MATLAB File Help: cv.integral Index
cv.integral

Calculates the integral of an image

s = cv.integral(src)
[s, sqsum, tilted] = cv.integral(src)
[...] = cv.integral(src, 'OptionName',optionValue, ...)


## Input

• src Source image as W x H, 8-bit, 16-bit or floating-point (single or double).

## Output

• s Integral image as (W+1) x (H+1), 32-bit integer or floating-point (single or double).
• sqsum Integral image for squared pixel values. It is (W+1) x (H+1), double-precision floating-point array.
• tilted Integral for the image rotated by 45 degrees. It is (W+1) x (H+1) array with the same data type as s.

## Options

• SDepth desired depth of the integral and the tilted integral images, int32, single, or double. default -1
• SQDepth desired depth of the integral image of squared pixel values, single or double. default -1

The functions calculate one or more integral images for the source image as follows:

 s(X,Y) = \sum_{x<X,y<Y} src(x,y)
sqsum(X,Y) = \sum_{x<X,y<Y} src(x,y)^2
tilted(X,Y) = \sum_{y<Y,abs(x-X+1)<=Y-y-1} src(x,y)


Using these integral images, you can calculate sum, mean, and standard deviation over a specific up-right or rotated rectangular region of the image in a constant time, for example:

 \sum_{x_1 <= x < x_2, y_1 <= y < y_2} src(x,y)
= s(x_2, y_2) - s(x_1, y_2) - s(x_2, y_1) + s(x_1, y_1)


It makes possible to do a fast blurring or fast block correlation with a variable window size, for example. In case of multi-channel images, sums for each channel are accumulated independently.