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On the classification of rank two representations of quasiprojective fundamental groups
"... Abstract. Suppose X is a smooth quasiprojective variety over C and ρ: π1(X, x) → SL(2, C) is a Zariskidense representation with quasiunipotent monodromy at infinity. Then ρ factors through a map X → Y with Y either a DMcurve or a Shimura modular stack. 1. ..."
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Abstract. Suppose X is a smooth quasiprojective variety over C and ρ: π1(X, x) → SL(2, C) is a Zariskidense representation with quasiunipotent monodromy at infinity. Then ρ factors through a map X → Y with Y either a DMcurve or a Shimura modular stack. 1.
Level Lines Selection with Variational Models for Segmentation and Encoding
, 2007
"... This paper discusses the interest of the Tree of Shapes of an image as a region oriented image representation. The Tree of Shapes offers a compact and structured representation of the family of level lines of an image. This representation has been used for many processing tasks such as filtering, r ..."
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Cited by 12 (1 self)
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This paper discusses the interest of the Tree of Shapes of an image as a region oriented image representation. The Tree of Shapes offers a compact and structured representation of the family of level lines of an image. This representation has been used for many processing tasks such as filtering, registration, or shape analysis. In this paper we show how this representation can be used for segmentation, rate distortion optimization, and encoding. We address the problem of segmentation and rate distortion optimization using Guigues algorithm on a hierarchy of partitions constructed using the simplified MumfordShah multiscale energy. To segment an image, we minimize the simplified MumfordShah energy functional on the set of partitions represented in this hierarchy. The rate distortion problem is also solved in this hierarchy of partitions. In the case of encoding, we propose a variational model to select a family of level lines of a gray level image in order to obtain a minimal description of it. Our energy functional represents the cost in bits of encoding the selected level lines while controlling the maximum error of the reconstructed image. In this case, a greedy algorithm is used to minimize the corresponding functional. Some experiments are displayed.