I dig deeper in internet to figure out what's the point of morphological processing on images, but i'd rather to hear the answer from people with experience, can you give me a hand with this? Thank you in advance
Answer
Many operations can be performed on images for enhancement and restoration. Sometimes, they seem mere handcraft and tinkering.
To make more sense of such workflows, and provide it with solid roots, it is useful to consider that images are classes of abstract objects, and operations as well-defined structural actions on the former. Depending on premises or assumptions on the image shape (is it binary, continuous-valued, what do we expect from filtering, what elements are meaningful, etc.), several constructions can be derived.
Standard linear filtering techniques in images assume that images are composed of linear superpositions of components. This yields convolution-based methods, and treating images as elements of a linear vector space (the underlying structure), with a strong "continuous" underlying theory. This can be related to Fourier or harmonic analysis, such a strong influence of least-squares method.
But image formation is often non-linear, for instance because of occlusion or saturation. So you have a collection of non-linear tools, with homomorphic, min, max or median filters for instance, or stack filters for bit-wise versions. Plus, they can be discretized in both values and space.
Mathematical morphology is another comprehensive framework, based on another underlying mathematical structure, lattices/set theory and related operations (erosion, dilation), with a strong discrete background (especially on image values).
Both have been proved recently connected in some ways, through the Cramer transform, see for instance An Explanation for the Logarithmic Connection between Linear and Morphological System Theory. Another interesting reading is 1989's Fourier analysis, mathematical morphology, and vision by C. Ronse.
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