Models, code, and papers for "Xianfeng Gu":

LMap: Shape-Preserving Local Mappings for Biomedical Visualization

Oct 25, 2018
Saad Nadeem, Xianfeng Gu, Arie Kaufman

Visualization of medical organs and biological structures is a challenging task because of their complex geometry and the resultant occlusions. Global spherical and planar mapping techniques simplify the complex geometry and resolve the occlusions to aid in visualization. However, while resolving the occlusions these techniques do not preserve the geometric context, making them less suitable for mission-critical biomedical visualization tasks. In this paper, we present a shape-preserving local mapping technique for resolving occlusions locally while preserving the overall geometric context. More specifically, we present a novel visualization algorithm, LMap, for conformally parameterizing and deforming a selected local region-of-interest (ROI) on an arbitrary surface. The resultant shape-preserving local mappings help to visualize complex surfaces while preserving the overall geometric context. The algorithm is based on the robust and efficient extrinsic Ricci flow technique, and uses the dynamic Ricci flow algorithm to guarantee the existence of a local map for a selected ROI on an arbitrary surface. We show the effectiveness and efficacy of our method in three challenging use cases: (1) multimodal brain visualization, (2) optimal coverage of virtual colonoscopy centerline flythrough, and (3) molecular surface visualization.

* S. Nadeem, X. Gu, and A. Kaufman. LMap: Shape-Preserving Local Mappings for Biomedical Visualization. IEEE Transactions on Visualization and Computer Graphics, 24(12):3111-3122, 2018 
* IEEE Transactions on Visualization and Computer Graphics, 24(12): 3111-3122, 2018 (12 pages, 11 figures) 

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Corresponding Supine and Prone Colon Visualization Using Eigenfunction Analysis and Fold Modeling

Oct 20, 2018
Saad Nadeem, Joseph Marino, Xianfeng Gu, Arie Kaufman

We present a method for registration and visualization of corresponding supine and prone virtual colonoscopy scans based on eigenfunction analysis and fold modeling. In virtual colonoscopy, CT scans are acquired with the patient in two positions, and their registration is desirable so that physicians can corroborate findings between scans. Our algorithm performs this registration efficiently through the use of Fiedler vector representation (the second eigenfunction of the Laplace-Beltrami operator). This representation is employed to first perform global registration of the two colon positions. The registration is then locally refined using the haustral folds, which are automatically segmented using the 3D level sets of the Fiedler vector. The use of Fiedler vectors and the segmented folds presents a precise way of visualizing corresponding regions across datasets and visual modalities. We present multiple methods of visualizing the results, including 2D flattened rendering and the corresponding 3D endoluminal views. The precise fold modeling is used to automatically find a suitable cut for the 2D flattening, which provides a less distorted visualization. Our approach is robust, and we demonstrate its efficiency and efficacy by showing matched views on both the 2D flattened colons and in the 3D endoluminal view. We analytically evaluate the results by measuring the distance between features on the registered colons, and we also assess our fold segmentation against 20 manually labeled datasets. We have compared our results analytically to previous methods, and have found our method to achieve superior results. We also prove the hot spots conjecture for modeling cylindrical topology using Fiedler vector representation, which allows our approach to be used for general cylindrical geometry modeling and feature extraction.

* IEEE Transactions on Visualization and Computer Graphics, 23(1):751-760, 2017 
* IEEE Transactions on Visualization and Computer Graphics, 23(1):751-760, 2017 (11 pages, 13 figures) 

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Variational Wasserstein Clustering

Jul 26, 2018
Liang Mi, Wen Zhang, Xianfeng Gu, Yalin Wang

We propose a new clustering method based on optimal transportation. We solve optimal transportation with variational principles, and investigate the use of power diagrams as transportation plans for aggregating arbitrary domains into a fixed number of clusters. We iteratively drive centroids through target domains while maintaining the minimum clustering energy by adjusting the power diagrams. Thus, we simultaneously pursue clustering and the Wasserstein distances between the centroids and the target domains, resulting in a measure-preserving mapping. We demonstrate the use of our method in domain adaptation, remeshing, and representation learning on synthetic and real data.

