Optimized Canonical Coordinate Frames for 3D Object Normalization

Abstract

In this paper, we describe a method to optimize an orthogonal system of axes for 3D objects in order to perform normalization with respect to orientation and scale. An energy function evaluates the quality of a system by considering symmetry, rectilinearity and the origin of the system within the current axis aligned bounding box. Starting with the PCA-axes as initial system, we find a canonical coordinate frame by minimizing the energy in an efficient and elaborate optimization process. We provide a fully automatic normalization pipeline with the possibility to manually set various intuitive parameters in order to influence the outcome. The symmetry part of our energy function uses a combination of plane reflective and rotational symmetries. In this context, we introduce a novel continuous symmetry measure which is entirely implemented on the GPU. The high efficiency of the implementation enables us to find an optimal alignment for 3D objects interactively, making our method suitable even for large 3D databases. We also demonstrate the applicability of our framework for 3D shape matching by approximating the Hausdorff distance for 3D models.