We propose a unified approach for bottom-up hierarchical image segmentation and object proposal generation for recognition, called Multiscale Combinatorial Grouping (MCG). For this purpose, we first develop a fast normalized cuts algorithm. We then propose a high-performance hierarchical segmenter that makes effective use of multiscale information. Finally, we propose a grouping strategy that combines our multiscale regions into highly-accurate object proposals by exploring efficiently their combinatorial space. We also present Single-scale Combinatorial Grouping (SCG), a faster version of MCG that produces competitive proposals in under five seconds per image. We conduct an extensive and comprehensive empirical validation on the BSDS500, SegVOC12, SBD, and COCO datasets, showing that MCG produces state-of-the-art contours, hierarchical regions, and object proposals.
* The efficient computation of normalized-cuts eigenvectors has been the subject of recent work, as it is often the computational bottleneck in grouping algorithms. Taylor @cite_47 presented a technique for using a simple watershed oversegmentation to reduce the size of the eigenvector problem, sacrificing accuracy for speed. We take a similar approach of solving the eigenvector problem in a reduced space, though we use simple image-pyramid operations on the affinity matrix (instead of a separate segmentation algorithm) and we see no loss in performance despite a 20 @math speed improvement. Maire and Yu @cite_45 presented a novel multigrid solver for producing eigenvectors at multiple scales, which speeds up fine-scale eigenvector computation by leveraging coarse-scale solutions. Our technique also uses the scale-space structure of an image, but instead of solving the problem at multiple scales, we simply reduce the scale of the problem, solve it at a reduced scale, and then upsample the solution while preserving the structure of the image. As such, our technique is faster and much simpler, requiring only a few lines of code wrapped around a standard sparse eigensolver.
@cite_47 @cite_45
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We reexamine the role of multiscale cues in image segmentation using an architecture that constructs a globally coherent scale-space output representation. This characteristic is in contrast to many existing works on bottom-up segmentation, which prematurely compress information into a single scale. The architecture is a standard extension of Normalized Cuts from an image plane to an image pyramid, with cross-scale constraints enforcing consistency in the solution while allowing emergence of coarse-to-fine detail. We observe that multiscale processing, in addition to improving segmentation quality, offers a route by which to speed computation. We make a significant algorithmic advance in the form of a custom multigrid eigensolver for constrained Angular Embedding problems possessing coarse-to-fine structure. Multiscale Normalized Cuts is a special case. Our solver builds atop recent results on randomized matrix approximation, using a novel interpolation operation to mold its computational strategy according to cross-scale constraints in the problem definition. Applying our solver to multiscale segmentation problems demonstrates speedup by more than an order of magnitude. This speedup is at the algorithmic level and carries over to any implementation target. We give an approximation algorithm for non-uniform sparsest cut with the following guarantee: For any @math , given cost and demand graphs with edge weights @math respectively, we can find a set @math with @math at most @math times the optimal non-uniform sparsest cut value, in time @math provided @math . Here @math is the @math 'th smallest generalized eigenvalue of the Laplacian matrices of cost and demand graphs; @math (resp. @math ) is the weight of edges crossing the @math cut in cost (resp. demand) graph and @math is the sparsity of the optimal cut. In words, we show that the non-uniform sparsest cut problem is easy when the generalized spectrum grows moderately fast. To the best of our knowledge, there were no results based on higher order spectra for non-uniform sparsest cut prior to this work. Even for uniform sparsest cut, the quantitative aspects of our result are somewhat stronger than previous methods. Similar results hold for other expansion measures like edge expansion, normalized cut, and conductance, with the @math 'th smallest eigenvalue of the normalized Laplacian playing the role of @math in the latter two cases. Our proof is based on an l1-embedding of vectors from a semi-definite program from the Lasserre hierarchy. The embedded vectors are then rounded to a cut using standard threshold rounding. We hope that the ideas connecting @math -embeddings to Lasserre SDPs will find other applications. Another aspect of the analysis is the adaptation of the column selection paradigm from our earlier work on rounding Lasserre SDPs [GS11] to pick a set of edges rather than vertices. This feature is important in order to extend the algorithms to non-uniform sparsest cut. This paper proposes a parallel algorithm using CUDA GPU to accelerate the process of image segmentation algorithm based on Normalized Cut. After giving a summary of the key concepts and theory of normalized cut and CUDA, detailed implementation issues are discussed including the calculation of affinity matrix, transforming symmetric matrices to symmetric tridiagonal matrices, calculation of generalized eigenvalue value and its associated eigenvetor, the choice of splitting point, stopping criterion etc. This algorithm doesn't sparse the similarity matrix, so there is no information loss in transforming, which will lead to a more real and reliable segmentation. The experiment shows that the parallel algorithm using CUDA not only segment the image reliably but also have a great performance speed-up. We propose a unified solution to both linear placement and partitioning. Our approach combines the well-known eigenvector optimization method with the recursive max-flow min-cut method. A linearized eigenvector method is proposed to improve the linear placement. A hypergraph maxflow algorithm is then adopted to efficiently find the max-flow min-cut. In our unified approach, the max-flow min-cut provides an optimal ordered partition subject to the given seeds and the eigenvector placement provides heuristic information for seed selection. Experimental results on MCNC benchmarks show that our approach is superior to other methods for both linear placement and partitioning problems. On average, our approach yields an improvement of 45.1 over eigenvector approach in terms of total wire length, and yields an improvement of 26.9 over PARABOLI[6] in terms of cut size.