Separable Distance Transformation and its Applications

Metric based description and analysis of shapes a fundamental notion in image analysis and processing. Among classical tools, the distance transform (DT) [54, 39] of a binary image I : Zd → {0,1} consists in labeling each point of a digital object E, defined as pixels with value 1 for instance on I, with its shortest distance to the complement of E. In the literature, DT has been widely used as a powerful tool in computer vision applications such as shape matching [21], pedestrian detection [27], human tracking [14], action recognition [34], robot motion planning [40, 72], or computation of morphological operators [20]. An other application of the DT is the computation of the medial axis (MA) of a digital shape [6, 44, 55], which is defined as the set of the centers of the largest balls contained in the treated object. MA is a very interesting shape representation because it is reversibility, i.e. one can reconstruct the original object from its MA balls. Again, MA can be found in the literature in various applications such as surface reconstruction [1], shape simplification [63], volume representation [10] or smoothing [49]. In the literature, many techniques have been proposed to compute the DT and then the MA given a metric with a trade-off between algorithmic performances and the accuracy of the metric compared to the Euclidean one. Hence, we can consider distances based on chamfer masks [54, 8, 51, 30] or sequences of chamfer distances [54, 45, 47, 61]; the vector displacement based Euclidean distance [23, 50, 46, 21]; the Voronoi diagram based Euclidean distance [9, 33, 35, 41] or the square of the