We consider the problem of learning an object model for feature matching. The matching system is Bayesian in nature with separate likelihood and prior parts. The likelihood is based on Gabor filter responses, which are modelled as probability distributions in the filter response vector space. The prior model for the object shape is learnt in two stages: in the first stage we assume only the mea...

The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely character...

The paper discusses how the set of shape primitives to be used for decomposing a shape into meaningful parts may affect the performance of the decomposition method, and proposes a new set of shape primitives to be used when the input shape is represented by its skeleton. The suggested shape primitives comhine the qualitative, general notion of shape needed to cope with the large variability of ...

There are many connected characters in cursive Uyghur handwriting, which makes the segmentation and recognition of Uyghur words very difficult. To enable large vocabulary Uyghur word recognition using character models, we propose a character separation method for over-segmentation in online cursive Uyghur handwriting. After removing delayed strokes from the handwritten words, potential breakpoi...

The features of a class of cubic curves with a shape factor are analyzed by means of the theory of envelope and topological mapping. The effects of the shape factor on the cubic curves are made clear. Necessary and sufficient conditions are derived for the curve to have one or two inflection points, a loop or a cusp, or to be locally or globally convex. Those conditions are completely character...

One of the challenging problems for shape editing is to adapt shapes with diversified structures for various editing needs. In this paper we introduce a shape editing approach that automatically adapts the structure of a shape being edited with respect to user inputs. Given a category of shapes, our approach first classifies them into groups based on the constituent parts. The group-sensitive p...

We propose a general method for finding pointwise correspondence between 2-D shapes based on the concept of order structure and using geometric hashing. The problem of finding correspondence and the problem of establishing shape equivalence can be considered as one and the same problem. Given shape equivalence, we can in general find pointwise correspondence and the existence of a unambiguous c...

In deformable model segmentation, the geometric training process plays a crucial role in providing shape statistical priors and appearance statistics that are used as likelihoods. Also, the geometric training process plays a crucial role in providing shape probability distributions in methods finding significant differences between classes. The quality of the training seriously affects the fina...

Shape description is one of the key parts of image content description for image retrieval. Most of existing shape descriptors are usually either application dependent or non-robust, making them undesirable for generic shape description. In this paper, a generic Fourier descriptor (GFD) is proposed to overcome the drawbacks of existing shape representation techniques. The proposed shape descrip...

Any closed, connected Riemannian manifold M can be smoothly embedded by its Laplacian eigenfunction maps into Rm for some m. We call the smallest such m the maximal embedding dimension of M. We show that the maximal embedding dimension of M is bounded from above by a constant depending only on the dimension of M, a lower bound for injectivity radius, a lower bound for Ricci curvature, and a vol...