Robust Fitting of Implicit Polynomials with Quantized Coefficients to 2D Data

This work presents a new approach to contour representation and coding. It consists of an improved fitting of high-degree (4 to 18) implicit polynomials (IPs) to the contour, which is robust to coefficient quantization. The proposed approach to solve the fitting problem is a modification of the 3L linear solution developed by Lei et al and is more robust to noise and to coefficient quantization. We use an analytic approach to limit the maximal fitting error between each data point and the zero-set generated by the quantized polynomial coefficients. We than show that consideration of the quntization error (which led to a specific sensitivity criterion) also brought about a significant improvement in fitting IPs to noisy data, as compared to the 3L algorithm.