Convolution

Updated 02 Oct 2026

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What it is
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  combines a function or signal with a shifted, reversed kernel using weighted sums
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Image formula
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  $(f*h)[m,n]=\sum_i\sum_jh[i,j]f[m-i,n-j]$ .
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Distinguish from correlation
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  correlation applies the kernel without the reversal used in convolution.
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  in two dimensions, converting a correlation kernel to the corresponding convolution kernel involves a $180^\circ$ rotation and appropriate anchor placement.
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  a kernel unchanged by that rotation gives the same result under matching conventions.
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Example
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  for the 1D neighborhood $1,2,3$ and kernel $1,0,-1$ , direct correlation gives $-2$ ; using the reversed kernel gives $2$
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Project clarification
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  apply_convolution calls cv2.filter2D.
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  its average, sharpening, and edge kernels are symmetric, so the naming does not change their numerical results. The distinction matters when adding asymmetric kernels.
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Reference
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  https://docs.opencv.org/5.0/main_modules/imgproc_filter.html

Linked references 3