‎this contribution mainly focuses on some aspects of lipschitz groups‎, ‎i.e.‎, ‎metrizable groups with lipschitz multiplication and inversion map‎. ‎in the main result it is proved that metric groups‎, ‎with a translation-invariant metric‎, ‎may be characterized as particular group objects in the category of metric spaces and lipschitz maps‎. ‎moreover‎, ‎up to an adjustment of the metric‎, ‎a...

a module is said to be $pi$-extending provided that every projection invariant submodule is essential in a direct summand of the module. in this paper, we focus on direct summands and indecomposable decompositions of $pi$-extending modules. to this end, we provide several counter examples including the tangent bundles of complex spheres of dimensions bigger than or equal to 5 and certain hyper ...

The extremal and partly marginally trapped surfaces in Minkowski 4-space, which are invariant under the group of boost isometries, are classified. Moreover, it is shown that there do not exist extremal surfaces of this kind with constant Gaussian curvature. A procedure is given in order to construct a partly marginally trapped surface by gluing two marginally trapped surfaces which are invarian...

In camera-based object recognition and classification, surface color is one of the most important characteristics. However, apparent object color may differ significantly according to the illumination and surface conditions. Such a variation can be an obstacle in utilizing color features. Geusebroek et al.’s color invariants can be a powerful tool for characterizing the object color regardless ...

An important issue in developing a model-based vision system is the speciication of features that are-(a) invariant to viewing and scene conditions, and also-(b) speciic, i.e., the feature must have diierent values for diierent classes of objects. We formulate a new approach for establishing invariant features. Our approach is unique in the eld since it considers not just surface reeection and ...

Shape recognition deals with the study geometric structures. Modern surface processing methods can cope with non-rigidity by measuring the lack of isometry, deal with similarity by multiplying the Euclidean arc-length by the Gaussian curvature, and manage equi-affine transformations by resorting to the special affine arc-length definition in classical affine geometry. Here, we propose a computa...

In this paper we study the moduli space of representations of a surface group (i.e., the fundamental group of a closed oriented surface) in the real symplectic group Sp(2n,R). The moduli space is partitioned by an integer invariant, called the Toledo invariant. This invariant is bounded by a Milnor–Wood type inequality. Our main result is a count of the number of connected components of the mod...

In camera-based object recognition and classification, surface color is one of the most important characteristics. However, apparent object color may differ significantly according to the illumination and surface conditions. Such a variation can be an obstacle in utilizing color features. Geusebroek et al.’s color invariants can be a powerful tool for characterizing the object color regardless ...

The most general conformally invariant bending energy of a closed four-dimensional surface, polynomial in the extrinsic curvature and its derivatives, is constructed. This invariance manifests itself as a set of constraints on the corresponding stress tensor. If the topology is fixed, there are three independent polynomial invariants: two of these are the straighforward quartic analogues of the...