@inbook{1444,
abstract = {The paper surveys the mirror symmetry conjectures of Hausel-Thaddeus and Hausel-Rodriguez-Villegas concerning the equality of certain Hodge numbers of SL(n, ℂ) vs. PGL(n, ℂ) flat connections and character varieties for curves, respectively. Several new results and conjectures and their relations to works of Hitchin, Gothen, Garsia-Haiman and Earl-Kirwan are explained. These use the representation theory of finite groups of Lie-type via the arithmetic of character varieties and lead to an unexpected conjecture for a Hard Lefschetz theorem for their cohomology.},
author = {Tamas Hausel},
booktitle = {Geometric Methods in Algebra and Number Theory},
pages = {193 -- 217},
publisher = {Springer},
title = {{Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve}},
doi = {10.1007/0-8176-4417-2_9},
volume = {235},
year = {2005},
}
@article{1447,
abstract = {Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper we will give two proofs that the injectivity part of the Hard Lefschetz theorem survives for toric hyperkähler varieties. We explain how this implies the g-inequalities for rationally representable matroids. We show how the geometrical intuition in the first proof, coupled with results of Chari [3], leads to a proof of the g-inequalities for general matroid complexes, which is a recent result of Swartz [20]. The geometrical idea in the second proof will show that a pure O-sequence should satisfy the g-inequalities, thus showing that our result is in fact a consequence of a long-standing conjecture of Stanley.},
author = {Tamas Hausel},
journal = {Open Mathematics},
number = {1},
pages = {26 -- 38},
publisher = {Central European Science Journals},
title = {{Quaternionic geometry of matroids}},
doi = {10.2478/BF02475653},
volume = {3},
year = {2005},
}
@article{1463,
abstract = {We study an integration theory in circle equivariant cohomology in order to prove a theorem relating the cohomology ring of a hyperkähler quotient to the cohomology ring of the quotient by a maximal abelian subgroup, analogous to a theorem of Martin for symplectic quotients. We discuss applications of this theorem to quiver varieties, and compute as an example the ordinary and equivariant cohomology rings of a hyperpolygon space.},
author = {Tamas Hausel and Proudfoot, Nicholas J},
journal = {Topology},
number = {1},
pages = {231 -- 248},
publisher = {Elsevier},
title = {{Abelianization for hyperkähler quotients}},
doi = {10.1016/j.top.2004.04.002},
volume = {44},
year = {2005},
}
@inproceedings{3175,
abstract = {This paper addresses the novel problem of automatically synthesizing an output image from a large collection of different input images. The synthesized image, called a digital tapestry, can be viewed as a visual summary or a virtual 'thumbnail' of all the images in the input collection. The problem of creating the tapestry is cast as a multi-class labeling problem such that each region in the tapestry is constructed from input image blocks that are salient and such that neighboring blocks satisfy spatial compatibility. This is formulated using a Markov Random Field and optimized via the graph cut based expansion move algorithm. The standard expansion move algorithm can only handle energies with metric terms, while our energy contains non-metric (soft and hard) constraints. Therefore we propose two novel contributions. First, we extend the expansion move algorithm for energy functions with non-metric hard constraints. Secondly, we modify it for functions with "almost" metric soft terms, and show that it gives good results in practice. The proposed framework was tested on several consumer photograph collections, and the results are presented.},
author = {Rother, Carsten and Kumar, Sanjiv and Vladimir Kolmogorov and Blake, Andrew},
pages = {589 -- 596},
publisher = {IEEE},
title = {{Digital tapestry}},
doi = {10.1109/CVPR.2005.130},
volume = {1},
year = {2005},
}
@inproceedings{3176,
abstract = {This paper demonstrates the high quality, real-time segmentation techniques. We achieve real-time segmentation of foreground from background layers in stereo video sequences. Automatic separation of layers from colour/contrast or from stereo alone is known to be error-prone. Here, colour, contrast and stereo matching information are fused to infer layers accurately and efficiently. The first algorithm, layered dynamic programming (LDP), solves stereo in an extended 6-state space that represents both foreground/background layers and occluded regions. The stereo-match likelihood is then fused with a contrast-sensitive colour model that is learned on the fly, and stereo disparities are obtained by dynamic programming. The second algorithm, layered graph cut (LGC), does not directly solve stereo. Instead the stereo match likelihood is marginalised over foreground and background hypotheses, and fused with a contrast-sensitive colour model like the one used in LDP. Segmentation is solved efficiently by ternary graph cut. Both algorithms are evaluated with respect to ground truth data and found to have similar performance, substantially better than stereo or colour/contrast alone. However, their characteristics with respect to computational efficiency are rather different. The algorithms are demonstrated in the application of background substitution and shown to give good quality composite video output.
},
author = {Vladimir Kolmogorov and Criminisi, Antonio and Blake, Andrew and Cross, Geoffrey and Rother, Carsten},
pages = {1186 -- 1186},
publisher = {IEEE},
title = {{Bi-layer segmentation of binocular stereo video}},
doi = {10.1109/CVPR.2005.90},
year = {2005},
}