* Accepted to ECCV 2018 

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Brenier approach for optimal transportation between a quasi-discrete measure and a discrete measure

Jan 17, 2018
Ying Lu, Liming Chen, Alexandre Saidi, Xianfeng Gu

Correctly estimating the discrepancy between two data distributions has always been an important task in Machine Learning. Recently, Cuturi proposed the Sinkhorn distance which makes use of an approximate Optimal Transport cost between two distributions as a distance to describe distribution discrepancy. Although it has been successfully adopted in various machine learning applications (e.g. in Natural Language Processing and Computer Vision) since then, the Sinkhorn distance also suffers from two unnegligible limitations. The first one is that the Sinkhorn distance only gives an approximation of the real Wasserstein distance, the second one is the `divide by zero' problem which often occurs during matrix scaling when setting the entropy regularization coefficient to a small value. In this paper, we introduce a new Brenier approach for calculating a more accurate Wasserstein distance between two discrete distributions, this approach successfully avoids the two limitations shown above for Sinkhorn distance and gives an alternative way for estimating distribution discrepancy.


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Kernel Estimation from Salient Structure for Robust Motion Deblurring

May 24, 2014
Jinshan Pan, Risheng Liu, Zhixun Su, Xianfeng Gu

Blind image deblurring algorithms have been improving steadily in the past years. Most state-of-the-art algorithms, however, still cannot perform perfectly in challenging cases, especially in large blur setting. In this paper, we focus on how to estimate a good kernel estimate from a single blurred image based on the image structure. We found that image details caused by blurring could adversely affect the kernel estimation, especially when the blur kernel is large. One effective way to eliminate these details is to apply image denoising model based on the Total Variation (TV). First, we developed a novel method for computing image structures based on TV model, such that the structures undermining the kernel estimation will be removed. Second, to mitigate the possible adverse effect of salient edges and improve the robustness of kernel estimation, we applied a gradient selection method. Third, we proposed a novel kernel estimation method, which is capable of preserving the continuity and sparsity of the kernel and reducing the noises. Finally, we developed an adaptive weighted spatial prior, for the purpose of preserving sharp edges in latent image restoration. The effectiveness of our method is demonstrated by experiments on various kinds of challenging examples.

* Signal Processing: Image Communication, 2013 
* This work has been accepted by Signal Processing: Image Communication, 2013 

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Geometric Understanding of Deep Learning

May 31, 2018
Na Lei, Zhongxuan Luo, Shing-Tung Yau, David Xianfeng Gu

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great successes. Unfortunately, the understanding on how it works remains unclear. It has the central importance to lay down the theoretic foundation for deep learning. In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it. We further introduce the concepts of rectified linear complexity for deep neural network measuring its learning capability, rectified linear complexity of an embedding manifold describing the difficulty to be learned. Then we show for any deep neural network with fixed architecture, there exists a manifold that cannot be learned by the network. Finally, we propose to apply optimal mass transportation theory to control the probability distribution in the latent space.


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A Geometric View of Optimal Transportation and Generative Model

Dec 19, 2017
Na Lei, Kehua Su, Li Cui, Shing-Tung Yau, David Xianfeng Gu

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of GAN model, we show that the discriminator computes the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can give the optimal transportation map by a close-form formula. Therefore, it is sufficient to solely optimize the discriminator. This shows the adversarial competition can be avoided, and the computational architecture can be simplified. Preliminary experimental results show the geometric method outperforms WGAN for approximating probability measures with multiple clusters in low dimensional space.


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Robot Coverage Path Planning for General Surfaces Using Quadratic Differentials

Jan 26, 2017
Yu-Yao Lin, Chien-Chun Ni, Na Lei, Xianfeng David Gu, Jie Gao

Robot Coverage Path planning (i.e., provide full coverage of a given domain by one or multiple robots) is a classical problem in the field of robotics and motion planning. The goal is to provide nearly full coverage while also minimize duplicately visited area. In this paper we focus on the scenario of path planning on general surfaces including planar domains with complex topology, complex terrain or general surface in 3D space. The main idea is to adopt a natural, intrinsic and global parametrization of the surface for robot path planning, namely the holomorphic quadratic differentials. Except for a small number of zero points (singularities), each point on the surface is given a uv-coordinates naturally represented by a complex number. We show that natural, efficient robot paths can be obtained by using such coordinate systems. The method is based on intrinsic geometry and thus can be adapted to general surface exploration in 3D.

