Low-Rank Matrix Recovery (LRMR) has recently been applied to saliency detection by decomposing image features into a low-rank component associated with background and a sparse component associated with visual salient regions. Despite its great potential, existing LRMR-based saliency detection methods seldom consider the inter-relationship among elements within these two components, thus are prone to generating scattered or incomplete saliency maps. In this paper, we introduce a novel and efficient LRMR-based saliency detection model under a coarse-to-fine framework to circumvent this limitation. First, we roughly measure the saliency of image regions with a baseline LRMR model that integrates a @math -norm sparsity constraint and a Laplacian regularization smooth term. Given samples from the coarse saliency map, we then learn a projection that maps image features to refined saliency values, to significantly sharpen the object boundaries and to preserve the object entirety. We evaluate our framework against existing LRMR based methods on three benchmark datasets. Experimental results validate the superiority of our method as well as the effectiveness of our suggested coarse-to-fine framework, especially for images containing multiple objects.
Although above extensions improved algorithm robustness to cluttered backgrounds, there still remain two open problems. First, extra priors @cite_20 or complicated operations (such as saliency fusion @cite_10 @cite_45 ) may incur expensive computational cost. Second, these methods neglect the spatial relationship among image regions, which cannot ensure the entirety of detected objects. The first work that attempts to address above two limitations is the recently proposed structured matrix decomposition (SMD) by Peng @cite_46 . Specifically, SMD introduces two new regularization terms to Eq. ): a tree-structured sparse constraint that is used to preserve inter-correlations among sparse elements and a Laplacian regularization term that is adopted to enlarge the difference between foreground and background. This way, the spatial relationship among sparse elements and the coherence between low rank component and sparse component are explicitly modeled and optimized in a unified model. The objective of SMD is formulated as:
@cite_46 @cite_45 @cite_10 @cite_20
2346506533 2610921592 2485294266 1977580401
Low-rank recovery models have shown potential for salient object detection, where a matrix is decomposed into a low-rank matrix representing image background and a sparse matrix identifying salient objects. Two deficiencies, however, still exist. First, previous work typically assumes the elements in the sparse matrix are mutually independent, ignoring the spatial and pattern relations of image regions. Second, when the low-rank and sparse matrices are relatively coherent, e.g., when there are similarities between the salient objects and background or when the background is complicated, it is difficult for previous models to disentangle them. To address these problems, we propose a novel structured matrix decomposition model with two structural regularizations: (1) a tree-structured sparsity-inducing regularization that captures the image structure and enforces patches from the same object to have similar saliency values, and (2) a Laplacian regularization that enlarges the gaps between salient objects and the background in feature space. Furthermore, high-level priors are integrated to guide the matrix decomposition and boost the detection. We evaluate our model for salient object detection on five challenging datasets including single object, multiple objects and complex scene images, and show competitive results as compared with 24 state-of-the-art methods in terms of seven performance metrics. In this paper, we present a novel salient object detection method, efficiently combining Laplacian sparse subspace clustering (LSSC) and unified low-rank representation (ULRR). Unlike traditional low-rank matrix recovery (LRMR) based saliency detection methods which mainly extract saliency from pixels or super-pixels, our method advocates the saliency detection on the super-pixel clusters generated by LSSC. By doing so, our method succeeds in extracting large-size salient objects from cluttered backgrounds, against the detection of small-size salient objects from simple backgrounds obtained by most existing work. The entire algorithm is carried out in two stages: region clustering and cluster saliency detection. In the first stage, the input image is segmented into many super-pixels, and on top of it, they are further grouped into different clusters by using LSSC. Each cluster contains multiple super-pixels having similar features (e.g., colors and intensities), and may correspond to a part of a salient object in the foreground or a local region in the background. In the second stage, we formulate the saliency detection of each super-pixel cluster as a unified low-rankness and sparsity pursuit problem using a ULRR model, which integrates a Laplacian regularization term with respect to the sparse error matrix into the traditional low-rank representation (LRR) model. The whole model is based on a sensible cluster-consistency assumption that the spatially adjacent super-pixels within the same cluster should have similar saliency values, similar representation coefficients as well as similar reconstruction errors. In addition, we construct a primitive dictionary for the ULRR model in terms of the local-global color contrast of each super-pixel. On top of it, a global saliency measure covering the representation coefficients and a local saliency measure considering the sparse reconstruction errors are jointly employed to define the final saliency measure. Comprehensive experiments over diverse publicly available benchmark data sets demonstrate the validity of the proposed method. We study the problem of detecting a structured, low-rank signal matrix corrupted with additive Gaussian noise. This includes clustering in a Gaussian mixture model, sparse PCA, and submatrix localization. Each of these problems is conjectured to exhibit a sharp information-theoretic threshold, below which the signal is too weak for any algorithm to detect. We derive upper and lower bounds on these thresholds by applying the first and second moment methods to the likelihood ratio between these "planted models" and null models where the signal matrix is zero. Our bounds differ by at most a factor of root two when the rank is large (in the clustering and submatrix localization problems, when the number of clusters or blocks is large) or the signal matrix is very sparse. Moreover, our upper bounds show that for each of these problems there is a significant regime where reliable detection is information- theoretically possible but where known algorithms such as PCA fail completely, since the spectrum of the observed matrix is uninformative. This regime is analogous to the conjectured 'hard but detectable' regime for community detection in sparse graphs. Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in statistics, machine learning, computer vision, as well as signal and image processing. In theory, this problem can be solved by the natural convex joint mixed relaxations (i.e., l 1 -norm and trace norm) under certain conditions. However, all current provable algorithms suffer from superlinear per-iteration cost, which severely limits their applicability to large-scale problems. In this paper, we propose a scalable, provable and structured robust bilinear factorization (RBF) method to recover low-rank and sparse matrices from missing and grossly corrupted data, i.e., robust matrix completion (RMC), or incomplete and grossly corrupted measurements, i.e., compressive principal component pursuit (CPCP). Specifically, we first present two small-scale matrix trace norm regularized bilinear factorization models for RMC and CPCP problems, in which repetitively calculating SVD of a large-scale matrix is replaced by updating two much smaller factor matrices. Then, we apply the alternating direction method of multipliers (ADMM) to efficiently solve the RMC problems. Finally, we provide the convergence analysis of our algorithm, and extend it to address general CPCP problems. Experimental results verified both the efficiency and effectiveness of our method compared with the state-of-the-art methods.