Courant Institute of Mathematical Sciences

About: Courant Institute of Mathematical Sciences is a education organization based out in New York, New York, United States. It is known for research contribution in the topics: Nonlinear system & Boundary value problem. The organization has 2414 authors who have published 7759 publications receiving 439773 citations. The organization is also known as: CIMS & New York University Department of Mathematics.

On the Foundations of Relaxation Labeling Processes

Abstract: A large class of problems can be formulated in terms of the assignment of labels to objects. Frequently, processes are needed which reduce ambiguity and noise, and select the best label among several possible choices. Relaxation labeling processes are just such a class of algorithms. They are based on the parallel use of local constraints between labels. This paper develops a theory to characterize the goal of relaxation labeling. The theory is founded on a definition of con-sistency in labelings, extending the notion of constraint satisfaction. In certain restricted circumstances, an explicit functional exists that can be maximized to guide the search for consistent labelings. This functional is used to derive a new relaxation labeling operator. When the restrictions are not satisfied, the theory relies on variational cal-culus. It is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality. A procedure nearly identical to the relaxation operator derived under restricted circum-stances serves in the more general setting. Further, a local convergence result is established for this operator. The standard relaxation labeling formulas are shown to approximate our new operator, which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here. Observations about con-vergence and generalizations to higher order compatibility relations are described.

Motion illusions as optimal percepts

Abstract: ing incorrect velocities. We show that these ‘illusions’ arise naturally in a system that attempts to estimate local image velocity. We formulated a model of visual motion perception using standard estimation theory, under the assumptions that (i) there is noise in the initial measurements and (ii) slower motions are more likely to occur than faster ones. We found that specific instantiation of such a velocity estimator can account for a wide variety of psychophysical phenomena.

The dirichlet problem for nonlinear second‐order elliptic equations I. Monge‐ampégre equation

Abstract: On considere le probleme de Dirichlet pour des equations elliptiques non lineaires pour une fonction reelle u definie dans la fermeture Ω d'un domaine borne Ω dans R n avec une frontiere ∂Ω C ∞

Geometric Hashing: A General And Efficient Model-based Recognition Scheme

Abstract: A general method for model-based object recognition in occluded scenes is presented. It is based on geometric hashing. The method stands out for its efficiency. We describe the general framework of the method and illustrate its applications for various recogni- tion problems both in 3-D and 2-D. Special attention is given to the recognition of 3-D objects in occluded scenes from 2-D gray scale images. New experimental results are included for this important case.

The relaxation schemes for systems of conservation laws in arbitrary space dimensions

Abstract: We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stiff lower order term that approximates the original system with a small dissipative correction. The new system can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers temporally. Numerical results for 1-D and 2-D problems are presented. The second-order schemes are shown to be total variation diminishing (TVD) in the zero relaxation limit for scalar equations. ©1995 John Wiley & Sons, Inc.