Lefschetz Center for Dynamical Systems Seminar
Cognitive & Linguistic Sciences Colloquium Series
Refreshments will be served before the talk in Room 124-125
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Abstract: Visual grouping and figure-ground discrimination were first studied by the Gestalt school of visual perception nearly a century ago. By the use of cleverly constructed examples, they were able to demonstrate the role of factors such as proximity, similarity, curvilinear continuity and common fate in visual grouping and factors such as convexity, size, and symmetry in figure-ground discrimination. However, this left open (at least) three major problems (1) there wasn't a precise operationalization of these factors for general images, (2) the interaction of these cues was ill understood (3) and there was no justification for why these factors might be helpful to an observer interacting with the visual world.
In my research group, we have tackled these problems in the framework of what we call "ecological statistics". We start with a set of natural images and use human observers to mark the perceptual groups and assign figure-ground labels to the various boundary contours. We construct computational models of various grouping and figure-ground factors inspired by corresponding mechanisms in visual cortex. Finally we calibrate and optimally combine the grouping and figure-ground factors by using the principle that vision evolved to be adaptive to the statistics of objects in the natural world.
Over the last few years of research in this framework, we have been able to quantitatively characterize the grouping cues of brightness, color, and texture similarity and curvilinear continuity, and figure-ground cues of size, lower-region and convexity. I shall summarize some of these results in my talk; more can be found on http://http.cs.berkeley.edu/projects/vision/grouping/. This research is joint work with Charless Fowlkes, David Martin and Xiaofeng Ren.
Brown Applied Mathematics Pattern Theory and Vision Seminar
Brown Analysis Seminar
Scientific Computing Seminar
Department of Mathematics and Statistics, University of Massachusetts at Amherst | |
Abstract: Hybrid deterministic/stochastic systems, arising as couplings of microscopic models and deterministic macroscopic equations are commonplace in a wide array of applications, ranging from catalysis and deposition processes to stochastic models for tropical and open ocean convection. A major challenge in all these problems arises in the direct numerical simulation of realistic size systems due to scale and model disparities, while due to nonlinear interactions across a wide range of scales, the stochasticity inherited from the microscopic model can play a subtle but important role in the dynamic behavior of the overall system.
In this talk we attempt to address directly or indirectly these issues; one of the primary tools we have developed for this purpose is a new mathematical framework for the hierarchical stochastic coarse-graining of microscopic dynamics. Computational comparisons of coarse-grained and microscopic simulations along with accompanying rigorous estimates on the loss of information between the time-dependent coarse-grained and microscopic probability distribution functions highlight the validity regimes of the method. Furthermore we discuss spatial adaptivity for microscopic simulations constructed using the coarse-grained stochastic processes tools we have already developed. The adaptivity criterion is based, in analogy to PDE finite element methods, on a posteriori estimates on the loss of information between the coarse-grained and the microscopic pdf.
The presented results are joint work with A. J. Majda (Courant), P. Plechac (Warwick), A. Sopasakis (UMass), J. Trashorras (Paris IX) and D.G. Vlachos (Chem.Eng. Delaware).
Department of Mathematics Colloquium
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