour differences between two pictures. 

Here's the a short intro to that: Colour entropy indicates how dispersedly/compactly distributed the colours of the individual selections are within the three-dimensional RGB colour space. Entropy is defined as the -∑ pi*log2(pi) , where pi is the probability of occurrence of a colour (i.e. counts for each colour divided by the total number of pixels in an image), and log2 is the logarithm in base 2. An image that contains just a single colour has the minimum entropy value of 0, whilst an image containing equal proportions of each of the 16’777’216 colours of the RGB colour space has the maximum entropy value of 24.

I quickly did this montage (attached picture) and you can see that there is difference in the (a) number of RGB colours of the original pictures (b) distribution of the RGB colours in 3D space and (c) in colour entropy between the two pictures. I would report the value of camouflage as the deltaEntropy, as this indicates the best how "different" the colours within pictures are. In your case the two pictures only differ by 0.1 - so a relatively tiny difference in colour distribution.. obviously running more comparisons between pictures would allow you to create an index for camouflage.

I programmed an ImageJ Macro that can do those entropy calculations for colour images (MatLab would only do Entropy for Grayscale pictures)- If you're interested, please send me a direct message and I can send you the code over with some further instructions.

Dear Ronny,

I don't know of any tool that could be used directly, but it sounds like an interesting problem and I can think of a couple of image analysis techniques that could be applied. Maybe I could lend you a hand if you could provide me with two or three sample images.

Cheers,

Fernando

I think image segmentation can be one approach. The poor the segmentation of the birds, the better the camouflage.

Hi Fernando,

I have now attached an example photo that is representative.

Best regards,

Ronny

Thank you Ronny, very illustrative. So you always have one picture of the background and one with the bird? There is a very simple technique which is used for motion detection in video called "background subtraction". It literally means: take video frame (n+1) and subtract frame (n) from it. If there is any difference, then there has been movement.

Doing this in open air is not very robust, since a simple breeze will make the grass blades sway, but it may help as a first approximation to the problem. If you are not a lot into programming you can use photoshop/gimp. In any of them, you can create two layers and put one image in each layer. Then "blend" them using the "difference" or "subtraction" modes (see attached link to see how this is done in gimp). The result should be a rather dark picture, assuming that the viewpoint hasn't changed much, with the lighter regions pointing out the differences between images. A simple eye-measure of the difference area might be a measure of camouflage.

Maybe applying a border detection filter before the blending might help for comparing patterns.

I can download the pictures and tinker a little bit with matlab. Wavelet and Fourier analysis may be used to have a more accurate and robust measure.

Would you be interested in developing a robust measure or just want to have a so-so assessment?

Hope that helps.

Cheers,

Fernando

http://docs.gimp.org/en/gimp-concepts-layer-modes.html

http://docs.gimp.org/2.6/en/plug-in-sobel.html

Second thought:

When playing with blend modes, maybe it would be wise to work in a different colour space than RGB, maybe grayscale or HSV/HSL.

Cheers,

Fernando

To Fernando. Yes, I have both photos with and without the bird (I've updated the origninal post). Good to hear that this could make it more easy.

The Photoshop/Gimp seems to be a good approach since I know both programs, although it would be nice to get a precise measure/value or index.

Regards,

Ronny

In your case I'd suggest to look into "colour entropy", something that I extensively used in my previous research to measure colour differences between two pictures. 

Here's the a short intro to that: Colour entropy indicates how dispersedly/compactly distributed the colours of the individual selections are within the three-dimensional RGB colour space. Entropy is defined as the -∑ pi*log2(pi) , where pi is the probability of occurrence of a colour (i.e. counts for each colour divided by the total number of pixels in an image), and log2 is the logarithm in base 2. An image that contains just a single colour has the minimum entropy value of 0, whilst an image containing equal proportions of each of the 16’777’216 colours of the RGB colour space has the maximum entropy value of 24.

