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.