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Hey! I is the flattened image (i.e., a matrix where each row represents the RGB values of a single pixel) T and N are some matrices, basically of appropriate
by andersource 5y ago
Hey!
I is the flattened image (i.e., a matrix where each row represents the RGB values of a single pixel)
T and N are some matrices, basically of appropriate dimensions such that the transformation you quoted results in an image of the same shape as the original and also such that we can optimize certain objectives with respect to the variables that define the transformation.
The why this is the desired transformation is a tricky question, it's definitely not the only and quite probably not the best way to formulate this problem - just the first way that I tried and worked reasonably well. I tried to explain my intuition for this in the article after the definition.
- adampk 5y agoReally appreciate the response thank you, great article! So is "T" and "N" conventionally used in numerical optimization as the transform "variables" (like X and Y are in calculus)?
- andersource 5y agoGladly! > So is "T" and "N" conventionally used in numerical optimization as the transform "variables" (like X and Y are in calculus)? Not really, numerical optimization offers a general toolbox for various problems, which are usually defined based on domain-specific notation and concepts. So the concept of a transformation like the one described in the article is not general to numerical optimization, but specific to the optimization being done here. That being said, when talking about techniques, theorems and algorithms in numeric optimization there are conventions. So you usually move between the more theory-oriented notation to a domain-specific notation (in the article I mostly used the domain-specific, lazy notation I chose). Bear in mind that my perspective is not very academic so I might feel less strongly about (and be less aware of) rigorous mathematical conventions.