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...

Shape comparisons of two groups of objects often have two goals: to create a classifier to separate the groups and to provide information that shows differences between classes. We examine issues that are important for shape analysis in a study comparing schizophrenic patients to normal subjects. For this study, non-linear classifiers provide large accuracy gains over linear ones. Using volume ...

We treat the problem of chromosome segmentation with the aid of shape analysis and classification. Our approach consists of a combination of two phases, a purely rule–based phase and a phase driven by constrained discriminant analysis. In the first phase, obvious prototypical shape elements related to touchings and overlaps are recursively identified, in the second, remaining complex and ambigu...

This paper presents an innovative tool and method that allow efficient innovation of shape and topology of virtual parts at both mesh and CAD levels using optimization methods. The method consists of automatic variations of shapes in CAD/CAE environments that allow effective search for new shapes that are not considered initially by designers.

Shape analysis aims at determining invariants of heapallocated structures that arise during the execution of a program. Current shape analysis techniques are stateless, i.e. they only model the structures arising on the heap and completely ignore their memory locations and where they were allocated. This paper proposes an extended, allocation-site aware shape analysis and briefly sketches field...

We describe Thor (Tool for Heap-Oriented Reasoning), a tool based on separation logic that is capable of reasoning automatically about heap-manipulating programs. There are several such systems in development now. However, Thor is unique in that it provides not only shape analysis, but also arithmetic reasoning via a novel combination procedure. Also, considerable effort has been put into makin...

We present a geometric approach to statistical shape analysis of closed curves in images. The basic idea is to specify a space of closed curves satisfying given constraints, and exploit the differential geometry of this space to solve optimization and inference problems. We demonstrate this approach by: (i) defining and computing statistics of observed shapes, (ii) defining and learning a param...

Shape is one of the most important properties of objects. This lecture summarizes the algorithms for shape analysis. Several commonly used simple descriptors are stated first. Then the algorithms are classified into boundary (or external) descriptors and regional (or internal) descriptors based on the boundary tracking only and boundary plus the interior tracking respectively. The characteristi...

We present a new framework for multidimensional shape analysis. The proposed framework represents solid objects as points on an infinite-dimensional Riemannian manifold and distances between objects as minimal length geodesic paths. Intershape distance forms the foundation for shape-based statistical analysis. The proposed method incorporates a metric that naturally prevents self-intersections ...

In this paper, I will describe a computer vision-based musical performance system that uses morphological assessments to provide control data. Using shape analysis allows the system to provide qualitative descriptors of the scene being captured while ensuring its use in a wide variety of different settings. This system was implemented under Max/MSP/Jitter, augmented with a number of external ob...