* 8 pages, 13 figures, IEEE ICRA 2017 

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Mode Collapse and Regularity of Optimal Transportation Maps

Feb 08, 2019
Na lei, Yang Guo, Dongsheng An, Xin Qi, Zhongxuan Luo, Shing-Tung Yau, Xianfeng Gu

This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp\`{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse. According to the regularity theory of Monge-Amp\`{e}re equation, if the support of the target measure is disconnected or just non-convex, the optimal transportation mapping is discontinuous. General DNNs can only approximate continuous mappings. This intrinsic conflict leads to the convergence difficulty and mode collapse in GANs. We test our hypothesis that the supports of real data distribution are in general non-convex, therefore the discontinuity is unavoidable using an Autoencoder combined with discrete optimal transportation map (AE-OT framework) on the CelebA data set. The testing result is positive. Furthermore, we propose to approximate the continuous Brenier potential directly based on discrete Brenier theory to tackle mode collapse. Comparing with existing method, this method is more accurate and effective.


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Latent Space Optimal Transport for Generative Models

Sep 16, 2018
Huidong Liu, Yang Guo, Na Lei, Zhixin Shu, Shing-Tung Yau, Dimitris Samaras, Xianfeng Gu

Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which can be important for datasets such as facial images. A GAN can transform a simple distribution to a latent-space data distribution and thus preserve the manifold structure, but optimizing a GAN involves solving a Min-Max optimization problem, which is difficult and not well understood so far. Therefore, we propose a GAN-like method to transform a simple distribution to a data distribution in the latent space by solving only a minimization problem. This minimization problem comes from training a discriminator between a simple distribution and a latent-space data distribution. Then, we can explicitly formulate an Optimal Transport (OT) problem that computes the desired mapping between the two distributions. This means that we can transform a distribution without solving the difficult Min-Max optimization problem. Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions. Results on the MNIST and the CelebA datasets validate the effectiveness of the proposed method.


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Classification of lung nodules in CT images based on Wasserstein distance in differential geometry

Jun 30, 2018
Min Zhang, Qianli Ma, Chengfeng Wen, Hai Chen, Deruo Liu, Xianfeng Gu, Jie He, Xiaoyin Xu

Lung nodules are commonly detected in screening for patients with a risk for lung cancer. Though the status of large nodules can be easily diagnosed by fine needle biopsy or bronchoscopy, small nodules are often difficult to classify on computed tomography (CT). Recent works have shown that shape analysis of lung nodules can be used to differentiate benign lesions from malignant ones, though existing methods are limited in their sensitivity and specificity. In this work we introduced a new 3D shape analysis within the framework of differential geometry to calculate the Wasserstein distance between benign and malignant lung nodules to derive an accurate classification scheme. The Wasserstein distance between the nodules is calculated based on our new spherical optimal mass transport, this new algorithm works directly on sphere by using spherical metric, which is much more accurate and efficient than previous methods. In the process of deformation, the area-distortion factor gives a probability measure on the unit sphere, which forms the Wasserstein space. From known cases of benign and malignant lung nodules, we can calculate a unique optimal mass transport map between their correspondingly deformed Wasserstein spaces. This transportation cost defines the Wasserstein distance between them and can be used to classify new lung nodules into either the benign or malignant class. To the best of our knowledge, this is the first work that utilizes Wasserstein distance for lung nodule classification. The advantages of Wasserstein distance are it is invariant under rigid motions and scalings, thus it intrinsically measures shape distance even when the underlying shapes are of high complexity, making it well suited to classify lung nodules as they have different sizes, orientations, and appearances.


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Copy-move Forgery Detection based on Convolutional Kernel Network

Jul 05, 2017
Yaqi Liu, Qingxiao Guan, Xianfeng Zhao

In this paper, a copy-move forgery detection method based on Convolutional Kernel Network is proposed. Different from methods based on conventional hand-crafted features, Convolutional Kernel Network is a kind of data-driven local descriptor with the deep convolutional structure. Thanks to the development of deep learning theories and widely available datasets, the data-driven methods can achieve competitive performance on different conditions for its excellent discriminative capability. Besides, our Convolutional Kernel Network is reformulated as a series of matrix computations and convolutional operations which are easy to parallelize and accelerate by GPU, leading to high efficiency. Then, appropriate preprocessing and postprocessing for Convolutional Kernel Network are adopted to achieve copy-move forgery detection. Particularly, a segmentation-based keypoints distribution strategy is proposed and a GPU-based adaptive oversegmentation method is adopted. Numerous experiments are conducted to demonstrate the effectiveness and robustness of the GPU version of Convolutional Kernel Network, and the state-of-the-art performance of the proposed copy-move forgery detection method based on Convolutional Kernel Network.

