Extraction of quadrics from noisy point-clouds using a sensor noise model

Fitting optimum quadrics on segmented noisy range-image is a challenging task. The algebraic least-squares fit usually considered in the literature is biased, although it is fast to compute. We extend our previous work in planar patch extraction using a detailed sensor noise model to the extraction of quadrics. First, the fast least-squares method is modified to detect degeneracy automatically and it is used to aid segmentation. The final segmented quadric patch is then refined using a numerical maximum likelihood approach which employs the sensor range error model. Experimental results for artificial data and two different 3D sensors are provided to show the feasibility of our approach.