I quickly did this montage (attached picture) and you can see that there is difference in the (a) number of RGB colours of the original pictures (b) distribution of the RGB colours in 3D space and (c) in colour entropy between the two pictures. I would report the value of camouflage as the deltaEntropy, as this indicates the best how "different" the colours within pictures are. In your case the two pictures only differ by 0.1 - so a relatively tiny difference in colour distribution.. obviously running more comparisons between pictures would allow you to create an index for camouflage.

I programmed an ImageJ Macro that can do those entropy calculations for colour images (MatLab would only do Entropy for Grayscale pictures)- If you're interested, please send me a direct message and I can send you the code over with some further instructions.

In addition to the suggested approaches given so far to measure camouflage, another approach is to search for and measure the presence of convex or concave structures under camouflage conditions.    The basic idea is to detect 3D objects having either convex or concave patches. 

This is the approach described in great detail in terms of camouflage detection in natures and in military installations in

A. Tankus, Y. Yeshurum, Convexity-based visual camouflage breaking:

https://www.cs.tau.ac.il/~hezy/papers/j27.pdf

Good camouflage is synonymous with "merging with the background", and visual attention is only drawn to regions where there is no background.  A model of visual attention that depends on the absence of background may be of interest - http://www.ee.ucl.ac.uk/~fstentif/attention.pdf

Interesting problem!

While I like the entropy suggestion by Michael, it has two major drawbacks:

- The smaller the bird (with respect to the picture size), the better it would be camouflaged.

- If the bird has the same color histogram as the background, it would be perfectly camouflaged, while the layout of the colors is very important. If the bird would have a light beak, dark rump and brownish wings, it clearly stands out. So, texture has to be taken in account.

@Michael and @Lambert,

In addition to entropy, colour and texture, the more challenging task will be to detect regular geometric stuctures masked by some form of camouflage.   Since colour and texture will be part of both the surface of a camouflaged object as well as the background, foreground and overlay objects (e.g., branches), you are more likely to detect some part of a camouflaged surface patch, since surface patches will have a geometric regularity that nature lacks.   For this reason, I am suggesting that detection of convex or concave objects be in included in the arsenal of tricks used in the detection process.   Do you agree?

Hi James!

You're saying that "surface patches will have a geometric regularity that nature lacks".

I'm not quite sure what you mean; the pictures with or without bird are both depicting nature. If you want to detect repeating patterns in the bird's plumage, that might well be bird-species specific... Except the eye and some small specks near the head, I don't see many convex patches.

Hi Lambert,

Yes, in terms of the image of the bird, there are not many convex patches.   But then if you consider military camouflage of objects such as rocket launchers, then the search for convex patches is more promising.   By its very nature, the surface of an bird with camouflage markings is very different from the surface of man-made objects.   

The camouflage of this bird is indeed much worse in a rocket launcher environment :-) !

I just want to show the beautiful background subtraction image. The bird appears in pastel colors. Grass that has moved in the wind, seems b&w. Even the eggs can be spotted: apparently not moved, but reflecting more sunlight in absence of the bird (the bird's own shadow?).

The pastel colors are 'medium' differences in R, G and B pixel-values (10 or so); these differences can be used for segmentation purposes.

It seems the bird is too colorful to be perfectly camouflaged.

Hi Lambert,

The example of the bird in your post is very interesting.   For that image, I suggest using either edge-detection on the colour channels and put the edges detected in each colour channel into a single composite image or use the watershed method using mathematical morphology.    A composite image constructed from colour channel edges is sometimes quite amazing.    The colour channel edges can be found using a standard edge detection methods such as Canny's method.    Then you can display each colour channel edges separately as well as in a composite image.    Are you using Matlab for your programming?

From your picture in the last post, you can see many convex sets (tiny rectangles) spanning the wing that is visible.

From my experience, birds seem to favour nesting places where the bird (its colour and geometry) blends in with surroundings. 

Do you have any other examples of bird images with camouflage?

Thank you for all the answers. I understand that task is more complex than I thought when posting the question, and that it requires Matlab or ImageJ programming skills. At the same time the tools have much more potential than I thought of, and I'm very grateful for the help here.

