MATLAB: Finding the means of a large number of individual matrices.

for loopimage processingmatrixmatrix arraymean

As part of an image processing task, I've split a 944×752 (grayscale) image into 11092 8×8 matrices. I've tried using the following for loop to calculate and individually store the means of each matrix:

start=0;
stop=11091;
for cell=start:1:stop
    m=mean2(['out_' int2str(cell)]);
    eval(['xbar_' int2str(cell) '=m'])  
end

This is coming up with results, but the numbers are completely incorrect, for example if I manually enter;

 k=mean2(out_3953)

Then k=148.3594, but if I call the result for the corresponding 8×8 block as produced by my for loop, the outcome is 81.375.

I'm new to Matlab and coding in general, so any help or advice would be greatly appreciated.

Best Answer

You've really have numbered variables all the way up to out_11091? Wow!

In this forum, we keep telling people not to use eval just to avoid this issue. As soon as you start numbering variables, you're doing it wrong. Very wrong if your numbers go all the way to 11091. Use an array of variable (cell array) or matrices of higher dimension to store all these related variables.

In your case:

%someimage: 2D matrix that can be divided evenly into 8x8 blocks
assert(all(mod(size(someimage), 8) == 0), 'image cannot be divided evenly into 8x8 blocks')
blocks = mat2cell(someimage, repmat(8, 1, size(someimage, 1)/8), repmat(8, 1, size(someimage, 2)/8)  %divide image into 8x8 blocks. Store blocks into cell array
xbar = zeros(size(blocks));  %predeclare for faster code
for ib = 1:numel(blocks)
   xbar(ib) = mean2(blocks{ib});
end

See how easy the loop is. You don't even need the loop if you use cellfun:

%no need to predeclare xbar since it's created by cellfun
xbar = cellfun(@mean2, blocks);

edit: or as Adam suggest instead of a cell array use a 3D matrix. Easily obtained from the blocks cell array

blocks3D = cat(3, blocks{:});

and the mean is then:

xbar = mean(mean(blocks3D, 1), 2);

The downside of this is you loose the shape of the block matrix. You could always reshape xbar afterward:

xbar = reshape(xbar, size(someimage)/8)

Related Solutions

MATLAB: Concatenate arrays within a loop,

Easy, given any number of arrays in a cell array C. You could use a loop like this, although it is inefficient because the output array is not preallocated:

C = {[1,2],[3,4],...} % cell array of arrays.
A = C{1};
for k = 2:numel(C)
    A = [A;C{k}];
end

Simpler and more efficient would be to concatenate them all at once, without a loop, e.g.:

A = vertcat(C{:})

Whatever you do, do NOT try to access variable names dynamically in a loop! Read this to know why:

https://www.mathworks.com/matlabcentral/answers/304528-tutorial-why-variables-should-not-be-named-dynamically-eval

Using an array (e.g. a cell array) and indexing is much simpler, neater, much more efficient, less buggy, and easier to debug.

MATLAB: Finding Mean for Blocks of Image

See this demo. It will be very easy for you to adapt it. Basically you do this:

meanFilterFunction = @(theBlockStructure) mean2(theBlockStructure.data(:)) * ones(2,2, class(theBlockStructure.data));
blockSize = [32 32];
blockyImage = blockproc(grayImage, blockSize, meanFilterFunction);

Here's the full demo:

% Demo code to divide the image up into 16 pixel by 16 pixel blocks
% and replace each pixel in the block by the median, mean, or standard
% deviation of all the gray levels of the pixels in the block.
%
clc;
clearvars;
close all;
workspace;
fontSize = 16;
% Read in a standard MATLAB gray scale demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
if ~exist(folder, 'dir')
  % If that folder does not exist, don't use a folder
  % and hope it can find the image on the search path.
  folder = [];
end
baseFileName = 'cameraman.tif';
fullFileName = fullfile(folder, baseFileName);
grayImage = imread(fullFileName);
% Get the dimensions of the image.  numberOfColorBands should be = 1.
[rows columns numberOfColorBands] = size(grayImage)
% Display the original gray scale image.
subplot(2, 2, 1);
imshow(grayImage, []);
title('Original Grayscale Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'Position', get(0,'Screensize')); 
set(gcf,'name','Image Analysis Demo','numbertitle','off') 
% Define the function that we will apply to each block.
% First in this demo we will take the median gray value in the block
% and create an equal size block where all pixels have the median value.
% Image will be the same size since we are using ones() and so for each block
% there will be a block of 8 by 8 output pixels.
medianFilterFunction = @(theBlockStructure) median(theBlockStructure.data(:)) * ones(size(theBlockStructure.data), class(theBlockStructure.data));
% Block process the image to replace every pixel in the 


% 8 pixel by 8 pixel block by the median of the pixels in the block.
blockSize = [8 8];
% Quirk: must cast grayImage to single or double for it to work with median().
% blockyImage8 = blockproc(grayImage, blockSize, medianFilterFunction); % Doesn't work.
blockyImage8 = blockproc(single(grayImage), blockSize, medianFilterFunction); % Works.
[rows columns] = size(blockyImage8);
% Display the block median image.
subplot(2, 2, 2);
imshow(blockyImage8, []);
caption = sprintf('Block Median Image\n32 blocks. Input block size = 8, output block size = 8\n%d rows by %d columns', rows, columns);
title(caption, 'FontSize', fontSize);
% Block process the image to replace every pixel in the 
% 4 pixel by 4 pixel block by the mean of the pixels in the block.
% The image is 256 pixels across which will give 256/4 = 64 blocks.
% Note that the size of the output block (2 by 2) does not need to be the size of the input block!
% Image will be the 128 x 128 since we are using ones(2, 2) and so for each of the 64 blocks across
% there will be a block of 2 by 2 output pixels, giving an output size of 64*2 = 128.
% We will still have 64 blocks across but each block will only be 2 output pixels across,
% even though we moved in steps of 4 pixels across the input image.
meanFilterFunction = @(theBlockStructure) mean2(theBlockStructure.data(:)) * ones(2,2, class(theBlockStructure.data));
blockSize = [4 4];
blockyImage64 = blockproc(grayImage, blockSize, meanFilterFunction);
[rows columns] = size(blockyImage64);
% Display the block mean image.
subplot(2, 2, 3);
imshow(blockyImage64, []);
caption = sprintf('Block Mean Image\n64 blocks. Input block size = 4, output block size = 2\n%d rows by %d columns', rows, columns);
title(caption, 'FontSize', fontSize);
% Block process the image to replace every pixel in the 
% 8 pixel by 8 pixel block by the standard deviation
% of the pixels in the block.
% Image will be smaller since we are not using ones() and so for each block
% there will be just one output pixel, not a block of 8 by 8 output pixels.
blockSize = [8 8];
StDevFilterFunction = @(theBlockStructure) std(double(theBlockStructure.data(:)));
blockyImageSD = blockproc(grayImage, blockSize, StDevFilterFunction);
[rows columns] = size(blockyImageSD);
% Display the block standard deviation filtered image.
subplot(2, 2, 4);
imshow(blockyImageSD, []);
title('Standard Deviation Filtered Image', 'FontSize', fontSize);
caption = sprintf('Block Standard Deviation Filtered Image\n32 blocks. Input block size = 8, output block size = 1\n%d rows by %d columns', rows, columns);
title(caption, 'FontSize', fontSize);

Best Answer

Related Solutions

MATLAB: Concatenate arrays within a loop,

MATLAB: Finding Mean for Blocks of Image

Related Question