Unsupervised segmentation and approximation of digital curves with rate-distortion curve modeling

•A new algorithm for unsupervised segmentation of digital curves is introduced.•This method gives solutions with the best balance between error and description length.•A multiplicative criterion for evaluation of solutions is introduced.

This paper considers the problem of unsupervised segmentation and approximation of digital curves and trajectories with a set of geometrical primitives (model functions). An algorithm is proposed based on a parameterized model of the Rate–Distortion curve. The multiplicative cost function is then derived from the model. By analyzing the minimum of the cost function, a solution is defined that produces the best possible balance between the number of segments and the approximation error. The proposed algorithm was tested for polygonal approximation and multi-model approximation (circular arcs and line segments for digital curves, and polynomials for trajectory). The algorithm demonstrated its efficiency in comparisons with known methods with a heuristic cost function. The proposed method can additionally be used for segmentation and approximation of signals and time series.