Due to suggested approaches and the discussion above I have got several new ideas and I hope to spend more time working with camouflage in birds. Learning using Matlab and ImageJ will be of priority the following month. 

I have attached two more picture pairs from my dataset.

Dear Lambert,

Have you tried working in HSV/HSL? I would bet that, for similar levels of brightness/luminance/call_it_what_you_like, difference in hue should be the most significant.

I will give it a try myself over the weekend. My feeling is that the spectrum of a Fourier transform, or maybe some wavelet one, over, say, the H values of an HSV image should not change much from the background image to the with-bird image if camouflage is good. If it is not good, there should be a significant salience in the spectrum.

I am very happy to see such an active discussion on this interesting subject, thank you all!

Cheers,

Fernando

Just for the beauty of it, I attached a subtraction image of the second photo-pair. Again pastel colors. One can see the beak of one of its young popping out!

The second image-pair is the easiest to segment. Not because that bird is the least camouflaged, but because the surroundings (e.g. the nest) hardly move.

The third photo-pair causes troubles: the nest is pushed down when the bird stands on it. In order to segment such images, I think deformable registration is needed, to get rid of back-ground changes.

James, I use proprietary image-processing software from the Netherlands Cancer Institute (partly written by myself) and Octave (comparable to Matlab, but free and open source). Because there are so many edges (also in the plumage), my gut-feeling is that edge-detection will not help a lot in order to segment the bird.

Good suggestion Fernando; I look forward to seeing your results!

I found this paper that may be relevant: http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0087310#pone.0087310-Alain1

They use Mean Square Error (MSE), Peak Signal Noise Ratio (PSNR), and Universal Image Quality Index (UIQI) individually as predictors for camouflage performance. 

In addition to what has already been observed (e.g., Fred Stentiford's incisive comments about visual attention and merging with the background that is part and parcel with natural camouflage), it may be of interest to consider achromatic and chromatic signals emanating from natural avian (relating to bird) camouflage.   For example, it helps to calibrate a camera's photon capture in terms of the short wave length, medium wave length and long wave length receptors of birds such as starlings or in terms of the SML, MWL and LWL receptors of hawks searching for dinner in the form cleverly camouflaged meals such as pheasants.    This is the approach in the study of camouflage in

M. Stevens, I.C. Cuthill, Disruptive coloration, crypsis and edge detection in early visual processing,  Proceedings of the Royal Society B Biological Sciences 273, 2006:

http://rspb.royalsocietypublishing.org/content/273/1598/2141.full.pdf

Yes, good point. The level of camouflage should be determined from the predator's point of view. I know some insects can see ultra-violet. Are raptors or foxes capable of seeing a different part of the spectrum than we (humans) can; can foxes even see color?

Good question, Lambert.

Understanding raptor vision can shed light on the evolution of anti-preditor behaviour (and appearance) in birds (see p. 2).   Apparently, raptors relied on head and eye movement to track prey.   See

C. O'Rourke, Eye of the hawk: Visual system properties of three species of diurnal raptors with different foraging ecologies, M.Sc.. Thesis, California State Univ. Long Beach, 2009:

http://media.proquest.com/media/pq/classic/doc/1906674541/fmt/ai/rep/SPDF?_s=xf8Hf2NRcp8f9Ap%2FVcynUIenxvk%3D

It is observed that red-tailed hawks have relatively small binocular areas and wide blind areas:

C.T. O'Rourke, M.I. Hall, T. Pitlik, E. Fernandez-Juricic, Hawk eyes I: Diurnal raptors differ in visual  fields and degree of eye movement, PLoS ONE 5(9), 2010:

http://estebanfj.bio.purdue.edu/papers/PLOS%20ONE%20hawk%20eyes%20I.pdf

Thanks for the ongoing discussion, I learn a lot. In my study area, the red fox (Vulpes vulpes) is a common predator on ground nesting birds. I assume that the vision of the red fox is similar to domestic dogs, i.e. “red-green color-blind”. 

So, not a Vulture but a Vulpes is the culprit!

