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Image matting is of great importance in both computer vision and graphics applications. Most existing state-of-the-art techniques rely on large sparse matrices such as the matting Laplacian. However, solving these linear systems is often time-consuming, which is unfavored for the user interaction. In this paper, we propose a fast method for high quality matting. We first derive an efficient algorithm...
Dimensionality reduction plays a fundamental role in data processing, for which principal component analysis (PCA) is widely used. In this paper, we develop the Laplacian PCA (LPCA) algorithm which is the extension of PCA to a more general form by locally optimizing the weighted scatter. In addition to the simplicity of PCA, the benefits brought by LPCA are twofold: the strong robustness against noise...
Structural perception of data plays a fundamental role in pattern analysis and machine learning. In this paper, we develop a new structural perception of data based on local contexts. We first identify the contextual set of a point by finding its nearest neighbors. Then the contextual distance between the point and one of its neighbors is defined by the difference between their contribution to the...
Discriminant feature extraction plays a fundamental role in pattern recognition. In this paper, we propose the linear Laplacian discrimination (LLD) algorithm/or discriminant feature extraction. LLD is an extension of linear discriminant analysis (LDA). Our motivation is to address the issue that LDA cannot work well in cases where sample spaces are non-Euclidean. Specifically, we define the within-class...
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