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3D Mumford-Shah Based Active Mesh [chapter]

Alexandre Dufour, Nicole Vincent, Auguste Genovesio
2006 Lecture Notes in Computer Science  
In this paper, we propose a fully automated deformable 3D mesh model that deforms using the reduced Mumford-Shah functional to segment and track objects with fuzzy boundaries.  ...  Current methods utilize edge-based forces to attract the mesh surface toward the image entities.  ...  Conclusion and Future Works A new deformable mesh model based on the reduced Mumford-Shah functional has been proposed, joining the theories of explicit active mesh, region-based information and 3D visualization  ... 
doi:10.1007/11892755_21 fatcat:tj2g6j3fr5gfnjlwkghrcuqcba

Variational mesh decomposition

Juyong Zhang, Jianmin Zheng, Chunlin Wu, Jianfei Cai
2012 ACM Transactions on Graphics  
The algorithm extends the Mumford-Shah model to 3D meshes that contains a data term measuring the variation within a segment using eigenvectors of a dual Laplacian matrix whose weights are related to the  ...  The efficiency is achieved by solving the Mumford-Shah model through a saddle-point problem that is solved by a fast primal-dual method.  ...  -We present a mesh segmentation algorithm using the convexified version of the Mumford-Shah model based on total variation.  ... 
doi:10.1145/2167076.2167079 fatcat:ayxiihbnpjea5k2ix6zcfyuu7i

A Variational Approach for Detecting Feature Lines on Meshes

Weihua Tong, Xuecheng Tai
2016 Journal of Computational Mathematics  
This paper introduces a unified variational framework for detecting generic feature lines on polygonal meshes. The classic Mumford-Shah model is extended to surfaces.  ...  Several measure functions are devised for different types of feature lines, and we apply our approach to various polygonal meshes ranging from synthetic to measured models.  ...  ., extending the Mumford-Shah model to 3D or surface cases. Dufour et al.  ... 
doi:10.4208/jcm.1510-m4510 fatcat:6zoimjlesraabdvihkephk7kcu

The Piecewise Smooth Mumford–Shah Functional on an Arbitrary Graph

L. Grady, C.V. Alvino
2009 IEEE Transactions on Image Processing  
Present day optimization of the Mumford-Shah functional is predominated by active contour methods.  ...  The Mumford-Shah functional has had a major impact on a variety of image analysis problems including image segmentation and filtering and, despite being introduced over two decades ago, it is still in  ...  Our graph formulation of the Mumford-Shah energy allows nonstandard applications such as clustering or mesh smoothing.  ... 
doi:10.1109/tip.2009.2028258 pmid:19635698 fatcat:inyuw77aj5arbntnya2rtoimfe

An Improved Image Segmentation Algorithm CT Superpixel Grid Using Active Contour

Yuntao Wei, Xiaojuan Wang, Wenqing Wu
2021 Wireless Communications and Mobile Computing  
on the growth graph, and the target edge was obtained as the initial contour; finally, the Mumford-Shah model in the active contour model was improved; the energy functional was constructed based on the  ...  A superpixel mesh CT image improved segmentation algorithm using active contour was proposed.  ...  Based on the initial contours obtained, this paper uses the level set method to improve the Mumford-Shah model in the active contour model.  ... 
doi:10.1155/2021/2906868 fatcat:5ytsz3zkgrhqnmlttshyuxb3om

Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes

Heike Benninghoff, Harald Garcke
2017 Journal of Scientific Computing  
We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D image data.  ...  Finally, the parametric method is applied to segmentation of medical 3D images.  ...  In Section 2, we present a region-based active surface model where we extend the Mumford-Shah model [28] and the Chan-Vese model [16] to 3D images.  ... 
doi:10.1007/s10915-017-0401-3 fatcat:jy22ftv4rrbctjp7zgvmbfjsxm

Segmentation of Three-dimensional Images with Parametric Active Surfaces and Topology Changes [article]

Heike Benninghoff, Harald Garcke
2015 arXiv   pre-print
We consider a piecewise constant version of the Mumford-Shah and the Chan-Vese functionals and perform a region-based segmentation of 3D image data.  ...  Finally, the parametric method is applied to segmentation of medical 3D images.  ...  In Section 2, we present a region-based active surface model where we extend the Mumford-Shah model [28] and the Chan-Vese model [16] to 3D images.  ... 
arXiv:1506.07136v1 fatcat:3kshgcfwkbgyhakztdlth24jpm

Augmenting CT cardiac roadmaps with segmented streaming ultrasound

Qi Duan, Guy Shechter, Luis F. Gutiérrez, Douglas Stanton, Lyubomir Zagorchev, Andrew F. Laine, Daniel R. Elgort, Kevin R. Cleary, Michael I. Miga
2007 Medical Imaging 2007: Visualization and Image-Guided Procedures  
In this work, using a customized segmentation method based on a 3D active mesh, endocardial borders of the left ventricle were extracted from US image streams (4D data sets) at a frame rate of approximately  ...  Static X-ray computed tomography (CT) volumes are often used as anatomic roadmaps during catheter-based cardiac interventions performed under X-ray fluoroscopy guidance.  ...  The 3D active mesh model is deformed under external forces derived from a minimization of the Mumford-Shah energy functional [5] : ( ) 2 2 \ ( , ) C E f C f g dV f dV ds β α Ω Ω = − + ∇ + ∫ ∫ C γ ∫ (3  ... 
doi:10.1117/12.711431 dblp:conf/miigp/DuanSGSZLE07 fatcat:dyur7jefxnfovmz53qz6u6sv2a

