Narrow Results

The notion of the amenability of a locally compact group has been extended in various ways. Two weaker versions of amenability, weak amenability and the approximation property, have been defined for locally compact groups (by Haagerup and Haagerup and Kraus, respectively) and Bekka has defined a notion of amenability for representations of locally compact groups. Correspondences can be viewed as a generalization of representations of such groups. Using this viewpoint, Ananthraman–Delaroche has defined a notion of (left) amenability for correspondences. In this paper, we define notions of weak amenability and the approximation property for correspondences (and representations of locally compact groups), and obtain various results concerning these notions. Ananthraman–Delaroche showed that if N ⊂ M is an inclusion of von Neumann algebras, and if the associated inclusion correspondence is left amenable, then various approximation properties of N (semidiscreteness, the weak* completely bounded approximation property, and the weak* operator approximation property) are shared by M. We show that if this correspondence has the (weaker) approximation property, then if N has the weak* operator approximation property, so does M. An application of this result to crossed products is also given.

We show that if a product system comes from a quantum Markov semigroup, then it carries a natural Borel structure with respect to which the semigroup may be realized in terms of a measurable representation. We show, too, that the dual product system of a Borel product system also carries a natural Borel structure. We apply our analysis to study the order interval consisting of all quantum Markov semigroups that are subordinate to a given one.

Equidistribution of the orbits of points, subvarieties or of periodic points in complex dynamics is a fundamental problem. It is often related to strong ergodic properties of the dynamical system and to a deep understanding of analytic cycles, or more generally positive closed currents, of arbitrary dimension and degree. The later topic includes the study of the potentials and super-potentials of positive closed currents, their intersection with or without dimension excess. In this paper, we will survey some results and tools developed during the last two decades. Related concepts, new techniques and open problems will be presented.

Correspondence is one of the major problems that must be solved in stereo vision. Correlation has been commonly used in the past for this problem. However, most classical linear correlation methods fail near depth discontinuities and in the presence of occlusions. Many robust methods have been proposed that claim to effectively deal with some or all of these issues. Many of these robust methods are transformation-based, however, other robust methods are non-transformation based. This paper gives five requirements that should be met by a transformation-based robust correlation method. We compare some of the robust correspondence methods and demonstrate their utility on different data sets. Based on these results, we propose a solution to the correspondence problem which represents a compromise between the speed of classical correlation and the improved results obtained from a more robust correspondence method. Also, we propose a median filtering technique that removes noise from the disparity maps while preserving certain image features usually removed by ordinary median filtering.

In this paper we present a novel technique for non-rigid medical image registration and correspondence finding based on a multiple-layer flexible mesh template matching technique. A statistical anatomical model is built in the form of a tetrahedral mesh, which incorporates both shape and density properties of the anatomical structure. After the affine transformation and global deformation of the model are computed by optimizing an energy function, a multiple-layer flexible mesh template matching is applied to find the vertex correspondence and achieve local deformation. The multiple-layer structure of the template can be used to describe different scale of anatomical features; furthermore, the template matching is flexible which makes the correspondence finding robust. A leave-one-out validation has been conducted to demonstrate the effectiveness and accuracy of our method.

In this article, we introduce a general concept of fuzzy operators. These operators are then used to generalize the possibilistic conditioning formulation proposed by Nguyen [1]. This generalization depends on the relation which exists between this conditioning and the probabilistic t-norm. By using other t-norms, other conditionings are obtained, and their properties are studied. One application of normalized possibilistic conditioning is the measure of the dependency between two fuzzy statistical variables. The measure constructed can be considered as the possibilistic counterpart of mutual information commonly used in statistics.

To generate a 3D computer model of a free-form object, multiple range images (point clouds) covering its entire surface are acquired from different viewpoints. These views are then aligned in a common coordinate basis by minimizing the distance error between their corresponding points. Establishing correspondences automatically is an inherently challenging problem due to the lack of any type of information other than the geometrical information extracted from the point clouds. Existing "automatic" correspondence techniques achieve automatism at the expense of other important specifications namely, applicability to free-form objects, accuracy, efficiency, robustness to resolution and surface sampling, robustness to overlap, robustness to noise and finally their applicability to simultaneous multiview correspondence. There is also a lack of a review paper that describes and critically analyzes these techniques. In this paper, we present such an extensive review and carry out the analysis of each technique according to the above listed indispensable criteria. Our analysis shows that none of these techniques fully meets these criteria and that there is still a need for the development of practical automatic correspondence algorithms.

This paper presents a technique for designing a fillet joining two objects along two rail contours, one on each object's surface. Most fillet generation methods join surfaces which are either intersecting or in close proximity. They are ill-suited for joining farther-apart objects smoothly. Our method takes into account the relative spatial orientations and the neighborhoods of the rail contours so as to achieve a smooth join. We present a general reparametrization procedure for establishing correspondence between rail contours of arbitrary orientations. Intermediate contours defining the cross sectional shape of the fillet are designed through specifying a shape control parameter and two scaling functions. Finally, a lofting surface connecting the contours, and is at tangent continuity with the base surfaces, is generated. Objects of complex topological shapes can be created by joining handles and branches as fillets, thus ensuring topological integrity.

In this article we present a new variant of the light field representation that supports improved image reconstruction by accommodating sparse correspondence information. This places our representation somewhere between a pure, two-plane parameterized, light field and a lumigraph representation, with its continuous geometric proxy. Our approach factors the rays of a light field into one of two separate classes. All rays consistent with a given correspondence are implicitly represented using a new auxiliary data structure, which we call a surface camera, or scam. The remaining rays of the light field are represented using a standard two-plane parameterized light field. We present an efficient rendering algorithm that combines ray samples from scams with those from the light field. The resulting image reconstructions are noticeably improved over that of a pure light field.

The idea of associating a graph with the zero-divisors of a commutative ring was originated by Beck. The problems concerning zero-divisor graphs have been studied extensively in the past 10 years. DeMeyer and DeMeyer presented some properties for the correspondence between zero-divisor graphs and their semigroups. It is very important to have adequate examples before the complete resolution of this difficult problem. However, the computing cost is enormous even when there are only 6 vertices. We present a program with elaborate optimization and pruning that can solve the correspondence between zero-divisor graphs with 6 vertices and their semigroups rapidly.

In this paper, we mainly consider the relationship between the complex irreducible characters of a π-separable group and the complex irreducible characters of its Hall π-subgroup. If a π-group S acts on a π-separable group G, let H be an S-invariant Hall π-subgroup of G and C_NG(H)/H(S)=1. Then we construct a natural bijection from the set Lin_S(H) onto the set Irr_π′,S(G). Furthermore, we get a bijection from the linear characters of H onto Irr_π′(G).