Modified ASLIC

[ailich]

In the original Achanta et al 2012 paper they state "simply defining D to be the five-dimenensional Euclidean distance in labxy space will cause inconsistencies in clustering behavior for different superpixel sizes... To combine the two distances into a single measure, it is necessary to normalize color proximity and spatial proximity by their respective maximum distances within a cluster." They then use step to normalize spatial distance since that is the expected maximum in a cluster, and state that compactness can be specified as a constant since "determining the maximum color distance is not so straightforward, as color distances can vary significantly from cluster to cluster and image to image." However, later they test a variant of SLIC called ASLIC that adaptively changes the compactness and maximum spatial distance parameter for each cluster. In this method, "instead of using constant values, ASLIC dynamically normalizes the proximities for each cluster using its maximum observed spatial and color distances (ms,mc) from the previous iteration." The equation in this case is

$$D= \sqrt{(\frac{d_c}{m_c})^2 + (\frac{d_s}{m_s})^2}$$

The method has the benefit of not needing to set compactness but it did have decreased performance relative to traditional SLIC. I suspect part of this decreased performance is because of the decreased flexibility since the spectral and spatial space are now always treated with equal weight since they will both range from approximately 0 to 1 (though if a larger maximum distance is found in the next iteration it can be larger than 1), and they found that SLIC had better performance when they reduced compactness below the default so playing with that weighting can improve results. My idea for a modification is that the user can specify a spectral weight parameter, w, which determines how much more you'd like to weight spectral vs spatial distance (or alternatively w could be spatial weight. Both should be essentially equivalent). That would make the equation

$$D= \sqrt{(\frac{d_c*w}{m_c})^2 + (\frac{d_s}{m_s})^2}$$

This would allow for intuitive testing of parameters compared to compactness in SLIC such as "I'd like to test the results when I weight spectral distance to be 10 times more important relative spatial distance."