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基于三路径网络的医学图像分割方法

模式识别与人工智能 2024年第1期37卷 1-12页

作者：蒋清婷叶海良曹飞龙中国计量大学理学院应用数学系杭州310018

卷积神经网络由于强大的特征提取能力在医学图像分割任务上取得一定进展,但仍需提升边缘分割的准确性.为此,文中提出基于边缘选择图推理的三路径网络,包括目标定位路径、边缘选择路径和细化路径.在目标定位路径中,设计多尺度特征融合模... 详细信息

卷积神经网络由于强大的特征提取能力在医学图像分割任务上取得一定进展,但仍需提升边缘分割的准确性.为此,文中提出基于边缘选择图推理的三路径网络,包括目标定位路径、边缘选择路径和细化路径.在目标定位路径中,设计多尺度特征融合模块,聚合高级特征,实现病变区域的定位.在边缘选择路径中,构造边缘选择图推理模块,用于低级特征的边缘筛选,并进行图推理,保证病变区域的边缘形状.在细化路径中,建立渐进式组级细化模块,逐步细化不同尺度特征的结构信息与细节信息.此外,引入融合加权Focal Tversky损失和加权交并比损失的复合损失,减轻类不平衡的影响.在公开数据集上的实验表明,文中方法性能较优.

关键词：图神经网络医学图像分割深度学习边缘学习

Random Sampling Scattered Data with Multivariate Bernstein Polynomials

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Chinese Annals of Mathematics,Series B 2014年第4期35卷 607-618页

作者： feilong cao Sheng XIA Department of Mathematics China Jiliang University

In this paper, the multivariate Bernstein polynomials defined on a simplex are viewed as sampling operators, and a generalization by allowing the sampling operators to take place at scattered sites is studied. Both stochastic and deterministic aspects are applied in the study. On the stochastic aspect, a Chebyshev type estimate for the sampling operators is established. On the deterministic aspect, combining the theory of uniform distribution and the discrepancy method, the rate of approximating continuous fimction and Lp convergence for these operators are studied, respectively.

关键词： Approximation Bernstein polynomials Random sampling Scattereddata

Spherical Scattered Data Quasi-interpolation by Gaussian Radial Basis Function

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Chinese Annals of Mathematics,Series B 2015年第3期36卷 401-412页

作者： Zhixiang CHEN feilong cao Department of Mathematics Shaoxing University Department of Mathematics China Jiliang University

Since the spherical Gaussian radial function is strictly positive definite, the authors use the linear combinations of translations of the Gaussian kernel to interpolate the scattered data on spheres in this article. Seeing that target functions axe usually outside the native spaces, and that one has to solve a large scaled system of linear equations to obtain combinatorial coefficients of interpolant functions, the authors first probe into some problems about interpolation with Gaussian radial functions. Then they construct quasi- interpolation operators by Gaussian radial function, and get the degrees of approximation. Moreover, they show the error relations between quasi-interpolation and interpolation when they have the same basis functions. Finally, the authors discuss the construction and approximation of the quasi-interpolant with a local support function.

关键词： Scattered data Approximation Spherical Gaussian radial basis function Modulus of continuity

Adaptive sparse and dense hybrid representation with nonconvex optimization

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Frontiers of Computer Science 2020年第4期14卷 65-78页

作者： Xuejun WANG feilong cao Wenjian WANG School of Computer Science and Technology Shanxi UniversityTaiyuan030006China School of Science China Jiliang UniversityHangzhou310018China Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education Taiyuan030006China

Sparse representation has been widely used in signal processing,pattern recognition and computer vision *** achievements have been made in both theoretical researches and practical ***,there are two limitations on the application of *** is that sufficient training samples are required for each class,and the other is that samples should be *** order to alleviate above problems,a sparse and dense hybrid representation(SDR)framework has been proposed,where the training dictionary is decomposed into a class-specific dictionary and a non-class-specific *** putsℓ1 constraint on the coefficients of class-specific ***,it over-emphasizes the sparsity and overlooks the correlation information in class-specific dictionary,which may lead to poor classification *** overcome this disadvantage,an adaptive sparse and dense hybrid representation with non-convex optimization(ASDR-NO)is proposed in this *** trace norm is adopted in class-specific dictionary,which is different from general *** doing so,the dictionary structure becomes adaptive and the representation ability of the dictionary will be ***,a non-convex surrogate is used to approximate the rank function in dictionary decomposition in order to avoid a suboptimal solution of the original rank minimization,which can be solved by iteratively reweighted nuclear norm(IRNN)*** experiments conducted on benchmark data sets have verified the effectiveness and advancement of the proposed algorithm compared with the state-of-the-art sparse representation methods.

