Normalized cut (Ncut) is one of the popular image segmentation models in which the parametric similarity matrix should be given in advance. In this paper, we propose a normalized cut segmentation algorithm with an adaptive similarity measure and spatial regularization. The statistical Parzen-Rosenblatt window, expectation maximum (EM) method and the regularization technique in partial differential equation (PDE) are unified in a proposed variational framework. The introduced EM strategy makes our method can adaptively update the similarity matrix, and it can produce a better classification criterion than the existing Ncut based methods. While the regularization can guarantee the proposed algorithm has a robust performance under noise and it can also rectify the similarity measure with a priori spatial location. In addition, the existence theorem of the proposed model is given in the paper. Compared with some existing spectral clustering methods such as the traditional Ncut algorithm and the variational based Chan-Vese model, the numerical experiments show that our methods can provide promising segmentation results.
[rgb] 0.00,0.00,0.00 The normalization factor @math can improve the performance of image segmentation. To be more precisely, it can avoid the segmentation bias. However, this binary optimization of the normalized cut is NP-Hard. Fortunately, this problem can be relaxed to a generalized-eigenvalue problem @cite_55 Here the relaxation function @math of a binary variable can be used to label the segmentation, and @math is the degree matrix @cite_20 which is a diagonal matrix with @math .
@cite_55 @cite_20
2063149017 2170293972 2208417422 1995790019
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. Non-negative matrix factorization (NMF), i.e. V ap WH where both V, W and H are non-negative has become a widely used blind source separation technique due to its part based representation. The NMF decomposition is not in general unique and a part based representation not guaranteed. However, imposing sparseness both improves the uniqueness of the decomposition and favors part based representation. Sparseness in the form of attaining as many zero elements in the solution as possible is appealing from a conceptional point of view and corresponds to minimizing reconstruction error with an L0 norm constraint. In general, solving for a given L0 norm is an NP hard problem thus convex relaxation to regularization by the L1 norm is often considered, i.e., minimizing (1 2||V - WH||F 2 + lambda||H||1).An open problem is to control the degree of sparsity lambda imposed. We here demonstrate that a full regularization path for the L1 norm regularized least squares NMF for fixed W can be calculated at the cost of an ordinary least squares solution based on a modification of the least angle regression and selection (LARS) algorithm forming a non-negativity constrained LARS (NLARS). With the full regularization path, the L1 regularization strength lambda that best approximates a given L0 can be directly accessed and in effect used to control the sparsity of H. The MATLAB code for the NLARS algorithm is available for download. The heavy use of camera phones and other mobile devices all over the world has produced a market for mobile image analysis, including image segmentation to separate out objects of interest. Automatic image segmentation algorithms, when employed by many different users for multiple applications, cannot guarantee high quality results. Yet interactive algorithms require human effort that may become quite tedious. To reduce human effort and achieve better results, it is worthwhile to know in advance which images are difficult to segment and may require further user interaction or alternate processing. For this purpose, we introduce a new research problem: how to estimate the image segmentation difficulty level without actually performing image segmentation. We propose to formulate it as an estimation problem, and we develop a linear regression model using image features to predict segmentation difficulty level. Different image features, including graytone, color, gradient, and texture features are tested as the predictive variables, and the segmentation algorithm performance measure is the response variable. We use the benchmark images of the Berkeley segmentation dataset with corresponding F-measures to fit, test, and choose the optimal model. Additional standard image datasets are used to further verify the model's applicability to a variety of images. A new feature that combines information from the log histogram of log gradient and the local binary pattern histogram is a good predictor and provides the best balance of predictive performance and model complexity. Inspired by the success of MRF models for solving object segmentation problems, we formulate the binarization problem in this framework. We represent the pixels in a document image as random variables in an MRF, and introduce a new energy (or cost) function on these variables. Each variable takes a foreground or background label, and the quality of the binarization (or labelling) is determined by the value of the energy function. We minimize the energy function, i.e. find the optimal binarization, using an iterative graph cut scheme. Our model is robust to variations in foreground and background colours as we use a Gaussian Mixture Model in the energy function. In addition, our algorithm is efficient to compute, and adapts to a variety of document images. We show results on word images from the challenging ICDAR 2003 dataset, and compare our performance with previously reported methods. Our approach shows significant improvement in pixel level accuracy as well as OCR accuracy.