* 26 pages, 8 figures, submitted to Multimedia Tools and Applications 

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Adversarial Learning for Image Forensics Deep Matching with Atrous Convolution

Sep 08, 2018
Yaqi Liu, Xianfeng Zhao, Xiaobin Zhu, Yun Cao

Constrained image splicing detection and localization (CISDL) is a newly proposed challenging task for image forensics, which investigates two input suspected images and identifies whether one image has suspected regions pasted from the other. In this paper, we propose a novel adversarial learning framework to train the deep matching network for CISDL. Our framework mainly consists of three building blocks: 1) the deep matching network based on atrous convolution (DMAC) aims to generate two high-quality candidate masks which indicate the suspected regions of the two input images, 2) the detection network is designed to rectify inconsistencies between the two corresponding candidate masks, 3) the discriminative network drives the DMAC network to produce masks that are hard to distinguish from ground-truth ones. In DMAC, atrous convolution is adopted to extract features with rich spatial information, the correlation layer based on the skip architecture is proposed to capture hierarchical features, and atrous spatial pyramid pooling is constructed to localize tampered regions at multiple scales. The detection network and the discriminative network act as the losses with auxiliary parameters to supervise the training of DMAC in an adversarial way. Extensive experiments, conducted on 21 generated testing sets and two public datasets, demonstrate the effectiveness of the proposed framework and the superior performance of DMAC.

* 13 pages, 8 figures 

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Image Forgery Localization Based on Multi-Scale Convolutional Neural Networks

Feb 07, 2018
Yaqi Liu, Qingxiao Guan, Xianfeng Zhao, Yun Cao

In this paper, we propose to utilize Convolutional Neural Networks (CNNs) and the segmentation-based multi-scale analysis to locate tampered areas in digital images. First, to deal with color input sliding windows of different scales, a unified CNN architecture is designed. Then, we elaborately design the training procedures of CNNs on sampled training patches. With a set of robust multi-scale tampering detectors based on CNNs, complementary tampering possibility maps can be generated. Last but not least, a segmentation-based method is proposed to fuse the maps and generate the final decision map. By exploiting the benefits of both the small-scale and large-scale analyses, the segmentation-based multi-scale analysis can lead to a performance leap in forgery localization of CNNs. Numerous experiments are conducted to demonstrate the effectiveness and efficiency of our method.

* 7 pages, 6 figures 

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Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction

Nov 03, 2018
Huaxiu Yao, Xianfeng Tang, Hua Wei, Guanjie Zheng, Zhenhui Li

Traffic prediction has drawn increasing attention in AI research field due to the increasing availability of large-scale traffic data and its importance in the real world. For example, an accurate taxi demand prediction can assist taxi companies in pre-allocating taxis. The key challenge of traffic prediction lies in how to model the complex spatial dependencies and temporal dynamics. Although both factors have been considered in modeling, existing works make strong assumptions about spatial dependence and temporal dynamics, i.e., spatial dependence is stationary in time, and temporal dynamics is strictly periodical. However, in practice, the spatial dependence could be dynamic (i.e., changing from time to time), and the temporal dynamics could have some perturbation from one period to another period. In this paper, we make two important observations: (1) the spatial dependencies between locations are dynamic; and (2) the temporal dependency follows daily and weekly pattern but it is not strictly periodic for its dynamic temporal shifting. To address these two issues, we propose a novel Spatial-Temporal Dynamic Network (STDN), in which a flow gating mechanism is introduced to learn the dynamic similarity between locations, and a periodically shifted attention mechanism is designed to handle long-term periodic temporal shifting. To the best of our knowledge, this is the first work that tackles both issues in a unified framework. Our experimental results on real-world traffic datasets verify the effectiveness of the proposed method.

* Accepted by AAAI 2019 

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