In the task of forming high-level object-centered models from low-level image-based features, parts serve as an intermediate representation. A representation of parts for object recognition should be rich, stable, and invariant to changes in the viewing conditions. In addition, it should be capable of describing partially occluded shapes. This paper describes a method for decomposing shapes into parts. The method is based on pairs of negative curvature minima which have a good continuation at their boundary tangents. A measure of good continuation is proposed by using the coefficients of cocircularity, smoothness, and proximity. This method could recover parts in a direct computation, therefore efficient in calculation than the former. Currently, we assume that the shape is a closed planar curve.

A novel approach was proposed to recognize the non-rigid 3D objects from their corresponding 2D images by combining the benefits of the principal component analysis and the geometric hashing. For all of the object models to be recognized, we calculated the statistical point features of the training shapes using principal component analysis. The results of the analysis were a vector of eigenvalues and a matrix of eigenvectors. We calculated invariants of the new shapes that undergone a similarity transformation. Then added these invariants and the label of the model to the model database. To recognize objects, we calculated the necessary invariants from an unknown image and used them as the indexing keys to retrieve any possible matches with the model features from the model database. We hypothesized the existence of an instance of the model in the scene if the model's features scored enough hits on the vote count. This approach allowed us to store the rigid and the non-rigid object models in a model database and utilized them to recognize an instance of model from an unknown image.