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Journal articles on the topic 'Mumford-Shah method'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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1

Thanh, D. N. H., V. B. S. Prasath, N. V. Son, and L. M. Hieu. "An adaptive image inpainting method based on the modified mumford-shah model and multiscale parameter estimation." Computer Optics 43, no. 2 (2019): 251–57. http://dx.doi.org/10.18287/2412-6179-2019-43-2-251-257.

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Image inpainting is a process of filling missing and damaged parts of image. By using the Mumford-Shah image model, the image inpainting can be formulated as a constrained optimization problem. The Mumford-Shah model is a famous and effective model to solve the image inpainting problem. In this paper, we propose an adaptive image inpainting method based on multiscale parameter estimation for the modified Mumford-Shah model. In the experiments, we will handle the comparison with other similar inpainting methods to prove that the combination of classic model such the modified Mumford-Shah model

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2

Fan, Lumin, Lingli Shen, and Xinghua Zuo. "Feature Extraction and Recognition of Medical CT Images Based on Mumford-Shah Model." Advances in Mathematical Physics 2021 (September 23, 2021): 1–13. http://dx.doi.org/10.1155/2021/1545098.

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In this paper, we propose an improved algorithm based on the active contour model Mumford-Shah model for CT images, which is the subject of this study. After analyzing the classical Mumford-Shah model and related improvement algorithms, we found that most of the improvement algorithms start from the initialization strategy of the model and the minimum value solution of the energy generalization function, so we will also improve the classical Mumford-Shah model from these two perspectives. For the initialization strategy of the Mumford-Shah model, we propose to first reduce the dimensionality o

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3

Alberti, Giovanni, Guy Bouchitté, and Gianni Dal Maso. "The calibration method for the mumford-shah functional." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 329, no. 3 (1999): 249–54. http://dx.doi.org/10.1016/s0764-4442(00)88602-4.

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4

MORA, MARIA GIOVANNA. "LOCAL CALIBRATIONS FOR MINIMIZERS OF THE MUMFORD–SHAH FUNCTIONAL WITH A TRIPLE JUNCTION." Communications in Contemporary Mathematics 04, no. 02 (2002): 297–326. http://dx.doi.org/10.1142/s0219199702000646.

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We prove that, if u is a function satisfying all Euler conditions for the Mumford–Shah functional and the discontinuity set of u is given by three line segments meeting at the origin with equal angles, then there exists a neighbourhood U of the origin such that u is a minimizer of the Mumford–Shah functional on U with respect to its own boundary conditions on ∂U. The proof is obtained by using the calibration method.

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Wang, Zhan, Yun Hui Yan, De Wei Dong, and Ke Chen Song. "Texture Segmentation of Natural Images Based on Active Contour Model." Advanced Materials Research 546-547 (July 2012): 553–58. http://dx.doi.org/10.4028/www.scientific.net/amr.546-547.553.

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To segment complex texture natural environment images; the first, the texture features of natural images should be analysed and the texture features should be extracted; The second, texture images segmengtation can be achieved by using Mumford-Shah active contour model, this segmentation model can better process fuzzy, default boundary, and this model can be solved by level set method. This method can express well complex texture signal features of natural images. Through making texture segmentation experiment for standard texture synthesis image and natural environmental image, its results sh

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6

Wang, Hong-Yuan, and Fuhua Chen. "Semisupervised Soft Mumford-Shah Model for MRI Brain Image Segmentation." Applied Computational Intelligence and Soft Computing 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/8508329.

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One challenge of unsupervised MRI brain image segmentation is the central gray matter due to the faint contrast with respect to the surrounding white matter. In this paper, the necessity of supervised image segmentation is addressed, and a soft Mumford-Shah model is introduced. Then, a framework of semisupervised image segmentation based on soft Mumford-Shah model is developed. The main contribution of this paper lies in the development a framework of a semisupervised soft image segmentation using both Bayesian principle and the principle of soft image segmentation. The developed framework cla

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Lin, Guo Xiang, Wei Min Zhou, Yong Hui Tang, and Lin Sheng Li. "Contour Extraction of Inclusion Image with Mumford-Shah Model." Advanced Materials Research 591-593 (November 2012): 2410–13. http://dx.doi.org/10.4028/www.scientific.net/amr.591-593.2410.

