Matlab: Creating a binned RGB histogram

Question

I want to implement the following Matlab function:

function hist = binnedRgbHist(im, numChannelBins)

Given an image im and a number between 1 and 256 numChannelBins, it should create a histogram sized (numChannelBins)^3.

For example, if numChannelBins is 2, it should produce the following 8-sized histogram:

1. Number of pixels with R < 128, G < 128, B < 128
2. Number of pixels with R < 128, G < 128, B >= 128
3. Number of pixels with R < 128, G >= 128, B < 128
4. Number of pixels with R < 128, G >= 128, B >= 128
5. Number of pixels with R > 128, G < 128, B < 128
6. Number of pixels with R > 128, G < 128, B >= 128
7. Number of pixels with R > 128, G >= 128, B < 128
8. Number of pixels with R > 128, G >= 128, B >= 128

It is like creating a cube where each axis represents one of (R,G and B), where each axis is divided into 2 bins => Finally there are 8 bins in the cube.

My questions:

• It there a built-in function for it?
• If not, how is it better to implement it in manners of runtinme using the GPU? Should I better iterate over the pixels once and create the histogram manually, or should I better iterate over the bins and each time count the number of pixels which satisfy the bin's conditions?

Answer 1

accumarray is very suited for this. Let

• im: input image;
• N: number of bins per color component.

Then

result = accumarray(reshape(permute(ceil(im/255*N), [3 1 2]), 3, []).', 1, [N N N]);

How it works

1. ceil(im/255*N) quantizes each color vaue to 1, 2, ..., N.
2. reshape(permute(..., [3 1 2]), 3, []).' transforms the quantized image into a three-column matrix where each row is a pixel and each column is a (quantized) color component.
3. accumarray(..., 1, [N N N]) considers each row of that matrix as 3D index, and counts how many times each index appears, giving filling indices that don't appear with a 0.

Example 1

Data:

>> N = 2;
>> im = randi(256,4,5,3)
im(:,:,1) =
   113   152   157    65   229
   138    71   215    39    41
    13   108   230   160   153
   142   128   125   220   214
im(:,:,2) =
   208   215   182    27   230
   205   161     8    95   180
   225    53    73   129    31
   103    97   160    83   255
im(:,:,3) =
   242    29   185    89    55
   202   225   156   174    96
   160   197    35    87   113
   244   176   146    85   120

Result:

result(:,:,1) =
     1     1
     3     4
result(:,:,2) =
     2     4
     3     2

It can be checked for example that there is only 1 pixel with all R,G,B less than 128.

Example 2

Data:

>> im = repmat(150,20,30,3);
>> N = 4;

Result:

result(:,:,1) =
     0     0     0     0
     0     0     0     0
     0     0     0     0
     0     0     0     0
result(:,:,2) =
     0     0     0     0
     0     0     0     0
     0     0     0     0
     0     0     0     0
result(:,:,3) =
     0     0     0     0
     0     0     0     0
     0     0   600     0
     0     0     0     0
result(:,:,4) =
     0     0     0     0
     0     0     0     0
     0     0     0     0
     0     0     0     0

In this case all pixels belong to the same 3D-bin:

Answer 2

I see @Luis Mendo gave a great one-liner solution as I was writing this. In case it provides some deeper intuition, my solution makes use of histcounts and accumarray:

im             = randi([1 255],[10,5,3]);  %// A random 10-by-5 "image" 
numChannelBins = 2;

[~,~,binR]=histcounts(im(:,:,1),[1 ceil((1:numChannelBins)*(255/numChannelBins))]);
[~,~,binG]=histcounts(im(:,:,2),[1 ceil((1:numChannelBins)*(255/numChannelBins))]);
[~,~,binB]=histcounts(im(:,:,3),[1 ceil((1:numChannelBins)*(255/numChannelBins))]);
hist=accumarray([binR(:) binG(:) binB(:)],1,[numChannelBins,numChannelBins,numChannelBins])

Explanation:

• the three calls to histcounts bin the red, green, blue pixels separately -- the third output [~,~,binX] of histcounts gives the bin index for each pixel
• accumarray accumulates all the unique index triplets