TY - JOUR
AB - 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.
AU - Tamas Hausel
AU - Proudfoot, Nicholas J
ID - 1463
IS - 1
JF - Topology
TI - Abelianization for hyperkähler quotients
VL - 44
ER -
TY - CONF
AB - 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.
AU - Rother, Carsten
AU - Kumar, Sanjiv
AU - Vladimir Kolmogorov
AU - Blake, Andrew
ID - 3175
TI - Digital tapestry
VL - 1
ER -
TY - CONF
AB - 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.
AU - Vladimir Kolmogorov
AU - Criminisi, Antonio
AU - Blake, Andrew
AU - Cross, Geoffrey
AU - Rother, Carsten
ID - 3176
TI - Bi-layer segmentation of binocular stereo video
ER -
TY - CONF
AB - Tree-reweighted max-product (TRW) message passing [9] is a modified form of the ordinary max-product algorithm for attempting to find minimal energy configurations in Markov random field with cycles. For a TRW fixed point satisfying the strong tree agreement condition, the algorithm outputs a configuration that is provably optimal. In this paper, we focus on the case of binary variables with pairwise couplings, and establish stronger properties of TRW fixed points that satisfy only the milder condition of weak tree agreement (WTA). First, we demonstrate how it is possible to identify part of the optimal solution - i.e., a provably optimal solution for a subset of nodes - without knowing a complete solution. Second, we show that for submodular functions, a WTA fixed point always yields a globally optimal solution. We establish that for binary variables, any WTA fixed point always achieves the global maximum of the linear programming relaxation underlying the TRW method.
AU - Vladimir Kolmogorov
AU - Wainwright, Martin J
ID - 3181
TI - On the optimality of tree reweighted max product message passing
ER -
TY - CONF
AB - In the work of the authors (2003), we showed that graph cuts can find hypersurfaces of globally minimal length (or area) under any Riemannian metric. Here we show that graph cuts on directed regular grids can approximate a significantly more general class of continuous non-symmetric metrics. Using submodularity condition (Boros and Hammer, 2002 and Kolmogorov and Zabih, 2004), we obtain a tight characterization of graph-representable metrics. Such "submodular" metrics have an elegant geometric interpretation via hypersurface functionals combining length/area and flux. Practically speaking, we attend 'geo-cuts' algorithm to a wider class of geometrically motivated hypersurface functionals and show how to globally optimize any combination of length/area and flux of a given vector field. The concept of flux was recently introduced into computer vision by Vasilevskiy and Siddiqi (2002) but it was mainly studied within variational framework so far. We are first to show that flux can be integrated into graph cuts as well. Combining geometric concepts of flux and length/area within the global optimization framework of graph cuts allows principled discrete segmentation models and advances the slate of the art for the graph cuts methods in vision. In particular we address the "shrinking" problem of graph cuts, improve segmentation of long thin objects, and introduce useful shape constraints.
AU - Vladimir Kolmogorov
AU - Boykov, Yuri
ID - 3182
TI - What metrics can be approximated by geo cuts or global optimization of length area and flux
VL - 1
ER -