What is Convolution and Correlation in Image Processing?

Question

Image processing

I would like to understand what is the difference between these two concepts, on the fingers.

Answer 1

If we take one-dimensional signals, then the convolution is the element-wise product of the array (ie, the vector), and the correlation is the sum of this element-wise product (number. When normalized, this is the cosine of the angle between the vectors). In this case, it is necessary to follow the numbering (for convolution, the numbering of the signal and filter samples is opposite, and for the correlation of two signals, the numbering is unidirectional).
(more precisely, convolution is:
1) multiplication of polynomials
2) signal filtering, which is done through obtaining the spectrum, applying filter weights to transform the spectrum and inverse transform to obtain the filtered signal). )
For images, everything is applied to matrices.

Answer 2

Convolution and cross-correlation are essentially the same thing, only in one case the second signal is inverted (flipped), in the second it is not.

If the filter is symmetrical, then there is no difference.