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Faqiang Wang

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Computer Vision Machine Learning

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preprint2026arXiv

Continuous-tone Simple Points: An $\ell_0$-Norm of Cyclic Gradient for Topology-Preserving Data-Driven Image Segmentation

Topological features play an essential role in ensuring geometric plausibility and structural consistency in image analysis tasks such as segmentation and skeletonization. However, integrating topology-preserving learning based on simple points into deep learning tasks remains challenging, as existing simple point detection methods are confined to binary images and are non-differentiable, rendering them incompatible with gradient-based optimization in modern deep learning. Moreover, morphological and purely data-driven approaches often fail to guaranty topological consistency. To address these limitations, we propose a novel method that directly computes simple points on continuous-valued images, enabling differentiable topological inference. Building on this theory, we develop an efficient skeleton extraction algorithm that preserves topological structures in binary and continuous-valued images. Furthermore, we design a variational model that enforces topological constraints by preserving topologically non-removable (i.e., non-simple) points, which can be seamlessly integrated into any deep neural network segmentation with softmax or sigmoid outputs. Experimental results demonstrate that the proposed approach effectively improves topological integrity and structural accuracy across multiple benchmarks. The codes are available in https://github.com/levnsio/CSP.

preprint2020arXiv

A Variational Image Segmentation Model based on Normalized Cut with Adaptive Similarity and Spatial Regularization

Image segmentation is a fundamental research topic in image processing and computer vision. In the last decades, researchers developed a large number of segmentation algorithms for various applications. Amongst these algorithms, the Normalized cut (Ncut) segmentation method is widely applied due to its good performance. The Ncut segmentation model is an optimization problem whose energy is defined on a specifically designed graph. Thus, the segmentation results of the existing Ncut method are largely dependent on a pre-constructed similarity measure on the graph since this measure is usually given empirically by users. This flaw will lead to some undesirable segmentation results. In this paper, we propose a Ncut-based segmentation algorithm by integrating an adaptive similarity measure and spatial regularization. The proposed model combines the Parzen-Rosenblatt window method, non-local weights entropy, Ncut energy, and regularizer of phase field in a variational framework. Our method can adaptively update the similarity measure function by estimating some parameters. This adaptive procedure enables the proposed algorithm finding a better similarity measure for classification than the Ncut method. We provide some mathematical interpretation of the proposed adaptive similarity from multi-viewpoints such as statistics and convex optimization. In addition, the regularizer of phase field can guarantee that the proposed algorithm has a robust performance in the presence of noise, and it can also rectify the similarity measure with a spatial priori. The well-posed theory such as the existence of the minimizer for the proposed model is given in the paper. Compared with some existing segmentation methods such as the traditional Ncut-based model and the classical Chan-Vese model, the numerical experiments show that our method can provide promising segmentation results.

preprint2015arXiv

Iterated Support Vector Machines for Distance Metric Learning

Distance metric learning aims to learn from the given training data a valid distance metric, with which the similarity between data samples can be more effectively evaluated for classification. Metric learning is often formulated as a convex or nonconvex optimization problem, while many existing metric learning algorithms become inefficient for large scale problems. In this paper, we formulate metric learning as a kernel classification problem, and solve it by iterated training of support vector machines (SVM). The new formulation is easy to implement, efficient in training, and tractable for large-scale problems. Two novel metric learning models, namely Positive-semidefinite Constrained Metric Learning (PCML) and Nonnegative-coefficient Constrained Metric Learning (NCML), are developed. Both PCML and NCML can guarantee the global optimality of their solutions. Experimental results on UCI dataset classification, handwritten digit recognition, face verification and person re-identification demonstrate that the proposed metric learning methods achieve higher classification accuracy than state-of-the-art methods and they are significantly more efficient in training.

preprint2013arXiv

A Kernel Classification Framework for Metric Learning

Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several state-of-the-art metric learning methods, such as large margin nearest neighbor (LMNN) and information theoretic metric learning (ITML), into a kernel classification framework. First, doublets and triplets are constructed from the training samples, and a family of degree-2 polynomial kernel functions are proposed for pairs of doublets or triplets. Then, a kernel classification framework is established, which can not only generalize many popular metric learning methods such as LMNN and ITML, but also suggest new metric learning methods, which can be efficiently implemented, interestingly, by using the standard support vector machine (SVM) solvers. Two novel metric learning methods, namely doublet-SVM and triplet-SVM, are then developed under the proposed framework. Experimental results show that doublet-SVM and triplet-SVM achieve competitive classification accuracies with state-of-the-art metric learning methods such as ITML and LMNN but with significantly less training time.