There are a number of filters in different orientations at different positions etc.. so what do the weights in convolutional neural networks really represent? I'm more interested in the signal processing side of the question than "the proof by images" that is presented too often. Here my "own answer" comes from, Stéphane Mallat that gave a VERY good explanation.
An interesting recent article which may be relevant to your question:
http://www.evolvingai.org/fooling
This is just a small part of image processing when I say Blind "deconvolution", that is when 2 things are known say system transfer function and output then you find the input that gives you the response or vice-versa (in the z-transform) . Filtering with coefficients takes closer to the region of interest (say for classification...) also the characteristics in terms contrast .
An interesting recent article which may be relevant to your question:
http://www.evolvingai.org/fooling
Still SOM and combination of SVC and MLP works for digital time series
I think if you read the HMAX model, you may find more about your question. HMAX represents a bio-inspired model for vision.
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