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The target contour extraction is one of key questions in computer vision. Because of its intrinsic limitations, the traditional C-V method can not meet the requirements of inclusion image contour extraction. To overcome this shortcoming, this paper introduces image overlay to make some improvements on the C-V methods, which is based on simplified Mumford-Shah, and compares the different contour extraction results caused by traditional method and improved C-V method. The results vindicate the efficiency and feasibility of improved C-V method.

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8

Shah, Nilima, Dhanesh Patel, and Pasi Fränti. "Fast Mumford-Shah Two-Phase Image Segmentation Using Proximal Splitting Scheme." Journal of Applied Mathematics 2021 (April 13, 2021): 1–13. http://dx.doi.org/10.1155/2021/6618505.

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The Mumford-Shah model is extensively used in image segmentation. Its energy functional causes the content of the segments to remain homogeneous and the segment boundaries to become short. However, the problem is that optimization of the functional can be very slow. To attack this problem, we propose a reduced two-phase Mumford-Shah model to segment images having one prominent object. First, initial segmentation is obtained by the k-means clustering technique, further minimizing the Mumford-Shah functional by the Douglas-Rachford algorithm. Evaluation of segmentations with various error metric

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9

Yu Chen. "A Lattice Boltzmann Method for Piece-wise Constant Mumford Shah Model." International Journal of Digital Content Technology and its Applications 5, no. 12 (2011): 339–46. http://dx.doi.org/10.4156/jdcta.vol5.issue12.42.

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10

Yan Nei Law, Hwee Kuan Lee, and A. M. Yip. "A Multiresolution Stochastic Level Set Method for Mumford–Shah Image Segmentation." IEEE Transactions on Image Processing 17, no. 12 (2008): 2289–300. http://dx.doi.org/10.1109/tip.2008.2005823.

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11

Alberti, Giovanni, Guy Bouchitt�, and Gianni Dal Maso. "The calibration method for the Mumford-Shah functional and free-discontinuity problems." Calculus of Variations and Partial Differential Equations 16, no. 3 (2003): 299–333. http://dx.doi.org/10.1007/s005260100152.

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12

Vlachos, Marios, and Evangelos Dermatas. "Finger Vein Segmentation from Infrared Images Based on a Modified Separable Mumford Shah Model and Local Entropy Thresholding." Computational and Mathematical Methods in Medicine 2015 (2015): 1–20. http://dx.doi.org/10.1155/2015/868493.

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A novel method for finger vein pattern extraction from infrared images is presented. This method involves four steps: preprocessing which performs local normalization of the image intensity, image enhancement, image segmentation, and finally postprocessing for image cleaning. In the image enhancement step, an image which will be both smooth and similar to the original is sought. The enhanced image is obtained by minimizing the objective function of a modified separable Mumford Shah Model. Since, this minimization procedure is computationally intensive for large images, a local application of t

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13

Zhi, Zhanjiang, Yi Sun, and Zhi-Feng Pang. "Two-Stage Image Segmentation Scheme Based on Inexact Alternating Direction Method." Numerical Mathematics: Theory, Methods and Applications 9, no. 3 (2016): 451–69. http://dx.doi.org/10.4208/nmtma.2016.m1509.

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AbstractImage segmentation is a fundamental problem in both image processing and computer vision with numerous applications. In this paper, we propose a two-stage image segmentation scheme based on inexact alternating direction method. Specifically, we first solve the convex variant of the Mumford-Shah model to get the smooth solution, the segmentation are then obtained by apply the K-means clustering method to the solution. Some numerical comparisons are arranged to show the effectiveness of our proposed schemes by segmenting many kinds of images such as artificial images, natural images, and

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14

Zhi, Zhanjiang. "An Image Inpainting Method Based on a Convex Variant of the Mumford-Shah Model." Journal of Information and Computational Science 12, no. 11 (2015): 4349–56. http://dx.doi.org/10.12733/jics20106298.