关键词： sparse representation trace norm nonconvex optimization low rank matrix recovery iteratively reweighted nuclear norm

An oracle inequality for regularized risk minimizers with strongly mixing observations

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Frontiers of Mathematics in China 2013年第2期8卷 301-315页

作者： feilong cao Xing XING Institute of Metrology and Computational Science China Jiliang UniversityHangzhou 310018 China

We establish a general oracle inequality for regularized risk minimizers with strongly mixing observations, and apply this inequality to support vector machine （SVM） type algorithms. The obtained main results extend the previous known results for independent and identically distributed samples to the case of exponentially strongly mixing observations.

关键词： Oracle inequality exponentially strongly mixing regularized risk minimizer

Cubature Formula for Spherical Basis Function Networks

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Chinese Annals of Mathematics,Series B 2012年第6期33卷 807-814页

作者： Shaobo LIN feilong cao Zongben XU Xiaofei GUO Institute of Information and System Sciences Xi'an Jiaotong University Institute of Metrology and Computational Science China Jiliang University

Some mathematical models in geophysics and graphic processing need to compute integrals with scattered data on the *** cubature formula plays an important role in computing these spherical *** paper is devoted to establishing an exact positive cubature formula for spherical basis function *** authors give an existence proof of the exact positive cubature formula for spherical basis function networks,and prove that the cubature points needed in the cubature formula are not larger than the number of the scattered data.

关键词： Cubature formula Spherical basis function Scattered data

The essential rate of approximation for radial function manifold

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Science China Mathematics 2011年第9期54卷 1985-1994页

作者： LIN ShaoBo cao feilong XU ZongBeni Institute for Information and System Sciences Xi'an Jiaotong University Xi'an 710049 China Institute of Metrology and Computational Sciences China Jiliang University Hangzhou 310018 China

In this paper, we investigate the radial function manifolds generated by a linear combination of radial functions. Let Wp^r（B^d） be the usual Sobolev class of functions on the unit ball 54. We study the deviation from the radial function manifolds to WP^r（b^d）. Our results show that the upper and lower bounds of approximation by a linear combination of radial functions are asymptotically identical. We also find that the radial function manifolds and ridge function manifolds generated by a linear combination of ridge functions possess the same rate of approximation.

关键词： radial function rate of approximation Sobolev class ridge function

Lower estimation of approximation rate for neural networks

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Science in China(Series F) 2009年第8期52卷 1321-1327页

作者： cao feilong ZHANG YongQuan XU ZongBen College of Science China Jiliang University Hangzhou 310018 China Institute of Information and System Sciences Xi'an Jiaotong University Xi'an 710049 China

Let SFd and ∏φ,n,d ={∑j^n=1bjφ（wj.x＋θj）：bj,θj∈R,wj∈R^d} be the set of periodic and Lebesgue＇s square-integrable functions and the set of feedforward neural network （FNN） functions, respectively. Denote by dist （SFd , ∏φ,n,d） the deviation of the set SFd from the set ∏φ,n,d. A main purpose of this paper is to estimate the deviation. In particular, based on the Fourier transforms and the theory of approximation, a lower estimation for dist （SFd and ∏φ,n,d） is proved. That is, dist（SFd and ∏φ,n,d） ≥C/（nlog2n）1/2. The obtained estimation depends only on the number of neuron in the hidden layer, and is independent of the approximated target functions and dimensional number of input. This estimation also reveals the relationship between the approximation rate of FNNs and the topology structure of hidden layer.

关键词： feedforward neural networks approximation topology structure of hidden layer rate lower

Learning rates of regularized regression on the unit sphere

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Science China Mathematics 2013年第4期56卷 861-876页

作者： cao feilong LIN ShaoBo CHANG XiangYu XU ZongBen Institute of Metrology and Computational Science China Jiliang University Institute for Information and System Sciences Xi'an Jiaotong University

This paper addresses the learning algorithm on the unit *** main purpose is to present an error analysis for regression generated by regularized least square algorithms with spherical harmonics *** excess error can be estimated by the sum of sample errors and regularization *** study shows that by introducing a suitable spherical harmonics kernel,the regularization parameter can decrease arbitrarily fast with the sample size.

关键词： sphere regularized regression spherical harmonics kernel rate of convergence