Piecewise Linear Skeletonization Using Principal Curves

We propose an algorithm to find piecewise linear skeletons of hand-written characters by using principal curves. The development of the method was inspired by the apparent similarity between the definition of principal curves (smooth curves which pass through the “middle” of a cloud of points) and the medial axis (smooth curves that go equidistantly from the contours of a character image). The central fitting-and-smoothing step of the algorithm is an extension of the polygonal line algorithm [1, 2] which approximates principal curves of data sets by piecewise linear curves. The polygonal line algorithm is extended to find principal graphs and complemented with two steps specific to the task of skeletonization: an initialization method to capture the approximate topology of the character, and a collection of restructuring operations to improve the structural quality of the skeleton produced by the initialization method. An advantage of our approach over existing methods is that we optimize the skeleton graph by minimizing an intuitive and explicit objective function that captures the two competing criteria of smoothing the skeleton and fitting it closely to the pixels of the character image. We tested the algorithm on isolated hand-written digits and images of continuous handwriting. The results indicate that the proposed algorithm finds a smooth medial axis of the great majority of a wide variety of character templates, and substantially improves the pixelwise skeleton obtained by traditional thinning methods.