Combination of Texture, Color and Shape Operators to Describe Image Content: A Survey

In many image processing and computer vision applications, the main aim is to describe image contents. So, different visual properties such as color, texture and shape are extracted to make aim. In this respect, texture information play important role in image description and visual pattern classification. Texture is referred to a specific local distribution of intensities that is repeated throughout the image. Since now different operations or descriptors have been proposed to analysis texture characteristics. In the multi object images specific texture operators usually doesn’t provide accurate results. So, in many cases, combination of texture operators are used to achieve more discriminant features. In this paper, some combination methods are survived to analysis effect of combinational texture features in image content description. Also, in the result part, different related methods are compared in terms of accuracy and computational complexity.

The Process and Operations of Shape Generation and Manipulation during the Architectural Designing Activity

This piece of work is concerned with how shapes are generated, explored and transformed during the architectural designing process. It postulates that the relations and connections between sketches, produced during the design activity, can be defined in terms of shape transformations and described according to a closed list of shape operators. These latters provide a formal description of the shape exploration process and allow a deep understanding of its logic. To achieve its goal, this study creates a model to describe the different shape transformations, performed by designers, during the sketching activity.

Geometry of isoparametric null hypersurfaces of Lorentzian manifolds

We define two types of null hypersurfaces as; isoparametric and quasi isoparametric null hypersurfaces of Lorentzian space forms, based on the two shape operators associated with a null hypersurface. We prove that; on any screen conformal isoparametric null hypersurface, the screen geodesics lie on circles in the ambient space. Furthermore, we prove that the screen distributions of isoparametric (or quasi-parametric) null hypersurfaces with at most two principal curvatures are generally Riemannian products. Several examples are also given to illustrate the main concepts.

The complete classification of a class of conformally flat Lorentzian hypersurfaces in ℝ14

A three-dimensional Lorentzian hypersurface [Formula: see text] is called conformally flat if its induced metric is conformal to the flat Lorentzian metric, this property is preserved under the conformal transformation of [Formula: see text]. In this paper, using the projective light-cone model, we give a complete classification of those ones whose shape operators have two distinct real eigenvalues and cannot be diagonalizable. These hypersurfaces are conformal equivalent to cones, cylinders, or rotational hypersurfaces generated by B-scrolls (over null Frenet curves) in three-dimensional Lorentzian space forms.

A Decomposition Theorem for Immersions of Product Manifolds

We introduce polar metrics on a product manifold, which have product and warped product metrics as special cases. We prove a de Rham-type theorem characterizing Riemannian manifolds that can be locally or globally decomposed as a product manifold endowed with a polar metric. For such a product manifold, our main result gives a complete description of all its isometric immersions into a space form whose second fundamental forms are adapted to its product structure in the sense that the tangent spaces to each factor are preserved by all shape operators. This is a far-reaching generalization of a basic decomposition theorem for isometric immersions of Riemannian products due to Moore as well as of its extension by Nölker to isometric immersions of warped products.

Null parallel p-equidistant b-scrolls

In this paper, null parallel p-equidistant B-scrolls are defined in 3-dimensional Minkowski space R_1^3 . We prove necessary and sufficient conditions for these B-scrolls to be equivalent of their Cartan frames. The relations between matrices of the shape operators and the algebraic invariants (Gauss, mean curvatures, principal curvatures) of these B-scrolls are shown. Besides we give the relations between second Gauss curvatures, mean curvatures and the distribution parameters of non-developable null parallel p-equidistant B-scrolls. Finally, an example is given related to the null parallel p-equidistant B-scrolls in R_1^3.

On timelike parallel pi-Equidistant ruled surfaces with a timelike base curve in the Minkowski 3-space R3 1

In this paper, timelike parallel pi-equidistant ruled surfaces with atimelike base curve are dened and the shape operators, shape tensor, the qth fundamental forms and the characteristic polynomials of the shape tensors of thesesurfaces are obtained. Then, some relations between them are found. Finally, anexample for the timelike parallel p2 equidistant ruled surfaces by a timelike basecurve in the Minkowski 3-space R31 is given.

Umbilical Submanifolds of Sn × R

We give a complete classification of umbilical submanifolds of arbitrary dimension and codimension of ×ℝ, extending the classification of umbilical surfaces in ×ℝ by Souam and Toubiana as well as the local description of umbilical hypersurfaces in × ℝ by Van der Veken and Vrancken. We prove that, besides small spheres in a slice, up to isometries of the ambient space they come in a two-parameter family of rotational submanifolds whose substantial codimension is either one or two and whose profile is a curve in a totally geodesic ×ℝ or ×ℝ, respectively, the former case arising in a one-parameter family. All of them are diffeomorphic to a sphere, except for a single element that is diffeomorphic to Euclidean space. We obtain explicit parametrizations of all such submanifolds. We also study more general classes of submanifolds of × R and ℍn × ℝ. In particular, we give a complete description of all submanifolds in those product spaces for which the tangent component of a unit vector field spanning the factor ℝ is an eigenvector of all shape operators. We show that surfaces with parallel mean curvature vector in ×ℝ and ℍn×ℝ having this property are rotational surfaces, and use this fact to improve some recent results by Alencar, do Carmo, and Tribuzy. We also obtain a Dajczer-type reduction of codimension theorem for submanifolds of × ℝ and ℍn × ℝ.