Calculate 3-D integral image
Create a 3-D input image.
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)
regionSum = 1701
Verify that the sum of pixels is accurate.
sum(sum(sum(I(sR:eR, sC:eC, sP:eP))))
ans = 1701
I— Grayscale volume
Grayscale volume, specified as a 3-D numeric array.
J— Integral image
Integral image, returned as a numeric array. The function zero-pads the top, left and along
the first plane, resulting in
size(J) = size(I) + 1. side
of the integral image. The class of the output is
The resulting size of the output integral image equals:
size(I) + 1. Such sizing facilitates easy computation of pixel
sums along all image boundaries. The integral image,
is essentially a padded version of the value
In an integral image, every pixel is the summation of the pixels above and to the left of it. Using an integral image, you can rapidly calculate summations over image subregions. Use of integral images was popularized by the Viola-Jones algorithm. Integral images facilitate summation of pixels and can be performed in constant time, regardless of the neighborhood size.