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15

Klann, Esther. "A Mumford–Shah-Like Method for Limited Data Tomography with an Application to Electron Tomography." SIAM Journal on Imaging Sciences 4, no. 4 (2011): 1029–48. http://dx.doi.org/10.1137/100817371.

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16

Zhou, Luoyu, and Zhengbing Zhang. "An image segmentation method based on Mumford–Shah model with mask factor and neighborhood factor." Pattern Analysis and Applications 23, no. 1 (2018): 85–94. http://dx.doi.org/10.1007/s10044-018-0730-3.

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17

Spencer, Jack, and Ke Chen. "Stabilised bias field: segmentation with intensity inhomogeneity." Journal of Algorithms & Computational Technology 10, no. 4 (2016): 302–13. http://dx.doi.org/10.1177/1748301816668025.

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Automatic segmentation in the variational framework is a challenging task within the field of imaging sciences. Achieving robustness is a major problem, particularly for images with high levels of intensity inhomogeneity. The two-phase piecewise-constant case of the Mumford-Shah formulation is most suitable for images with simple and homogeneous features where the intensity variation is limited. However, it has been applied to many different types of synthetic and real images after some adjustments to the formulation. Recent work has incorporated bias field estimation to allow for intensity in

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18

RONDI, LUCA. "Reconstruction in the inverse crack problem by variational methods." European Journal of Applied Mathematics 19, no. 6 (2008): 635–60. http://dx.doi.org/10.1017/s0956792508007729.

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We deal with a variational approach to the inverse crack problem, that is the detection and reconstruction of cracks, and other defects, inside a conducting body by performing boundary measurements of current and voltage type. We formulate such an inverse problem in a free-discontinuity problems framework and propose a novel method for the numerical reconstruction of the cracks by the available boundary data. The proposed method is amenable to numerical computations and it is justified by a convergence analysis, as the error on the measurements goes to zero. We further notice that we use the Γ

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19

Cheng, Cun, and Li Zhang. "An efficient segmentation method based on dynamic graph merging." International Journal of Wavelets, Multiresolution and Information Processing 14, no. 06 (2016): 1650052. http://dx.doi.org/10.1142/s0219691316500521.

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A novel energy functional based on the Mumford–Shah model is established for performing automatic image segmentation. And in order to optimize the global model using graph-based methods, we develop a localized formula. Then, we propose a merging predicate for determining whether an edge connecting two neighboring pixels or regions merge. The dynamic graph merging (DGM) method is applied based on this merging predicate. That is, those edges with large energy merge and the edges with low energy are remained, such that the energy functional is minimized. Compared with other graph-based segmentati

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20

Eslami, Abouzar, Fateme Esfandiarpour, Ali Shakourirad, and Farzam Farahmand. "A MULTISCALE PHASE FIELD METHOD FOR JOINT SEGMENTATION-RIGID REGISTRATION — APPLICATION TO MOTION ESTIMATION OF HUMAN KNEE JOINT." Biomedical Engineering: Applications, Basis and Communications 23, no. 06 (2011): 445–56. http://dx.doi.org/10.4015/s1016237211002839.

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Image based registration of rigid objects has been frequently addressed in the literature to obtain an object's motion parameters. In this paper, a new approach of joint segmentation-rigid registration, within the variational framework of the phase field approximation of the Mumford-Shah's functional, is proposed. The defined functional consists of two Mumford-Shah equations, extracting the discontinuity set of the reference and target images due to a rigid spatial transformation. Multiscale minimization of the proposed functional after finite element discretization provided a sub-pixel, robus

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21

Cai, Xiaohao, Raymond Chan, and Tieyong Zeng. "A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford--Shah Model and Thresholding." SIAM Journal on Imaging Sciences 6, no. 1 (2013): 368–90. http://dx.doi.org/10.1137/120867068.

