An Efficient Representation for Computing Geodesics Between n-Dimensional Elastic Shapes

We propose an efficient representation for studying shapes of closed curves in R. This paper combines the strengths of two important ideas elastic shape metric and path-straightening methods and results in a very fast algorithm for finding geodesics in shape spaces. The elastic metric allows for optimal matching of features between the two curves while path-straightening ensures that the algorithm results in geodesic paths. For the novel representation proposed here, the elastic metric becomes the simple L metric, in contrast to the past usage where more complex forms were used. We present the step-by-step algorithms for computing geodesics and demonstrate them with 2-D as well as 3-D examples.