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This paper discusses a methodology for determining a functional representation of a random process from a collection of scattered pointwise samples. The present work specifically focuses onto random quantities lying in a high-dimensional stochastic space in the context of limited amount of information. The proposed approach involves a procedure for the selection of an approximation basis and th...

In this paper, we explain why Scale Space theories do not incorporate obvious restrictions imposed by the physics of image generation [20]. The heat equation (linear scale space) is not contrast invariant and destroys Tjunctions [12]. The same is true for the recently proposed curvature equations (mean curvature motion [2] and a ne shortening [27] [2]) : They break the symmetry of junctions [4]...

in this paper, we prove the generalized hyers-ulam(or hyers-ulam-rassias ) stability of the following composite functional equation f(f(x)-f(y))=f(x+y)+f(x-y)-f(x)-f(y) in various normed spaces.