Adaptive Constructive Polynomial Fitting

To extract geometric primitives from edges, we use an incremental linear-time fitting algorithm, which is based on constructive polynomial fitting. In this work, we propose to determine the polynomial order by observing the regularity and the increase of the fitting cost. When using a fixed polynomial order under- or even overfitting could occur. Second, due to a fixed treshold on the fitting cost, arbitrary endpoints are detected for the segments, which are unsuitable as feature points. We propose to allow a variable segment thickness by detecting discontinuities and irregularities in the fitting cost. Our method is evaluated on the MPEG-7 core experiment CE-Shape-1 database part B [1]. In the experimental results, the edges are approximated closely by the polynomials of variable order. Furthermore, the polynomial segments have robust endpoints, which are suitable as feature points. When comparing adaptive constructive polynomial fitting (ACPF) to non-adaptive constructive polynomial fitting (NACPF), the average Hausdorff distance per segment decreases by 8.85% and the object recognition rate increases by 10.24%, while preserving simplicity and computational efficiency.