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Fitting sphere to quantized depth information

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
Bence Molnár
Revision date


This notebook presents different techniques to estimate radius and position of a sphere in case of quantized depth information obtained from low resolution sensors like Microsoft Kinect XBOX. First algebraic, geometric and directional least squares estimations were applied to the quantized data directly. Then two techniques Self-Organizing Map (SOM) and RANdom SAmple Consensus (RANSAC) were employed as preprocessing methods to smooth and reduce quantized data. To solve the resulted nonlinear algebraic systems Gröbner basis with Gauss-Jacobi method as global method as well as Newton method with pseudoinverse and direct minimization as local methods applying the result of the algebraic method as initial guess have been used. In order to decrease the computation time parallel computation on multi-core machine could be utilized . According to this case study all of these methods can be accepted from engineering point of view, although the geometrical approach with initial condition based on the solution of the algebraic method was proved to be the most effective.

*Wolfram Technology > Image Processing

low resolution sensors, quantized data, sphere fitting, SOM, Gröbner basis, Gauss Jacobi, RANSAC
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Kinect.nb (727.5 KB) - Mathematica Notebook
f_03_05.dat (55.5 KB) - Unknown MIME type