We present a modified distance measure for use with distance transforms of anti-aliased, area sampled grayscale images of arbitrary binary contours. The modified measure can be used in any vector-propagation Euclidean distance transform. Our test implementation in the traditional SSED8 algorithm shows a considerable improvement in accuracy and homogeneity of the distance field compared to a tra...

The high-quality simulation of the penumbra effect in real-time shadows is a challenging problem in shadow mapping. The existing shadow map filtering techniques are prone to aliasing and light leaking artifacts which decrease the shadow visual quality. In this paper, we aim to minimize both problems with the Euclidean distance transform shadow mapping. To reduce the perspective aliasing artifac...

The Gromov-Hausdorff distance (dGH) proves to be a useful measure between shapes. In order approximate dGH for X,Y⊂Rd, we look into its relationship with dH,iso, the infimum Hausdorff under Euclidean isometries. As already known dimension d≥2, dH,iso cannot bounded above by constant factor times dGH. For d=1, however, prove that dH,iso≤54dGH. We also show bound is tight. effect, X,Y⊂R at most n...

Over the past decade, Euclidean distance matrices, or EDMs, have been receiving increased attention for two main reasons. The first reason is that the many applications of EDMs, such as molecular conformation in bioinformatics, dimensionality reduction in machine learning and statistics, and especially the problem of wireless sensor network localization, have all become very active areas of res...