In this chapter, a new rotation-invariant generalization of the analytic signal will be presented to analyze intrinsic 1D and 2D local image structures. By combining differential geometry and Clifford analysis, the monogenic curvature tensor can be derived to perform a split of identity and to enable simultaneous estimation of local amplitude, phase, main orientation and angle of intersection i...

Tensor voting (TV) methods have been developed in a series of papers by Medioni and coworkers during the last years. The method has been proved efficient for feature extraction and grouping and has been applied successfully in a diversity of applications such as contour and surface inferences, motion analysis, etc. We present here two studies on improvements of the method. The first one consist...

This paper addresses a gap in the arsenal of curvature continuous tensor-product spline constructions: an algorithm is provided to fill n-sided holes in C bi-3 spline surfaces using n patches of degree bi-6. Numerous experiments illustrate good highlight line and curvature distribution on the resulting surfaces.

Interactive visualization is a very convenient tool to explore complex scientific data or to try different parameter settings for a given processing algorithm. In this article, we present a tool to efficiently analyze the curvature tensor on the boundary of potentially large and dynamic digital objects (mean and Gaussian curvatures, principal curvatures, principal directions and normal vector f...

Nonlinear dynamical systems can be uniquely investigated by a geometric theory (KCC-theory). The five KCC-invariants express intrinsic properties of the nonlinear dynamical systems. The second invariant as a curvature tensor determines the stability of the systems. The third invariant as a torsion tensor expresses the chaotic behavior. As an example, the KCC-theory is applied to a geodynamical ...

Abstract. On the basis of the second gradient operator defined on curved surfaces, the second category of integral theorems for tensor fields, including the second divergence theorems, the second gradient theorems, the second curl theorems and the second circulation theorems, are systematically demonstrated. Simple conservation laws about the mean curvature and Gauss curvature are deduced from ...

Some properties of the star product of the Weyl type (i.e. associated with the Weyl ordering) are proved. Fedosov construction of the ∗−product on a 2– dimensional phase space with a constant curvature tensor is presented. Eigenvalue equations for momentum p and position q on a 2-dimensional phase space with constant curvature tensors are solved. PACS numbers: 03.65.Ca

In this paper, we study half-lightlike submanifolds of a semi-Riemannian manifold such that the shape operator of screen distribution is conformal to the shape operator of screen transversal distribution. We mainly obtain some results concerning the induced Ricci curvature tensor and the null sectional curvature of screen transversal conformal half-lightlike submanifolds. 2010 Mathematics Subje...

We establish new conditions ensuring that a Riemannian metric may be constructed, up to a conformal factor, from the skewsymmetries of its Riemann curvature tensor.

In the present paper we studied the properties of them−projective curvature tensor in LP-Sasakian, Einstein LP-Sasakian and η−Einstein LPSasakian manifolds.