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Linear Algorithm for Digital Euclidean Connected Skeleton

The skeleton is an essential shape characteristic providing a compact representation of the studied shape. Its computation on the image grid raises many issues. Due to the effects of discretization, the required properties of the skeleton - thinness, homotopy to the shape, reversibility, connectivity - may become incompatible. However, as regards practical use, the choice of a specific skeletonization algorithm depends on the application. This allows to classify the desired properties by order of importance, and tend towards the most critical ones. Our goal is to make a skeleton dedicated to shape matching for recognition. So, the discrete skeleton has to be thin - so that it can be represented by a graph -, robust to noise, reversible - so that the initial shape can be fully reconstructed - and homotopic to the shape. We propose a linear-time skeletonization algorithm based on the squared Euclidean distance map from which we extract the maximal balls and ridges. After a thinning and pruning process, we obtain the skeleton. The proposed method is finally compared to fairly recent methods.