Tony F. Chan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Tony F. Chan has a total of 328 co-authors. Here are the top co-authors by number of shared publications:
- Paul Thompson
Imaging Genetics Center, Mark and Mary Stevens Neuroimaging & Informatics Institute, Keck School of Medicine of the University of Southern California, Marina del Rey, California, USA
26 shared publications - Lok Ming Lui
Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, China
20 shared publications Yalin Wang
17 shared publicationsXianfeng Gu
State University of New York at Stony Brook, Department of Computer Science, Room 2425, Computer Science Building, State University of New York at Stony Brook, 11794-4400, USA
16 shared publicationsShing-Tung Yau
Harvard University
14 shared publications- Xue-Cheng Tai
Norwegian Research Center, Bergen, Norway
12 shared publications
Latest Publications
- 25 November 2021
- Published by Taylor & Francis
- p. 191-207
ISO 14971: Application of Risk Management to Medical Devices
The development of ISO 14971 was not carried out in a vacuum but instead was shaped by precedent activities in the European Union (EU) to establish risk management standards quite early in the 1990s. The first step made by the EU was the publication in 1997 of a European Standard, EN (European Norm) 1441 on Risk Analysis for Medical Devices. The framework focused on using a specific set of methods called Failure Mode and Effect Analysis (FMEA), for medical device risk analysis. ISO adopted this European Standard in 1997, when it essentially duplicated its publication under the title “Medical Device—Risk Analysis,” ISO 14971-1. This standard was useful for prioritizing activities but remained incomplete because of its focus on the particular use of a single approach, 192namely FMEA. Thus, a working group was formed to incorporate risk management practices already defined in the IEC 60601 Standard Series, a set of standards focusing on medical electrical equipment, into its new international standard, designated as ISO 14971, in 2000. This standard then replaced the ISO/IEC 14971-1 standard and was recognized as both a European-harmonized standard (GHTF SG3/N15R8:2005 [1]) and an FDA-recognized standard. It emphasized a more complete risk management framework, shown in Fig. 16.1.
- 25 November 2021
- Published by Taylor & Francis
- p. 191-207
ISO 14971: Application of Risk Management to Medical Devices
The development of ISO 14971 was not carried out in a vacuum but instead was shaped by precedent activities in the European Union (EU) to establish risk management standards quite early in the 1990s. The first step made by the EU was the publication in 1997 of a European Standard, EN (European Norm) 1441 on Risk Analysis for Medical Devices. The framework focused on using a specific set of methods called Failure Mode and Effect Analysis (FMEA), for medical device risk analysis. ISO adopted this European Standard in 1997, when it essentially duplicated its publication under the title “Medical Device—Risk Analysis,” ISO 14971-1. This standard was useful for prioritizing activities but remained incomplete because of its focus on the particular use of a single approach, 192namely FMEA. Thus, a working group was formed to incorporate risk management practices already defined in the IEC 60601 Standard Series, a set of standards focusing on medical electrical equipment, into its new international standard, designated as ISO 14971, in 2000. This standard then replaced the ISO/IEC 14971-1 standard and was recognized as both a European-harmonized standard (GHTF SG3/N15R8:2005 [1]) and an FDA-recognized standard. It emphasized a more complete risk management framework, shown in Fig. 16.1.
- Open Access
- 1 January 2018
- Published by International Press of Boston in Annals of Mathematical Sciences and Applications
- Vol. 3 (1) , 255-286
New region force for variational models in image segmentation and high dimensional data clustering
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- 1 January 2018
- Published by International Press of Boston in Annals of Mathematical Sciences and Applications
- Vol. 3 (1) , 255-286
Open AccessNew region force for variational models in image segmentation and high dimensional data clustering
International Press of Boston - publishers of scholarly mathematical and scientific journals and books
- Open Access
Guarantees of Riemannian Optimization for Low Rank Matrix Completion
We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $n\times n$ rank $r$ matrix are sampled independently and uniformly with replacement. We first prove that with high probability the Riemannian gradient descent and conjugate gradient descent algorithms initialized by one step hard thresholding are guaranteed to converge linearly to the measured matrix provided \begin{align*} m\geq C_\kappa n^{1.5}r\log^{1.5}(n), \end{align*} where $C_\kappa$ is a numerical constant depending on the condition number of the underlying matrix. The sampling complexity has been further improved to \begin{align*} m\geq C_\kappa nr^2\log^{2}(n) \end{align*} via the resampled Riemannian gradient descent initialization. The analysis of the new initialization procedure relies on an asymmetric restricted isometry property of the sampling operator and the curvature of the low rank matrix manifold. Numerical simulation shows that the algorithms are able to recover a low rank matrix from nearly the minimum number of measurements.Open AccessGuarantees of Riemannian Optimization for Low Rank Matrix Completion
We study the Riemannian optimization methods on the embedded manifold of low rank matrices for the problem of matrix completion, which is about recovering a low rank matrix from its partial entries. Assume $m$ entries of an $n\times n$ rank $r$ matrix are sampled independently and uniformly with replacement. We first prove that with high probability the Riemannian gradient descent and conjugate gradient descent algorithms initialized by one step hard thresholding are guaranteed to converge linearly to the measured matrix provided \begin{align*} m\geq C_\kappa n^{1.5}r\log^{1.5}(n), \end{align*} where $C_\kappa$ is a numerical constant depending on the condition number of the underlying matrix. The sampling complexity has been further improved to \begin{align*} m\geq C_\kappa nr^2\log^{2}(n) \end{align*} via the resampled Riemannian gradient descent initialization. The analysis of the new initialization procedure relies on an asymmetric restricted isometry property of the sampling operator and the curvature of the low rank matrix manifold. Numerical simulation shows that the algorithms are able to recover a low rank matrix from nearly the minimum number of measurements. - Open Access
