Efficient Methods for 3D-Matching Problems

Matching problems deal with the analysis of 3D objects by means of efficient and fast algorithms chosen correspondingly to the chosen mathematical representation of the objects. In industrial applications, the main focus on efficiently tackling the matching problem is cheap and fast data acquisition and real time evaluation of the 3D object poses. As an alternative to 3D scanners, one finds various techniques to acquire 2D normal maps of scenes instead of 3D data, like photometric stereo. But despite the comparatively easy single shot acquisition, the data processing is complex and many assumptions are needed for accurate depth estimation. For this reason, normal maps have previously been rarely used for pose estimation of 3D Objects. We propose an approach to use normal maps for pose estimation using fast spherical and rotational nonuniform Fourier transforms to evaluate correlation integrals. We also discuss uniform samplings on the sphere and the rotation group to achieve improved results. Using the estimated orientation, accurate, monocular translation estimation techniques are discussed to build a complete 6D pose estimation. If time allows, we will discuss a related application from computational structural biology. Here, detecting local extrema of a correlation can be used to reconcile available protein structure data from different sources like X-ray crystallography or cryo-electron microscopy resulting in a refined protein model that combines the finer resolution information in the former with the native-state information at lower resolution in the latter. The main focus in solving the matching problem here is to incorporate additional knowledge about the proteins to improve results and to allow flexible motions like shear and hinge bending.