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    %% Compute Integral Image of 3-D Input Image
% 
%%
% Create a 3-D input image.

% Copyright 2015 The MathWorks, Inc.

I = reshape(1:125,5,5,5);
%% 
% Define a 3-by-3-by-3 sub-volume as |[startRow, startCol, startPlane,
% endRow, endCol, endPlane]|.
[sR, sC, sP, eR, eC, eP] = deal(2, 2, 2, 4, 4, 4);
%%  
% Create an integral image from the input image and compute the sum over a
% 3-by-3-by-3 sub-volume of I.
J = integralImage3(I);
regionSum = J(eR+1,eC+1,eP+1) - J(eR+1,eC+1,sP) - J(eR+1,sC,eP+1) ...
        - J(sR,eC+1,eP+1) + J(sR,sC,eP+1) + J(sR,eC+1,sP) ... 
        + J(eR+1,sC,sP) -J(sR,sC,sP)
%%
% Verify that the sum of pixels is accurate.
sum(sum(sum(I(sR:eR, sC:eC, sP:eP))))