Most of the natural textures are non-homogenous and stochastic by nature. In many cases these textures are also directional. In this paper we present a method for the retrieval of the non-homogenous directional textures. This method is directional histogram and it represents the directional distribution of the texture. The histogram can be formed using either directional filtering method or Hou...

Diierential operators have been widely used for multiscale geometric descriptions of images. The eecient computation of these diierential operators is always desirable. Moreover, it has not been clear whether such representations are invertible. For certain applications, it is usually required that such representations should be invertible so that one can facilitate the processing of informatio...

Transfinite mean value interpolation has recently emerged as a simple and robust way to interpolate a function f defined on the boundary of a planar domain. In this paper we study basic properties of the interpolant, including sufficient conditions on the boundary of the domain to guarantee interpolation when f is continuous. Then, by deriving the normal derivative of the interpolant and of a m...

We have constructed a sequence of solutions of the Helmholtz equation forming an orthogonal sequence on a given surface. Coefficients of these functions depend on an explicit algebraic formulae from the coefficient of the surface. Moreover, for exterior Helmholtz equation we have constructed an explicit normal derivative of the Dirichlet Green function. In the same way the Dirichlet-to-Neumann ...

S U M M A R Y Edge effects are distortions at the edge of a domain which are artifacts of the implicit assumptions of a numerical algorithm or of the limited span of data used to solve the problem (Sheriff, 1991, p. 96). During wavenumber domain filtering of potential-field data, (e.g., reduction to the pole, pseudogravity, and directional derivative, etc.), edge effect distortions are usually ...

and Applied Analysis 3 eigensurfaces for problem 1.1 holds if some unique continuation property is satisfied by the corresponding eigenfunctions. 2. Preliminaries Let H be a finite dimensional separable Hilbert space. We denote by ·, · and ‖ · ‖ the inner product and the norm of the space H, respectively. Let T : H → H be a compact operator. Lemma 2.1. All nonzero eigenvalues of the operator T ...

1: A new approach is presented for recovering shapes from noisy images. First, an edge-strength function, v, at every pixel is determined by implementing a segmentation functional. Then, the zero-crossings of the laplacian of the smoothed image are allowed to evolve under the influence of v. Each point on the zero-crossings moves in the direction of the normal with a velocity consisting of two ...

We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension we present a general construction for obtaining discrete spherical means of directional derivatives. The construction is based on using the Minkowski’s existence theorem ...

An approach is described which has the potential to unify edge preserving smoothing with segmentation based on differential edge detection at multiple scales. The analysis of n-D data is decomposed into independent 1-D problems. Smoothing in various directions along 1-D profiles through n-D data is driven by local structure separation, rather than by local contrast. Analytic expressions are obt...

In the Shape from Shading methods, an extended approach named Uni-directional Photometric Flow Fields is proposed in this paper. The reflectance property of the surface material is the uniform perfect diffuser, and the light source produces a uniform parallel beam and the illuminating direction is varied slightly only in the azimuth direction. The local surfacc orientation can be determined fro...