Viewpoint independent matching of planar curves in 3D space

Abstract

We present a new approach to match planar curves using the weak perspective projection model. This is based on a set of shape parameters that can be extracted from a closed or open contour, derived from the original image as a θ( s) boundary code. In order to reduce the complexity and increase the robustness of the matching process, the original parameters are reduced to a set of three intermediate variables, each of which can be calculated independently. These variables are contained within a system of linear equations which define the angles and the ratio of the heights of corresponding point pairs on the two contours with respect to a floating coordinate system. The shape matching process is scale and orientation independent, and the original parameters that describe the relative pose of the two contours in 3D space can be recovered subsequently. The approach can be applied to “featured” and “featureless” contours, to whole and partial contours, and is demonstrated on images of contours and mechanical parts and tools to recover identity and pose.