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22

MUSZKIETA, MONIKA. "OPTIMAL EDGE DETECTION BY TOPOLOGICAL ASYMPTOTIC ANALYSIS." Mathematical Models and Methods in Applied Sciences 19, no. 11 (2009): 2127–43. http://dx.doi.org/10.1142/s0218202509004066.

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In this paper, we consider a variational approach to the problem of edge detection without using a priori information. To begin with, we derive an asymptotic expansion of a functional inspired by the Mumford–Shah model at its global minimum. Then, we show that, according to our model, the optimal set of image edges is indicated by the set of points for which the dominant term of this expansion is minimal and the topological derivative associated with the considered functional is equal to zero. These two conditions form the basis for the introduced method to edge detection, which does not requi

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23

Gong, Jun Feng, and Xi Peng Xu. "A Fundamental Study on the Digital Recognition of Grinding Wheel." Key Engineering Materials 359-360 (November 2007): 504–8. http://dx.doi.org/10.4028/www.scientific.net/kem.359-360.504.

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In this paper, the 3D morphology of a grinding wheel was modeled by the depth from focus. Firstly, the picture information of different heights was extracted by the up-down moving of the microscope. The operator Laplacian was adopted to distinguish the distinct and fuzzy areas in a picture. Then, the distinct image and height information was obtained. The information of height was distorted due to the occurrence of noise. In order to reconstruct 3D surface, a method based on Min/Max curvature flow was developed to remove noises. In the end, an abrasive grain in the image of a grinding wheel wa

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24

SONG, Jin-Ping, and Shuai-Jie LI. "An Improved Mumford-Shah Model and Its Applications to Image Processing with the Piecewise Constant Level Set Method." Acta Automatica Sinica 33, no. 12 (2007): 1259–62. http://dx.doi.org/10.1360/aas-007-1259.

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25

WEI, WANG, and YANG XIN. "A MODIFIED MULTIPHASE LEVEL SET EVOLUTION SCHEME FOR AERIAL IMAGE SEGMENTATION." International Journal of Pattern Recognition and Artificial Intelligence 21, no. 07 (2007): 1195–212. http://dx.doi.org/10.1142/s0218001407005909.

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This paper describes an innovative aerial images segmentation algorithm. The algorithm is based upon the knowledge of image multiscale geometric analysis using contourlet transform, which can extract the image's intrinsic geometrical structure efficiently. The contourlet transform is introduced to represent the most distinguished and the rotation invariant features of the image. A modified Mumford–Shah model is applied to segment the aerial image by a multifeature level set evolution. To avoid possible local minima in the level set evolution, we adjust the weighting coefficients of the multisc

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26

Di, Y., G. Jiang, L. Yan, H. Liu, and S. Zheng. "MULTI-SCALE SEGMENTATION OF HIGH RESOLUTION REMOTE SENSING IMAGES BY INTEGRATING MULTIPLE FEATURES." ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XLII-1/W1 (May 31, 2017): 247–55. http://dx.doi.org/10.5194/isprs-archives-xlii-1-w1-247-2017.

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Most of multi-scale segmentation algorithms are not aiming at high resolution remote sensing images and have difficulty to communicate and use layers’ information. In view of them, we proposes a method of multi-scale segmentation of high resolution remote sensing images by integrating multiple features. First, Canny operator is used to extract edge information, and then band weighted distance function is built to obtain the edge weight. According to the criterion, the initial segmentation objects of color images can be gained by Kruskal minimum spanning tree algorithm. Finally segmentation ima

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27

Sashida, Satoshi, Yutaka Okabe, and Hwee Kuan Lee. "Comparison of multi-label graph cuts method and Monte Carlo simulation with block-spin transformation for the piecewise constant Mumford–Shah segmentation model." Computer Vision and Image Understanding 119 (February 2014): 15–26. http://dx.doi.org/10.1016/j.cviu.2013.11.001.

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28

Wang, Li-Lian, and Ying Gu. "Efficient Dual Algorithms for Image Segmentation Using TV-Allen-Cahn Type Models." Communications in Computational Physics 9, no. 4 (2011): 859–77. http://dx.doi.org/10.4208/cicp.221109.290710a.

