Xue-Cheng Tai spends much of his time researching Mathematical optimization, Mathematical analysis, Algorithm, Augmented Lagrangian method and Partial differential equation. His work on Iterative method as part of general Mathematical optimization study is frequently linked to Continuous optimization, bridging the gap between disciplines. His work deals with themes such as Level set method, Image restoration and Piecewise, which intersect with Algorithm.
The study incorporates disciplines such as Deblurring, Minification, Quadratic equation, Total variation denoising and Applied mathematics in addition to Augmented Lagrangian method. His studies deal with areas such as Image and Dual as well as Applied mathematics. Xue-Cheng Tai has researched Partial differential equation in several fields, including Noise reduction, Inverse problem and Pattern recognition.
His primary areas of investigation include Algorithm, Mathematical optimization, Image segmentation, Augmented Lagrangian method and Image processing. His biological study spans a wide range of topics, including Level set, Image restoration, Domain decomposition methods and Inpainting. His Mathematical optimization study combines topics in areas such as Regular polygon, Convex optimization, Cut and Applied mathematics.
He works mostly in the field of Image segmentation, limiting it down to topics relating to Piecewise and, in certain cases, Inverse problem, Constant, Total variation denoising and Classification of discontinuities. His Augmented Lagrangian method research includes elements of Fast Fourier transform, Geometry, Image, Euler's formula and Topology. His Image processing research is multidisciplinary, incorporating perspectives in Smoothing, Curvature and Range.
His primary areas of study are Algorithm, Image segmentation, Image processing, Regularization and Artificial intelligence. His Algorithm research integrates issues from Object, Level set, Piecewise and Minification. His study explores the link between Image segmentation and topics such as Gradient method that cross with problems in Feature.
His Image processing research is multidisciplinary, relying on both Range, Curvature, Smoothing and Euler's formula. Xue-Cheng Tai focuses mostly in the field of Range, narrowing it down to matters related to Nonlinear system and, in some cases, Applied mathematics. In his research, Convolution, Boundary and Frequency domain is intimately related to Pattern recognition, which falls under the overarching field of Artificial intelligence.
Xue-Cheng Tai mostly deals with Artificial intelligence, Image segmentation, Segmentation, Image processing and Pattern recognition. His work carried out in the field of Artificial intelligence brings together such families of science as Computer vision and Laplace operator. His Image segmentation research incorporates themes from Algorithm, Dykstra's projection algorithm and Regular polygon.
His Image processing study frequently draws connections between adjacent fields such as Range. His Range research is multidisciplinary, incorporating elements of Euler's formula, Operator splitting, Applied mathematics and Minification. Softmax function and Convolution is closely connected to Regularization in his research, which is encompassed under the umbrella topic of Pattern recognition.
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Noise removal using fourth-order partial differential equation with applications to medical magnetic resonance images in space and time
M. Lysaker;A. Lundervold;Xue-Cheng Tai.
IEEE Transactions on Image Processing (2003)
Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models
Chunlin Wu;Xue-Cheng Tai.
Siam Journal on Imaging Sciences (2010)
A binary level set model and some applications to Mumford-Shah image segmentation
J. Lie;M. Lysaker;Xue-Cheng Tai.
IEEE Transactions on Image Processing (2006)
Scale Space and Variational Methods in Computer Vision
Xue-Cheng Tai;Knut Mørken;Marius Lysaker;Knut-Andreas Lie.
Lecture Notes in Computer Science (2009)
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
Marius Lysaker;Xue-Cheng Tai.
International Journal of Computer Vision (2006)
A study on continuous max-flow and min-cut approaches
Jing Yuan;Egil Bae;Xue-Cheng Tai.
computer vision and pattern recognition (2010)
Noise removal using smoothed normals and surface fitting
M. Lysaker;S. Osher;Xue-Cheng Tai.
IEEE Transactions on Image Processing (2004)
A variant of the level set method and applications to image segmentation
Johan Lie;Marius Lysaker;Xue Cheng Tai.
Mathematics of Computation (2006)
Electrical impedance tomography using level set representation and total variational regularization
Eric T. Chung;Tony F. Chan;Xue-Cheng Tai.
Journal of Computational Physics (2005)
Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients
Tony F. Chan;Xue-Cheng Tai.
Journal of Computational Physics (2004)
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