D. Mumford

Publications274
h-index74
Citations34,374
Highly Influential Citations2,421
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Optimal approximations by piecewise smooth functions and associated variational problems
Abstract : This reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamental…
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Tata Lectures on Theta I
and motivation: theta functions in one variable.- Basic results on theta functions in several variables.
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The irreducibility of the space of curves of given genus
© Publications mathematiques de l’I.H.E.S., 1969, tous droits reserves. L’acces aux archives de la revue « Publications mathematiques de l’I.H.E.S. » (http://www.…
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Geometric Invariant Theory
“Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to…
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Towards an Enumerative Geometry of the Moduli Space of Curves
The goal of this paper is to formulate and to begin an exploration of the enumerative geometry of the set of all curves of arbitrary genus g. By this we mean setting up a Chow ring for the moduli…
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Hierarchical Bayesian inference in the visual cortex.
  • T. Lee, D. Mumford
  • Biology, Computer Science
    Journal of the Optical Society of America. A…
  • 1 July 2003
TLDR
This work proposes a new theoretical setting based on the mathematical framework of hierarchical Bayesian inference for reasoning about the visual system, and suggests that the algorithms of particle filtering and Bayesian-belief propagation might model these interactive cortical computations.
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Statistics of natural images and models
TLDR
Results ranging from the simplest single pixel intensity to joint distribution of 3 Haar wavelet responses are reported, which shed light on old issues such as the near scale-invariance of image statistics and some are entirely new.
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Elastica and Computer Vision
I want to discuss the problem from differential geometry of describing those plane curves C which minimize the integral $$\int\limits_C {(\alpha k^2 + \beta )ds.}$$ Here α and β are constants,…
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Stability of projective varieties
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Communications on Pure and Applied Mathematics
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