8 results on '"Jong Chul Ye"'
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2. Mumford–Shah Loss Functional for Image Segmentation With Deep Learning
- Author
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Boah Kim and Jong Chul Ye
- Subjects
FOS: Computer and information sciences ,Computer Science - Machine Learning ,Similarity (geometry) ,Computer science ,Computer Vision and Pattern Recognition (cs.CV) ,Computer Science - Computer Vision and Pattern Recognition ,Machine Learning (stat.ML) ,02 engineering and technology ,Machine Learning (cs.LG) ,Statistics - Machine Learning ,0202 electrical engineering, electronic engineering, information engineering ,Segmentation ,Characteristic function (convex analysis) ,Artificial neural network ,business.industry ,Deep learning ,Pattern recognition ,Image segmentation ,Computer Graphics and Computer-Aided Design ,Computer Science::Computer Vision and Pattern Recognition ,Softmax function ,Unsupervised learning ,020201 artificial intelligence & image processing ,Artificial intelligence ,business ,Software - Abstract
Recent state-of-the-art image segmentation algorithms are mostly based on deep neural networks, thanks to their high performance and fast computation time. However, these methods are usually trained in a supervised manner, which requires large number of high quality ground-truth segmentation masks. On the other hand, classical image segmentation approaches such as level-set methods are formulated in a self-supervised manner by minimizing energy functions such as Mumford-Shah functional, so they are still useful to help generation of segmentation masks without labels. Unfortunately, these algorithms are usually computationally expensive and often have limitation in semantic segmentation. In this paper, we propose a novel loss function based on Mumford-Shah functional that can be used in deep-learning based image segmentation without or with small labeled data. This loss function is based on the observation that the softmax layer of deep neural networks has striking similarity to the characteristic function in the Mumford-Shah functional. We show that the new loss function enables semi-supervised and unsupervised segmentation. In addition, our loss function can be also used as a regularized function to enhance supervised semantic segmentation algorithms. Experimental results on multiple datasets demonstrate the effectiveness of the proposed method., Comment: Accepted for IEEE Transactions on Image Processing
- Published
- 2020
3. Grid-Free Localization Algorithm Using Low-Rank Hankel Matrix for Super-Resolution Microscopy
- Author
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Michael Unser, Junhong Min, Jong Chul Ye, and Kyong Hwan Jin
- Subjects
0301 basic medicine ,Signal processing ,Rank (linear algebra) ,Computer science ,Super-resolution microscopy ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Iterative reconstruction ,Grid ,Computer Graphics and Computer-Aided Design ,Fluorescence ,03 medical and health sciences ,symbols.namesake ,030104 developmental biology ,Taylor series ,symbols ,Hankel matrix ,Image resolution ,Algorithm ,Software - Abstract
Localization microscopy, such as STORM / PALM, can reconstruct super-resolution images with a nanometer resolution through the iterative localization of fluorescence molecules. Recent studies in this area have focused mainly on the localization of densely activated molecules to improve temporal resolutions. However, higher density imaging requires an advanced algorithm that can resolve closely spaced molecules. Accordingly, sparsitydriven methods have been studied extensively. One of the major limitations of existing sparsity-driven approaches is the need for a fine sampling grid or for Taylor series approximation which may result in some degree of localization bias toward the grid. In addition, prior knowledge of the point-spread function (PSF) is required. To address these drawbacks, here we propose a true grid-free localization algorithm with adaptive PSF estimation. Specifically, based on the observation that sparsity in the spatial domain implies a low rank in the Fourier domain, the proposed method converts source localization problems into Fourier-domain signal processing problems so that a truly gridfree localization is possible. We verify the performance of the newly proposed method with several numerical simulations and a live-cell imaging experiment.
- Published
- 2018
4. Asymptotic global confidence regions for 3-D parametric shape estimation in inverse problems
- Author
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Moulin, Pierre, Jong Chul Ye, and Bresler, Yoram
- Subjects
Maximum likelihood estimates (Statistics) -- Analysis ,Three-dimensional graphics -- Analysis ,Probabilities -- Analysis ,Image processing -- Methods ,Business ,Computers ,Electronics ,Electronics and electrical industries - Abstract
Fundamental performance bounds for statistical estimation of parametric surfaces embedded in [R.sup.3], in which the reconstruction of the shape of binary or homogenous objects could be represented by asymptotic global confidence regions that facilitate geometric inference and optimization of the imaging system is derived. Simulation results reveal the tightness of the resulting bound and the efficiency of the three-dimensional global confidence region approach.
