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How do you give a class to each pixel in an image using a linear classifier in a way that uses the surrounding pixels as context/input? I'm genuinely curious! You are right about the data, it's expensive to make and startups based on satelite imagery tend to keep them as it's their main advantage.

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In a most cases, you can reshape to a 1xN^2 vector for a NxN region. This was how object detection worked long before convolutional inputs were popular.

Have a look at mnist classification using a linear SVM, for example.

Classification makes sense, because you do a linear (or kernel) combination of the input and squash it using sigmoid to get a probability of a class. For segmentation you output a pixel mask so you would have a NxNx3 vector to predict 1 class for 1 pixel and then you would have to do it for all pixels so you'd have to encode the position as well. Alternatively, if you take a unique weight for each position you end up with get single FC layer with NxNx3 inputs and NxN outputs (N^4 parameters). I guess for me it's hard to imagine doing segmentation "back then" and I find it very fascinating.

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