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AbstractVariational image segmentation based on the Mumford and Shah model [31], together with implementation by the piecewise constant level-set method (PCLSM) [26], leads to fully nonlinear Total Variation (TV)-Allen-Cahn equations. The commonly-used numerical approaches usually suffer from the difficulties not only with the non-differentiability of the TV-term, but also with directly evolving the discontinuous piecewise constant-structured solutions. In this paper, we propose efficient dual algorithms to overcome these drawbacks. The use of a splitting-penalty method results in TV-Allen-Cah

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29

Weinmann, Andreas, and Martin Storath. "Iterative Potts and Blake–Zisserman minimization for the recovery of functions with discontinuities from indirect measurements." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2176 (2015): 20140638. http://dx.doi.org/10.1098/rspa.2014.0638.

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Signals with discontinuities appear in many problems in the applied sciences ranging from mechanics, electrical engineering to biology and medicine. The concrete data acquired are typically discrete, indirect and noisy measurements of some quantities describing the signal under consideration. The task is to restore the signal and, in particular, the discontinuities. In this respect, classical methods perform rather poor, whereas non-convex non-smooth variational methods seem to be the correct choice. Examples are methods based on Mumford–Shah and piecewise constant Mumford–Shah functionals and

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30

Shen, Jianhong (Jackie). "A Stochastic-Variational Model for Soft Mumford-Shah Segmentation." International Journal of Biomedical Imaging 2006 (2006): 1–14. http://dx.doi.org/10.1155/ijbi/2006/92329.

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In contemporary image and vision analysis, stochastic approaches demonstrate great flexibility in representing and modeling complex phenomena, while variational-PDE methods gain enormous computational advantages over Monte Carlo or other stochastic algorithms. In combination, the two can lead to much more powerful novel models and efficient algorithms. In the current work, we propose a stochastic-variational model forsoft(or fuzzy) Mumford-Shah segmentation of mixture image patterns. Unlike the classicalhardMumford-Shah segmentation, the new model allows each pixel to belong to each image patt

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31

Watanabe, Hiroshi, Satoshi Sashida, Yutaka Okabe, and Hwee Kuan Lee. "Monte Carlo methods for optimizing the piecewise constant Mumford–Shah segmentation model." New Journal of Physics 13, no. 2 (2011): 023004. http://dx.doi.org/10.1088/1367-2630/13/2/023004.

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32

Chambolle, Antonin. "Image Segmentation by Variational Methods: Mumford and Shah Functional and the Discrete Approximations." SIAM Journal on Applied Mathematics 55, no. 3 (1995): 827–63. http://dx.doi.org/10.1137/s0036139993257132.

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33

Antonelli, L., and V. De Simone. "Comparison of minimization methods for nonsmooth image segmentation." Communications in Applied and Industrial Mathematics 9, no. 1 (2018): 68–86. http://dx.doi.org/10.1515/caim-2018-0005.

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Abstract Segmentation is a typical task in image processing having as main goal the partitioning of the image into multiple segments in order to simplify its interpretation and analysis. One of the more popular segmentation model, formulated by Chan-Vese, is the piecewise constant Mumford-Shah model restricted to the case of two-phase segmentation. We consider a convex relaxation formulation of the segmentation model, that can be regarded as a nonsmooth optimization problem, because the presence of the l1-term. Two basic approaches in optimization can be distinguished to deal with its non diff

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34

RONDI, LUCA, and FADIL SANTOSA. "ANALYSIS OF AN INVERSE PROBLEM ARISING IN PHOTOLITHOGRAPHY." Mathematical Models and Methods in Applied Sciences 22, no. 05 (2012): 1150026. http://dx.doi.org/10.1142/s0218202511500266.

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We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods, much like the Ambrosio–Tortorelli's approximation of the Mumford–Shah functio

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35

Shan, Xiang, Daeyoung Kim, Etsuko Kobayashi, and Bing Li. "Regularized level set models using fuzzy clustering for medical image segmentation." Filomat 32, no. 5 (2018): 1507–12. http://dx.doi.org/10.2298/fil1805507s.