Mini-Workshop: Analytical and Numerical Methods in Image and Surface Processing

Peter Schröder, Martin Rumpf, Ulrich Reif, Gerhard Dziuk
2005 Oberwolfach Reports  
The focus was on variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, image and surface denoising based on geometric evolution problems in image  ...  As examples we would like to mention here: -Variational methods in image and surface processing such as active contour models, Mumford-Shah type functionals, -image and surface denoising based on geometric  ...  It is based on a level set formulation of the Mumford-Shah approach proposed by Chan and Vese in [1] , [2] , [3] .  ... 
doi:10.4171/owr/2005/10 fatcat:lxgstanio5bafdcbv4fzkrqmgi

Low-Cost Probabilistic 3D Denoising with Applications for Ultra-Low-Radiation Computed Tomography

Illia Horenko, Lukáš Pospíšil, Edoardo Vecchi, Steffen Albrecht, Alexander Gerber, Beate Rehbock, Albrecht Stroh, Susanne Gerber
2022 Journal of Imaging  
We perform a patient-specific performance evaluation for a broad range of denoising algorithms (including the most popular deep learning denoising approaches, wavelets-based methods, methods based on MumfordShah  ...  We introduce a parallel Probabilistic MumfordShah denoising model (PMS) and show that it markedly-outperforms the compared common denoising methods in denoising quality and cost scaling.  ...  Relation of Probabilistic Mumford-Shah and rSPA Algorithm to Regularized Mumford-Shah Framework (MS) and Rudin-Osher-Fatemi (ROF) Total Variation Model The Mumford-Shah formalism originally introduced  ... 
doi:10.3390/jimaging8060156 fatcat:2jsd6db55ze4jo3fsikr35jflq

Real-time segmentation of 4D ultrasound by Active Geometric Functions

Qi Duan, Elsa D. Angelini, Shunichi Homma, Andrew F. Laine
2008 2008 5th IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
Four-dimensional ultrasound based on matrix phased array transducers can capture the complex 4D cardiac motion in a complete and real-time fashion.  ...  In this context, a novel formulation framework of the minimal surface problem, called Active Geometric Functions (AGF), is proposed to reach truly real-time performance in segmenting 4D ultrasound data  ...  In 2001, Chan and Vese [17] proposed their famous "active contour without edges". The driving forces were derived via energy minimization of the Mumford-Shah segmentation functional [18] .  ... 
doi:10.1109/isbi.2008.4540975 dblp:conf/isbi/DuanAHL08 fatcat:koob5zds5rhtfoyrjurkbgem5i

Real-time segmentation by Active Geometric Functions

Qi Duan, Elsa D. Angelini, Andrew F. Laine
2010 Computer Methods and Programs in Biomedicine  
In this paper, a novel deformable model framework, Active Geometric Functions (AGF), was introduced to tackle the real time segmentation problem.  ...  In 2001, Chan and Vese [15] proposed their famous "active contour without edges". The driving forces were derived via energy minimization of the Mumford-Shah segmentation functional [16] .  ...  The total energy was defined by combination of Mumford-Shah energy functionals and a penalty term computed from the signed radial distance between the two surfaces.  ... 
doi:10.1016/j.cmpb.2009.09.001 pmid:19800708 pmcid:PMC3106291 fatcat:sl4yfcjyezfgtde5tjpdh3vsui

Convex multi-region segmentation on manifolds

Amael Delaunoy, Ketut Fundana, Emmanuel Prados, Anders Heyden
2009 2009 IEEE 12th International Conference on Computer Vision  
Secondly we show how to implement the proposed method on triangular meshes, and finally we show how to use and combine the method in other computer vision problems, such as 3D reconstruction.  ...  In particular, we propose a numerical method when the manifold is represented by a triangular mesh.  ...  As proved in [7, 11] , if u(x) is a minimizer of (2), then for a.e. µ ∈ [0, 1], the set Σ(µ) = {x ∈ Ω, u(x) > µ} is a minimizer of the Mumford-Shah functional [27] , implying that the solution to (1  ... 
doi:10.1109/iccv.2009.5459174 dblp:conf/iccv/DelaunoyFPH09 fatcat:p7mh3ck7xvactdf2wfmkx6c3zi

A correspondence-less approach to matching of deformable shapes [article]

Jonathan Pokrass, Alexander M. Bronstein, Michael M. Bronstein
2011 arXiv   pre-print
The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular meshes.  ...  The same authors addressed this problem using a Mumford-Shah [22, 10] -like regularization for rigid [3] and non-rigid [2] shapes.  ...  Here, we adopt this relaxation as well as the approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli [1] .  ... 
arXiv:1101.5687v1 fatcat:sntqwgy6nvcozfd33z4yaav7gi

Active Volume Models for Medical Image Segmentation

Tian Shen, Hongsheng Li, Xiaolei Huang
2011 IEEE Transactions on Medical Imaging  
To keep the model's surface triangulation optimized, surface remeshing is derived from another linear system based on Laplacian Mesh Optimization (LMO) [26], [27].  ...  Segmentation, validation and comparison results are presented from experiments on a variety of 2D and 3D medical images.  ...  A well-known example for the region modeling cost function is the Mumford-Shah functional [25] .  ... 
doi:10.1109/tmi.2010.2094623 pmid:21118771 fatcat:sachvjnbz5go7itm4xrsc7azvy
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