Abstract
In this paper, we present a new model to measure the contour point distortion for the B-spline-based shape coding, called accurate distortion measurement using analytical model (ADMAM). It models the distortion as the shortest distance of associate contour point from the approximating B-spline. Observing that this shortest path is perpendicular to the tangent vector of the approximating B-spline, we construct a parametric cubic equation by setting their dot product to be zero and address it by using Cartan's formula. The theoretical property and the experiments presented demonstrate that ADMAM can lead to the smallest bit-rate among all the distortion measurements that can guarantee the admissible distortion, when the operational rate-distortion optimal shape coding framework is applied. Moreover, if the original contour has NC points, it takes only O(NC) time for both a peak and mean-squared segment distortion measuring paradigms, which is the lowest complexity among all the existing distortion measurements.
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