An application of Fourier descriptors and convex hull for shape analysis is presented. Convex hull is used for dividing a shape into small parts. Amplitude spectrum which is invariant to scaling, translation and choosing a starting point is obtained from the Fourier descriptors (see e.g [1-3]) and used for comparison. All calculations are performed with the author's software and some algorithms...

Statistical shape analysis can be done in a Riemannian framework by endowing the set of shapes with a Riemannian metric. Sobolev metrics of order two and higher on shape spaces of parametrized or unparametrized curves have several desirable properties not present in lower order metrics, but their discretization is still largely missing. In this paper, we present algorithms to numerically solve ...

In this paper a fully automated segmentation system for the femur in the knee in Magnetic Resonance Images and the brain in Single Photon Emission Computed Tomography images is presented. To do this several data sets were first segmented manually. The resulting structures were represented by unorganised point clouds. With level set methods surfaces were fitted to these point clouds. The iterate...

Geometric moment invariants (GMIs) have been widely used as basic tool in shape analysis and information retrieval. Their structure and characteristics determine efficiency and effectiveness. Two fundamental building blocks or generating functions (GFs) for invariants are discovered, which are dot product and vector product of point vectors in Euclidean space. The primitive invariants (PIs) can...

We present a novel method that uses shape skeletons, and associated quantities, for feature-preserving smoothing of shapes in digital images. We preserve, or smooth out, features based on a saliency measure that relates feature size to local object size, both computed using the shape’s skeleton. Low-saliency convex features (cusps) are smoothed out, and low-saliency concave features (dents) are...

In order to improve the effectiveness of shape based classification there is an ongoing interest in creating new shape descriptors or creating new measures for descriptors that are already defined and used in shape classification tasks. Convexity is one of the most widely used shape descriptors and also one of the most studied in the literature. There are already several defined convexity measu...

Shape analysis methods have in the past few years become very popular, both for theoretical exploration as well as from an application point of view. Originally developed for planar curves, these methods have been expanded to higher dimensional curves, surfaces, activities, character motions and many other objects. In this paper, we develop a framework for shape analysis of curves in Lie groups...

In shape analysis, the concept of shape spaces has always been vague, requiring a caseby-case approach for every new type of shape. In this paper, we give a general definition for an abstract space of shapes embedded in a given manifold M. This notion allows to unify the shape spaces studied so far in the literature under a single banner, and offers a rigorous framework for several possible new...

In this technical report we derive the analytic form of the Hessian matrix for shape matching energy. Shape matching (Fig. 1) is a useful technique for meshless deformation, which can be easily combined with multiple techniques in real-time dynamics (refer to [MHTG05, BMM15] for more details). Nevertheless, it has been rarely applied in scenarios where implicit (such as backward differentiation...

Effective static analyses must precisely approximate both heap structure and information about values. During the last decade, shape analysis has obtained great achievements in the field of heap abstraction. Similarly, numerical and other value abstractions have made tremendous progress, and they are effectively applied to the analysis of industrial software. In addition, several generic static...