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.
On the other hand, frequency domain also provides a reliable avenue for salient object detection. For example, Hou and Zhang @cite_1 analyzed spectral residual of an image in spectral domain, where the high-frequency components are considered as background. A similar work was presented by Fang @cite_28 , where the standard Fast Fourier Transform (FFT) is substituted with Quaternion Fourier Transform (QFT). Other representative examples include @cite_29 @cite_42 .
@cite_28 @cite_29 @cite_42 @cite_1
2152233525 2099944953 2012300893 2039920533
We address the issue of visual saliency from three perspectives. First, we consider saliency detection as a frequency domain analysis problem. Second, we achieve this by employing the concept of nonsaliency. Third, we simultaneously consider the detection of salient regions of different size. The paper proposes a new bottom-up paradigm for detecting visual saliency, characterized by a scale-space analysis of the amplitude spectrum of natural images. We show that the convolution of the image amplitude spectrum with a low-pass Gaussian kernel of an appropriate scale is equivalent to an image saliency detector. The saliency map is obtained by reconstructing the 2D signal using the original phase and the amplitude spectrum, filtered at a scale selected by minimizing saliency map entropy. A Hypercomplex Fourier Transform performs the analysis in the frequency domain. Using available databases, we demonstrate experimentally that the proposed model can predict human fixation data. We also introduce a new image database and use it to show that the saliency detector can highlight both small and large salient regions, as well as inhibit repeated distractors in cluttered images. In addition, we show that it is able to predict salient regions on which people focus their attention. The fast Fourier transform (FFT) is used widely in signal processing for efficient computation of the FT of finite-length signals over a set of uniformly spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e., a nonuniform FT. Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function. The nonequispaced Fourier transform arises in a variety of application areas, from medical imaging to radio astronomy to the numerical solution of partial differential equations. In a typical problem, one is given an irregular sampling of N data in the frequency domain and one is interested in reconstructing the corresponding function in the physical domain. When the sampling is uniform, the fast Fourier transform (FFT) allows this calculation to be computed in O(N log N ) operations rather than O(N 2 ) operations. Unfortunately, when the sampling is nonuniform, the FFT does not apply. Over the last few years, a number of algorithms have been developed to overcome this limitation and are often referred to as nonuniform FFTs (NUFFTs). These rely on a mixture of interpolation and the judicious use of the FFT on an oversampled grid (A. Dutt and V. Rokhlin, SIAM J. Sci. Comput., 14 (1993), pp. 1368-1383). In this paper, we observe that one of the standard interpolation or "gridding" schemes, based on Gaussians, can be accelerated by a significant factor without precomputation and storage of the interpolation weights. This is of particular value in two- and three- dimensional settings, saving either 10 d N in storage in d dimensions or a factor of about 5-10 in CPUtime (independent of dimension). With the wide applications of saliency information in visual signal processing, many saliency detection methods have been proposed. However, some key characteristics of the human visual system (HVS) are still neglected in building these saliency detection models. In this paper, we propose a new saliency detection model based on the human visual sensitivity and the amplitude spectrum of quaternion Fourier transform (QFT). We use the amplitude spectrum of QFT to represent the color, intensity, and orientation distributions for image patches. The saliency value for each image patch is calculated by not only the differences between the QFT amplitude spectrum of this patch and other patches in the whole image, but also the visual impacts for these differences determined by the human visual sensitivity. The experiment results show that the proposed saliency detection model outperforms the state-of-the-art detection models. In addition, we apply our proposed model in the application of image retargeting and achieve better performance over the conventional algorithms.