Why do we need to flip the kernel in 2D convolution?
When performing the convolution, you want the kernel to be flipped with respect to the axis along which you’re performing the convolution because if you don’t, you end up computing a correlation of a signal with itself.
Why do we flip convolution?
“when you flip, then the convolution with an impulse response function of a system gives you the response of that system. If you don’t flip, the response comes out backwards.” <- I can’t image the response coming out backwards as a result of this…
How is the kernel flipped in a convolution?
Another interesting property of convolution is that convolving a kernel with a unit impulse (e.g. a matrix with a single 1 at its center and 0 otherwise), you get the kernel itself as a result. Correlation would flip the kernel, instead.
What happens when you do not flip the kernel?
If you do not flip the kernel, you simply obtain a different operation that is called cross correlation. When the filter is symmetric, like a Gaussian, or a Laplacian, convolution and correlation coincides. But when the filter is not symmetric, like a derivative, you get different results.
How to do a 2D convolution in image processing?
The first overlap which would then occur is as shown in Figure 4a and by performing the MAC operation over them; we get the result as 25 × 0 + 50 × 1 = 50. Following this, we can slide the kernel in horizontal direction till there are no more values which overlap between the kernel and the image matrices.
How is convolution performed in the Digital Domain?
In the digital domain, convolution is performed by multiplying and accumulating the instantaneous values of the overlapping samples corresponding to two input signals, one of which is flipped. This definition of 1D convolution is applicable even for 2D convolution except that, in the latter case, one of the inputs is flipped twice.