Based on dog-vision, described here:

http://biecoll.ub.uni-bielefeld.de/volltexte/2007/52/pdf/ICVS2007-6.pdf

I wrote a matlab/octave program to convert 'human' color-pictures to 'dog' color-pictures.

The third bird, perceived by a dog/fox :

@Lambert

How will the first picture look like with the "dog colour vision"? That is a Great Snipe (Gallinago media) with its nest on the ground. 

You could try yourself: download 'octave', install and run it. On the command prompt,

enter:

I=imread('camouflage.jpg');

Id = Human2Dog(I);

imshow(Id)

It should show this (less reddish, more greenish) :

This one is more illustrative. Above human; below dog :

Hello again, Lambert!

Your program to allow us to see the world the way a dog sees is great.    You may want to consider refining your program to take into account the vision capabilities for different breeds of dogs.   Most breeds of dogs differ in retina capabilities.   For example, pugs have very strong areas centralis but lack what is known as visual streak (common to Afghans, retrievers and wolves).    In dogs with visual streak capability, the photoreceptors of the retina are more dense along a horizontal band spanning the middle of the eye.   Dogs with visual streak have panoramic and peripheral vision that is very high quality.   For more about this, see

A.  Horowitz, Inside of a dog, Scribner, 2009:

http://kysmykseka.net/kysmyk/Wizardry/Misc/Simon.and.Schuster-Inside.of.a.Dog.What.Dogs.See.Smell.and.Know.2009.RETAiL.EBook.pdf

Well, I only did a color mapping. I could interpolate pixels at the central horizontal streak area, but (because the already large image would become even larger) instead, I down-sampled (10x) the area outside a horizontal streak.

I wonder if the sole comparison of two images (one of which includes the animal and the other not) can lead to defining a truly versatile camouflage index.  Situations exist where the animal, without really hiding behind anything, is nonetheless able to literally disappear in its surrounding.

For example, the attached photo shows what seems to be a very well camouflaged bird hidden inside a hole in a tree. I do not have the background picture without the bird, but one can easily imagine that the hole in the tree is just some dark place without any special feature.

In this particular case, the process of subtraction will not be of much help as it will just restore the original image of the bird, regardless of the quality of its camouflage.

The process of subtraction is necessary in order to segment the animal. Once that is done one can compare it with the background. You are right that comparison with the background that was occluded is not the best idea IF the animal can only be seen from one direction. In such cases it's better to compare with the immediate surroundings.

Do you know of software that quantifies the similarity between two patterns/textures?

I don't know of any software that quantifies the similarity between two textures.  I was thinking more of a two-step program that would :

(1) perform an inpainting operation on the background image to remove the hole and to replace it with information collected from the surroundings (see the example of figure 4 in the linked paper);

(2) subtract the resulting inpainted image from the original image containing the bird.

However, I don't think this would work for any type of texture.

http://www.ijera.com/special_issue/Humming%20Bird_March_2014/Version%20%201/AH3944.pdf

A pity this thread became so quiet... I there any progress on how to calculate a fox-vision-camouflage-index?

In addition to fox-vision-camouflage-index, it would also be interesting know if it possible to do a vision index for Goshawk (Accipiter gentilis) too. Since Goshawks could be a potential predator too. I will start learning Matlab this autumn, and I hope i could implement this in my study of camouflage. 

Are the birds in the photographs lifted from their nests by the goshawk, or are they captured rather in flight?

It may vary among the species. I think those birds relying on extreme camouflage are taken by suprise on the ground. And that they being revealed when they move. 

Dear Lambert,

I agree with you that the question for this thread merits many more observations and discussion.   For example, Ronny Steen has made a good observation about those birds that are sometimes taken by surprise when they are on the ground.   That probably happens due to the need to search for food.   And, no matter how well camouflaged a bird is when it is not in motion, such a bird will reveal itself (for some eyes such as other birds or hawks) whenever it starts moving.    I am guessing that the reason this thread and many other threads have gone quiet is due to the holidays.