I. Introduction Rational spline is a commonly used spline function. In many cases the rational spline curves better approximating functions than the usual spline functions. It has been observed that many simple shapes including conic section and quadric surfaces can not be represented exactly by piecewise polynomials, whereas rational polynomials can exactly represent all conic sections and qua...

CATS – Clustering After Transformation and Smoothing – is a technique for nonparametrically estimating and clustering a large number of curves. Our motivating example is a genetic microarray experiment but the method is very general. The method includes: transformation and smoothing multiple curves, multiple nonparametric testing for trends, clustering curves with similar shape, and nonparametr...

This report surveys current literature related to statistical shape analysis. There are two paradigms: (1) Models that have no prior knowledge about the shape. They evolve boundary curves in time while maintaining predefined smoothness constraints. (2) Models that have prior knowledge about a fixed shape. They use this knowledge to find object boundaries using the covariance matrix and the aver...

This paper aims to figure out difference of our impressions on curves that are used in shape designs, and also contribute industrial designers by implementing a smart computer aided design (CAD) systems which have as same feelings on curves as human designer’s. The proposed K-Vector is a mathematical form of classifying such curves by designer’s impressions.

English summary Skeletons are shape descriptors that are of a lower dimensionality than the shape they describe. They are centered within the shape, capture the shape’s symmetry, and describe the topology and articulation of the shape in a compact manner. These qualities make skeletonization a desirable pre-processing step in a variety of applications ranging from shape segmentation and retriev...

Introduction: Automatic arterial input function (AIF) selection has an essential role in quantification of cerebral perfusion parameters. The purpose of this study is to develop an optimal automatic method for AIF determination in dynamic susceptibility contrast magnetic resonance imaging (DSC-MRI) of glioma brain tumors by using a new preprocessing method.Material and Methods: For this study, ...

Shape descriptors are used in many computer vision tasks. Convexity is one of the most widely used shape descriptors in practical applications and also one of the most studied in the literature. There are already several defined convexity measures. The most standard one comes from the comparison between a given shape and its convex hull, but there also other approaches. Independently of whether...

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the ...

B-spline curves and their rational generalizations (NURBS curves) play central role and are widely used in computer aided design today. A B-spline curve is uniquely defined by its degree, control points and knot values, while in terms of NURBS curves the weight vector has to be specified in addition. The modification of a curve is also an essential problem in CAD systems, hence numerous methods...

Shape analysis of curves and surfaces is a very important tool in many applications ranging from computer vision to bioinformatics and medical imaging. There are many difficulties when analyzing shapes of parameterized curves and surfaces. Firstly, it is important to develop representations and metrics such that the analysis is invariant to parameterization in addition to the standard transform...