RECOGNITION OF THREE-DIMENSIONAL OBJECTS BY RENDERING FUNCTION MATCHING (COMPUTER VISION, NONLINEAR OPTIMIZATION, GRAPHICS)

ATTE JUHANI KORTEKANGAS, Purdue University

Abstract

Machine recognition of rigid objects is studied, based on fitting a synthesis result (rendering function) with observed image in the signal domain. The approach is demonstrated with a number of test cases. The matching problem is expressed as minimization of global least-squares geometric and photometric deviation of pixel-wise correspondence estimates. The rendering function is built from previously recorded gray-scale images framed for (nearly) planar regions. Linear transformations map the geometric face grid coordinates to a 3-D pseudo space whose pinhole projection corresponds to arbitrary rotation and translation of the target component, relaxing the need for explicit knowledge of range information. Further constraints are set (for planar faces) by node point pairs, and a rigid 3-d reference grid to be rotated and translated. The constraints make penalty terms of the global quadratic objective. A three-phase coordinate descent approach was developed for local minimization. The phases are (1) a discrete correspondence estimate mapping, (2) a linear least-squares optimizer, and (3) a non-linear least-squares rotation and translation optimizer. A fast and analytically simple iterative scheme was developed for optimizing step 3, shown to be globally convergent to a global optimum, achieving superlinear convergence rate near the optimum for problems with exact solution (the ideal with correct positive identification of accurately modeled targets). The theoretical motivation for a locally optimal solution strategy is based on the properties of a 3-D least-squares rotation and translation optimization problem, and a 2-D least-squares projection fitting problem considered. The latter problem extends to the former one by using several images simultaneously or by using range data. The pure 2-D problem needs a limited number of alternative branches to be tested to be solved exactly by local optimization. A number of experiments are reported to demonstrate the feasibility of the approach for discrimination between object candidates, coarse orientation choices for a single object and identification of local perturbation parameters between the states of the reference and observation. Algorithms are discussed for parallel computation of correspondence estimates, the most computation intensive subproblem.

Degree

Ph.D.

Subject Area

Computer science

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