In this paper, we propose a simple but effective method for fast image segmentation. We re-examine the locality-preserving character of spectral clustering by constructing a graph over image regions with both global and local connections. Our novel approach to build graph connections relies on two key observations: 1) local region pairs that co-occur frequently will have a high probability to reside on a common object; 2) spatially distant regions in a common object often exhibit similar visual saliency, which implies their neighborship in a manifold. We present a novel energy function to efficiently conduct graph partitioning. Based on multiple high quality partitions, we show that the generated eigenvector histogram based representation can automatically drive effective unary potentials for a hierarchical random field model to produce multi-class segmentation. Sufficient experiments, on the BSDS500 benchmark, large-scale PASCAL VOC and COCO datasets, demonstrate the competitive segmentation accuracy and significantly improved efficiency of our proposed method compared with other state of the arts.
Laplacian eigenmaps @cite_41 computes a low-dimensional embedding to preserve the pairwise affinity of data points in the manifold. Local linear embedding (LLE) @cite_1 , alternatively, preserves the linear structure among the local neighboring points. The locality-preserving character of these two methods implicitly encourages the clustering of data. However, Isomap @cite_26 , which preserves global data geodesic distances, does not possess the nature of clustering. Our method shows a distinct point of view on the side of manifold learning to enhance spectral clustering for image segmentation.
@cite_41 @cite_26 @cite_1
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Previous efforts in hashing intend to preserve data variance or pairwise affinity, but neither is adequate in capturing the manifold structures hidden in most visual data. In this paper, we tackle this problem by reconstructing the locally linear structures of manifolds in the binary Hamming space, which can be learned by locality-sensitive sparse coding. We cast the problem as a joint minimization of reconstruction error and quantization loss, and show that, despite its NP-hardness, a local optimum can be obtained efficiently via alternative optimization. Our method distinguishes itself from existing methods in its remarkable ability to extract the nearest neighbors of the query from the same manifold, instead of from the ambient space. On extensive experiments on various image benchmarks, our results improve previous state-of-the-art by 28-74 typically, and 627 on the Yale face data. Abstract Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our approach relies on radial basis functions (RBFs) to interpolate the inverse map everywhere on the low-dimensional image of the forward map. We demonstrate that the scale-free cubic RBF kernel performs better than the Gaussian kernel: it does not suffer from ill-conditioning, and does not require the choice of a scale. The proposed construction is shown to be similar to the Nystrom extension of the eigenvectors of the symmetric normalized graph Laplacian matrix. Based on this observation, we provide a new interpretation of the Nystrom extension with suggestions for improvement. Numerous methods or algorithms have been designed to solve the problem of nonlinear dimensionality reduction (NLDR). However, very few among them are able to embed efficiently 'circular' manifolds like cylinders or tori, which have one or more essential loops. This paper presents a simple and fast procedure that can tear or cut those manifolds, i.e. break their essential loops, in order to make their embedding in a low-dimensional space easier. The key idea is the following: starting from the available data points, the tearing procedure represents the underlying manifold by a graph and then builds a maximum subgraph with no loops anymore. Because it works with a graph, the procedure can preprocess data for all NLDR techniques that uses the same representation. Recent techniques using geodesic distances (Isomap, geodesic Sammon's mapping, geodesic CCA, etc.) or K-ary neighborhoods (LLE, hLLE, Laplacian eigenmaps) fall in that category. After describing the tearing procedure in details, the paper comments a few experimental results. (c) 2005 Elsevier B.V. All rights reserved. This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold @math into clusters lying around low-dimensional submanifolds of @math . Important examples of @math , for which the proposed clustering algorithm is computationally efficient, are the sphere, the set of positive definite matrices, and the Grassmannian. The clustering problem with these examples of @math is already useful for numerous application domains such as action identification in video sequences, dynamic texture clustering, brain fiber segmentation in medical imaging, and clustering of deformed images. The proposed clustering algorithm constructs a data-affinity matrix by thoroughly exploiting the intrinsic geometry and then applies spectral clustering. The intrinsic local geometry is encoded by local sparse coding and more importantly by directional information of local tangent spaces and geodesics. Theoretical guarantees are established for a simplified variant of the algorithm even when the clusters intersect. To avoid complication, these guarantees assume that the underlying submanifolds are geodesic. Extensive validation on synthetic and real data demonstrates the resiliency of the proposed method against deviations from the theoretical model as well as its superior performance over state-of-the-art techniques.