3,484 research outputs found
An L1 image transform for edge-preserving smoothing and scene-level intrinsic decomposition
Identifying sparse salient structures from dense pixels is a longstanding problem in visual computing. Solutions to this problem can benefit both image manipulation and understanding. In this paper, we introduce an image transform based on the L1 norm for piecewise image flattening. This transform can effectively preserve and sharpen salient edges and contours while eliminating insignificant details, producing a nearly piecewise constant image with sparse structures. A variant of this image transform can perform edge-preserving smoothing more effectively than existing state-of-the-art algorithms. We further present a new method for complex scene-level intrinsic image decomposition. Our method relies on the above image transform to suppress surface shading variations, and perform probabilistic reflectance clustering on the flattened image instead of the original input image to achieve higher accuracy. Extensive testing on the Intrinsic-Images-in-the-Wild database indicates our method can perform significantly better than existing techniques both visually and numerically. The obtained intrinsic images have been successfully used in two applications, surface retexturing and 3D object compositing in photographs.postprin
Thick hyperbolic 3-manifolds with bounded rank
We construct a geometric decomposition for the convex core of a thick
hyperbolic 3-manifold M with bounded rank. Corollaries include upper bounds in
terms of rank and injectivity radius on the Heegaard genus of M and on the
radius of any embedded ball in the convex core of M.Comment: 170 pages, 17 figure
Distributed Low-rank Subspace Segmentation
Vision problems ranging from image clustering to motion segmentation to
semi-supervised learning can naturally be framed as subspace segmentation
problems, in which one aims to recover multiple low-dimensional subspaces from
noisy and corrupted input data. Low-Rank Representation (LRR), a convex
formulation of the subspace segmentation problem, is provably and empirically
accurate on small problems but does not scale to the massive sizes of modern
vision datasets. Moreover, past work aimed at scaling up low-rank matrix
factorization is not applicable to LRR given its non-decomposable constraints.
In this work, we propose a novel divide-and-conquer algorithm for large-scale
subspace segmentation that can cope with LRR's non-decomposable constraints and
maintains LRR's strong recovery guarantees. This has immediate implications for
the scalability of subspace segmentation, which we demonstrate on a benchmark
face recognition dataset and in simulations. We then introduce novel
applications of LRR-based subspace segmentation to large-scale semi-supervised
learning for multimedia event detection, concept detection, and image tagging.
In each case, we obtain state-of-the-art results and order-of-magnitude speed
ups
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