A simple question about convolution over volume .
Say we have an image with dimensions $(n, n, 3)$ and we apply a filter of dimension $(k, k, 3)$ this outputs an matrix of dimension $(n-k+1, n-k+1)$.
Why do we sum across channels in this case. Don't we lose information by mixing different channels. In case of images, this implies mixing information in
R, G, B channels? For ex. when trying to detect traffic signal lights, such mixing can be fatal.