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Level set methods are a kind of general numerical analysis tools that are specialized for describing and controlling implicit interface dynamically. It receives widespread attention in medical image computing and analysis. There have been a lot of level set models designed and regularized for medical image segmentation. For the sake of simplicity and clarity, we merely concentrate on our recent works of regularizing level set methods with fuzzy clustering in this paper. It covers two most famous level set models, namely Hamilton-Jacobi functional and Mumford-Shah functional, for variational se

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36

Golański, Piotr, and Marek Szczekala. "The Structure of Classifiers of Hand Gestures with the Use of the Active Contour Model and Fourier Descriptors." Research Works of Air Force Institute of Technology 41, no. 1 (2018): 63–92. http://dx.doi.org/10.2478/afit-2018-0003.

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Abstract In this article, the research results of the usage of selected methods of the analysis of images for the recognition of hand gestures in human-computer interaction was depicted. The usage of this type of interaction is important in case of the so-called wearable computers (computer is integrated with the work clothing of an operator. For the recognition of gestures, the combination of two methods associated with the image processing was suggested and that is the Chan-Vese active contour model enabling to recognize objects on a given image, based on the curve evolution technique, Mumfo

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37

Ramos de Carvalho, Luís Eduardo, Sylvio Luiz Mantelli Neto, Eros Comunello, Antonio Carlos Sobieranski, and Aldo Von Wangenheim. "Can the Use of nonlinear Color Metrics systematically improve Segmentation?" Revista de Informática Teórica e Aplicada 25, no. 3 (2018): 23. http://dx.doi.org/10.22456/2175-2745.79885.

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Image segmentation is a procedure where an image is split into its constituent parts, according to some criterion. In the literature, there are different well-known approaches for segmentation, such as clustering, thresholding, graph theory and region growing. Such approaches, additionally, can be combined with color distance metrics, playing an important role for color similarity computation. Aiming to investigate general approaches able to enhance the performance of segmentation methods, this work presents an empirical study of the effect of a nonlinear color metric on segmentation procedure

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38

Chen, Qiang, and Chuanjiang He. "Integrating clustering with level set method for piecewise constant Mumford-Shah model." EURASIP Journal on Image and Video Processing 2014, no. 1 (2014). http://dx.doi.org/10.1186/1687-5281-2014-1.

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39

"A Novel Diagnostic Model for Lung Cancer Detection using Mumford-Shah and SVM Classifier." International Journal of Innovative Technology and Exploring Engineering 9, no. 3 (2020): 1342–46. http://dx.doi.org/10.35940/ijitee.b7072.019320.

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Lung cancer is one of the very deadly diseases in the world. However, diagnosing it at an early stage and treating it properly can protect lives. Although Computer Tomography (CT) scan imaging is one of the fruitful imaging in the field of medicine, it is the hardest for clinicians to clarify and recognize cancer from those images. And it is carried out with Mumford and Shah functional model, and support vector machine (SVM) classifier. Also, the system takes less computation time and thus, is highly efficient than existing algorithms which grab 98% accuracy. Further, the performance analysis

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40

Hintermüller, Michael, Steven-Marian Stengl, and Thomas M. Surowiec. "Uncertainty Quantification in Image Segmentation Using the Ambrosio–Tortorelli Approximation of the Mumford–Shah Energy." Journal of Mathematical Imaging and Vision, July 3, 2021. http://dx.doi.org/10.1007/s10851-021-01034-2.

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AbstractThe quantification of uncertainties in image segmentation based on the Mumford–Shah model is studied. The aim is to address the error propagation of noise and other error types in the original image to the restoration result and especially the reconstructed edges (sharp image contrasts). Analytically, we rely on the Ambrosio–Tortorelli approximation and discuss the existence of measurable selections of its solutions as well as sampling-based methods and the limitations of other popular methods. Numerical examples illustrate the theoretical findings.

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