Piecewise Linear Patch Reconstruction for Segmentation and Description of Non-smooth Image Structures

In this paper, we propose a unified energy minimization model for the segmentation of non-smooth image structures. The energy of piecewise linear patch reconstruction is considered as an objective measure of the quality of the segmentation of non-smooth structures. The segmentation is achieved by minimizing the single energy without any separate process of feature extraction. We also prove that the error of segmentation is bounded by the proposed energy functional, meaning that minimizing the proposed energy leads to reducing the error of segmentation. As a by-product, our method produces a dictionary of optimized orthonormal descriptors for each segmented region. The unique feature of our method is that it achieves the simultaneous segmentation and description for non-smooth image structures under the same optimization framework. The experiments validate our theoretical claims and show the clear superior performance of our methods over other related methods for segmentation of various image textures. We show that our model can be coupled with the piecewise smooth model to handle both smooth and non-smooth structures, and we demonstrate that the proposed model is capable of coping with multiple different regions through the one-against-all strategy

Two Criteria for Model Selection in Multiclass Support Vector Machines

Practical applications call for efficient model selection criteria for multiclass support vector machine (SVM) classification. To solve this problem, this paper develops two model selection criteria by combining or redefining the radius–margin bound used in binary SVMs. The combination is justified by linking the test error rate of a multiclass SVM with that of a set of binary SVMs. The redefinition, which is relatively heuristic, is inspired by the conceptual relationship between the radius–margin bound and the class separability measure. Hence, the two criteria are developed from the perspective of model selection rather than a generalization of the radius–margin bound for multiclass SVMs. As demonstrated by extensive experimental study, the minimization of these two criteria achieves good model selection on most data sets. Compared with the k-fold cross validation which is often regarded as a benchmark, these two criteria give rise to comparable performance with much less computational overhead, particularly when a large number of model parameters are to be optimized

Optimization of multiple view stereo vision

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