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Skeleton-geodesic Distances for Shape Recognition: Efficient Computation by Continuous Skeleton

We consider the problem of determining the distance between points of a planar shape, which would be informative and resistant to shape transformations, including flexible articulations. The proposed distance is defined as the length of the shortest path through the skeleton between the projections of the points on the skeleton and called skeleton-geodesic distance. To calculate the values of interest, a continuous medial representation of polygonal shape is used. The method of calculating the distance is based on the following principle: at first, calculate all skeleton-geodesic distances between pairs of “reference” points, which are the vertices of the skeleton, using the traditional graph algorithms; then refine them by adding the distances from the points in question to the nearest reference points. This approach allows us to achieve computational efficiency and to derive analytical formulas for direct calculation. An analogue of shape context using skeleton-geodesic distances and angles between branches of the skeleton is proposed. Examples of using these descriptors in the task of recognition of flexible objects are presented, showing that the distance proposed often provides greater performance compared to Euclidean or geodesic distances.