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However there is a well known problem with the fixed window approach, which was discovered by the very first people using this approach.
In low texture areas, like this leaf here, window must be large enough to grab enough texture for disambiguation. At the same time, a window must contain pixels which are approximately of the same disparity, otherwise our window cost function does not make much sense, since it implicitly assumes that all pixels in a window are at approximately the same disparity. If the window overlaps disparity discontinuity, it will contain pixels which belong to quite different disparities, and will smooth out object boundary instead of preserving it. So for this thin leaf here window must be small. These 2 constraints are contradictory, and so most often there is no fixed window size which will work for the whole image. For example, this is an answer computed with a fixed small window. Notice that object boundaries are ok, but the results are noisy in areas of low texture. For a larger window size, the results are good in low texture areas, but all object boundaries are smoothed out.