Shape matching of partially occluded curves invariant under projective transformation

This paper describes a method to identify partially occluded shapes which are randomly oriented in 3D space. The goal is to match the object contour present in an image with an object in a database. The approach followed is the alignment method which has been described in detail in the literature. Using this approach the recognition process is divided into two stages: first, the transformation between the viewed object and the model object is determined, and second, the model that best matches the viewed object is found. In the first stage, invariant points under projective transformation (based on bitangency) are used, which drastically reduced the selection space for alignment. Next, the curves are compared after the transformation matrix is estimated between the image and the model in order to determine the pose of the curve that undergoes the perspective projection. The evaluation process is performed using a novel estimation of the Hausdorff distance (HD), called the continuity HD. It evaluates partially occluded curves in the image in relation to the complete contour in the database. The experimental results showed that the present algorithm can cope with noisy figures, projective transformations, and complex occlusions.