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Calculate 3-D integral image



J = integralImage3(I) calculates the integral image, J, from grayscale volumetric image I.


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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

Input Arguments

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Grayscale volume, specified as a 3-D numeric array.

Data Types: single | double | int8 | int16 | int32 | uint8 | uint16 | uint32

Output Arguments

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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 double. The resulting size of the output integral image equals: size(J) = size(I) + 1. Such sizing facilitates easy computation of pixel sums along all image boundaries. The integral image, J, is essentially a padded version of the value cumsum(cumsum(cumsum(I),2),3).

Data Types: double

More About

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Integral Image

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.

Version History

Introduced in R2015b