Guarantees of Riemannian Optimization for Low Rank Matrix Recovery
We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The algorithms are first interpreted as iterative hard thresholding algorithms with subspace projections. Based on this connection, we show that provided the restricted isometry constant $R_{3r}$ of the sensing operator is less than $C_\kappa /\sqrt{r}$, the Riemannian gradient descent algorithm and a restarted variant of the Riemannian conjugate gradient algorithm are guaranteed to converge linearly to the underlying rank $r$ matrix if they are initialized by one step hard thresholding. Empirical evaluation shows that the algorithms are able to recover a low rank matrix from nearly the minimum number of measurements necessary.Open AccessGuarantees of Riemannian Optimization for Low Rank Matrix Recovery
We establish theoretical recovery guarantees of a family of Riemannian optimization algorithms for low rank matrix recovery, which is about recovering an $m\times n$ rank $r$ matrix from $p < mn$ number of linear measurements. The algorithms are first interpreted as iterative hard thresholding algorithms with subspace projections. Based on this connection, we show that provided the restricted isometry constant $R_{3r}$ of the sensing operator is less than $C_\kappa /\sqrt{r}$, the Riemannian gradient descent algorithm and a restarted variant of the Riemannian conjugate gradient algorithm are guaranteed to converge linearly to the underlying rank $r$ matrix if they are initialized by one step hard thresholding. Empirical evaluation shows that the algorithms are able to recover a low rank matrix from nearly the minimum number of measurements necessary. - 1 January 2015
- Published by Springer Nature
- p. 1501-1537
Numerical Methods and Applications in Total Variation Image Restoration
- 1 January 2015
- Published by Springer Nature
- p. 1501-1537
Numerical Methods and Applications in Total Variation Image Restoration
- 1 January 2015
- Published by Springer Nature
- p. 1539-1597
Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration
- 1 January 2015
- Published by Springer Nature
- p. 1539-1597
Mumford and Shah Model and Its Applications to Image Segmentation and Image Restoration
- 7 August 2014
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Pattern Analysis and Machine Intelligence
- Vol. 37 (4) , 890-897
Normal Estimation of a Transparent Object Using a Video
Reconstructing transparent objects is a challenging problem. While producing reasonable results for quite complex objects, existing approaches require custom calibration or somewhat expensive labor to achieve high precision. When an overall shape preserving salient and fine details is sufficient, we show in this paper a significant step toward solving the problem when the object's silhouette is available and simple user interaction is allowed, by using a video of a transparent object shot under varying illumination. Specifically, we estimate the normal map of the exterior surface of a given solid transparent object, from which the surface depth can be integrated. Our technical contribution lies in relating this normal estimation problem to one of graph-cut segmentation. Unlike conventional formulations, however, our graph is dual-layered, since we can see a transparent object's foreground as well as the background behind it. Quantitative and qualitative evaluation are performed to verify the efficacy of this practical solution.
- 7 August 2014
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Pattern Analysis and Machine Intelligence
- Vol. 37 (4) , 890-897
Normal Estimation of a Transparent Object Using a Video
Reconstructing transparent objects is a challenging problem. While producing reasonable results for quite complex objects, existing approaches require custom calibration or somewhat expensive labor to achieve high precision. When an overall shape preserving salient and fine details is sufficient, we show in this paper a significant step toward solving the problem when the object's silhouette is available and simple user interaction is allowed, by using a video of a transparent object shot under varying illumination. Specifically, we estimate the normal map of the exterior surface of a given solid transparent object, from which the surface depth can be integrated. Our technical contribution lies in relating this normal estimation problem to one of graph-cut segmentation. Unlike conventional formulations, however, our graph is dual-layered, since we can see a transparent object's foreground as well as the background behind it. Quantitative and qualitative evaluation are performed to verify the efficacy of this practical solution.
- 2 April 2014
- Published by Springer Nature
- p. 104-118
A Fast Algorithm for a Mean Curvature Based Image Denoising Model Using Augmented Lagrangian Method
- 2 April 2014
- Published by Springer Nature
- p. 104-118
A Fast Algorithm for a Mean Curvature Based Image Denoising Model Using Augmented Lagrangian Method
- 27 August 2013
- Published by Springer Nature in Journal of Mathematical Imaging and Vision
- Vol. 49 (1) , 191-201
Multi-class Transductive Learning Based on ℓ 1 Relaxations of Cheeger Cut and Mumford-Shah-Potts Model
- 27 August 2013
- Published by Springer Nature in Journal of Mathematical Imaging and Vision
- Vol. 49 (1) , 191-201
Multi-class Transductive Learning Based on ℓ 1 Relaxations of Cheeger Cut and Mumford-Shah-Potts Model
- 16 April 2013
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 57 (2) , 414-438
Image Segmentation Using Euler’s Elastica as the Regularization
- 16 April 2013
- Published by Springer Nature in Journal of Scientific Computing
- Vol. 57 (2) , 414-438
Image Segmentation Using Euler’s Elastica as the Regularization