- Published
- 2006
5. Annihilating Filter-Based Low-Rank Hankel Matrix Approach for Image Inpainting
- Author
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Kyong Hwan Jin and Jong Chul Ye
- Subjects
Mathematical optimization ,Matrix completion ,Markov random field ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Inpainting ,Block matrix ,Computer Graphics and Computer-Aided Design ,Matrix decomposition ,Matrix (mathematics) ,Kernel (image processing) ,Computer Science::Computer Vision and Pattern Recognition ,Algorithm ,Hankel matrix ,Software ,Mathematics - Abstract
In this paper, we propose a patch-based image inpainting method using a low-rank Hankel structured matrix completion approach. The proposed method exploits the annihilation property between a shift-invariant filter and image data observed in many existing inpainting algorithms. In particular, by exploiting the commutative property of the convolution, the annihilation property results in a low-rank block Hankel structure data matrix, and the image inpainting problem becomes a low-rank structured matrix completion problem. The block Hankel structured matrices are obtained patch-by-patch to adapt to the local changes in the image statistics. To solve the structured low-rank matrix completion problem, we employ an alternating direction method of multipliers with factorization matrix initialization using the low-rank matrix fitting algorithm. As a side product of the matrix factorization, locally adaptive dictionaries can be also easily constructed. Despite the simplicity of the algorithm, the experimental results using irregularly subsampled images as well as various images with globally missing patterns showed that the proposed method outperforms existing state-of-the-art image inpainting methods.
- Published
- 2015
6. Nonlinear multigrid algorithms for Bayesian optical diffusion tomography
- Author
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Charles A. Bouman, Jong Chul Ye, Rick P. Millane, and Kevin J. Webb
- Subjects
Optimization problem ,medicine.diagnostic_test ,Multiresolution analysis ,ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION ,Image processing ,Iterative reconstruction ,Computer Graphics and Computer-Aided Design ,Multigrid method ,medicine ,Maximum a posteriori estimation ,Tomography ,Optical tomography ,Algorithm ,Software ,Mathematics - Abstract
Optical diffusion tomography is a technique for imaging a highly scattering medium using measurements of transmitted modulated light. Reconstruction of the spatial distribution of the optical properties of the medium from such data is a difficult nonlinear inverse problem. Bayesian approaches are effective, but are computationally expensive, especially for three-dimensional (3-D) imaging. This paper presents a general nonlinear multigrid optimization technique suitable for reducing the computational burden in a range of nonquadratic optimization problems. This multigrid method is applied to compute the maximum a posteriori (MAP) estimate of the reconstructed image in the optical diffusion tomography problem. The proposed multigrid approach both dramatically reduces the required computation and improves the reconstructed image quality.
- Published
- 2001
7. Asymptotic Global Confidence Regions for 3-D Parametric Shape Estimation in Inverse Problems.
- Author
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Jong Chul Ye, Moulin, Pierre, and Bresler, Yoram
- Subjects
- *
PROBABILITY theory , *RANDOM fields , *GAUSSIAN processes , *CURVES , *SIMULATION methods & models , *BINARY number system - Abstract
This paper derives fundamental performance bounds for statistical estimation of parametric surfaces embedded in R3. Unlike conventional pixel-based image reconstruction approaches, our problem is reconstruction of the shape of binary or homogeneous objects. The fundamental uncertainty of such estimation problems can be represented by global confidence regions, which facilitate geometric inference and optimization of the imaging system. Compared to our previous work on global confidence region analysis for curves [two-dimensional (2-D) shapes], computation of the probability that the entire surface estimate lies within the confidence region is more challenging because a surface estimate is an inhomogeneous random field continuously indexed by a 2-D variable. We derive an asymptotic lower bound to this probability by relating it to the exceedence probability of a higher dimensional Gaussian random field, which can, in turn, be evaluated using the tube formula due to Sun. Simulation results demonstrate the tightness of the resulting bound and the usefulness of the three-dimensional global confidence region approach. [ABSTRACT FROM AUTHOR]
- Published
- 2006
- Full Text
- View/download PDF
8. Cramér-Rao Bounds for Parametric Shape Estimation in Inverse Problems.
- Author
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Jong Chul Ye, Bresler, Yoram, and Moulin, Pierre
- Subjects
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IMAGE processing , *MAGNETIC resonance imaging - Abstract
We address the problem of computing fundamental performance bounds for estimation of object boundaries from noisy measurements in inverse problems, when the boundaries are parameterized by a finite number of unknown variables. Our model applies to multiple unknown objects, each with its own unknown gray level, or color, and boundary parameterization, on an arbitrary known background. While such fundamental bounds on the performance of shape estimation algorithms can in principle be derived from the Cramér-Rao lower bounds, very few results have been reported due to the difficulty of computing the derivatives of a functional with respect to shape deformation. In this paper, we provide a general formula for computing CramérRao lower bounds in inverse problems where the observations are related to the object by a general linear transform, followed by a possibly nonlinear and noisy measurement system. As an illustration, we derive explicit formulas for computed tomography, Fourier imaging, and deconvolution problems. The bounds reveal that highly accurate parametric reconstructions are possible in these examples, using severely limited and noisy data. [ABSTRACT FROM AUTHOR]
- Published
- 2003
- Full Text
- View/download PDF
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