Abstract
Deformable mesh methods have become an alternative of choice to classical deformable models for 3D image understanding. They allow to render the evolving surface directly during the segmentation process in a fast and efficient way, avoiding both the additional time-cost and approximation errors induced by 3D reconstruction algorithms after segmentation. Current methods utilize edge-based forces to attract the mesh surface toward the image entities. These forces are inadequate in 3D fluorescence microscopy, where edges are not well defined by gradient. 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. Simultaneous rendering of the mesh evolution allows faster tweaking of the model parameters and offers biologists a more precise insight on the scene and hence better understanding of biological phenomena. We present evaluations on both synthetic and real 3D microscopy data.
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Chakraborty, A., Staib, L., Duncan, J.: Deformable Boundary Finding in Medical Images by Intergrating Gradient and Region Information. IEEE Transactions on Medical Imaging 15(6), 859–870 (1996)
Xu, C., Pham, D., Rettman, M., Yu, D., Prince, J.: Reconstruction of the Human Cerebral Cortex from Magnetic Resonance Images. IEEE Transactions on Medical Imaging 18(6), 467–480 (1999)
Paragios, N.: A Level Set Approach for Shape-Driven Segmentation and Tracking of the Left Ventricle. IEEE Transactions on Medical Imaging 22, 773–776 (2003)
Sarti, A., de Solorzano, C.O., Lockett, S., Malladi, R.: A Geometric Model for 3D Confocal Image Analysis. IEEE Transactions on Biomedical Engineering 47(12), 1600–1609 (2000)
Dufour, A., Shinin, V., Tajbaksh, S., Guillen, N., Olivo-Marin, J., Zimmer, C.: Segmenting and tracking fluorescent cells in dynamic 3d microscopy with coupled active surfaces. IEEE Transactions on Image Processing 14(9), 1396–1410 (2005)
Miller, J.: Geometrically deformed models for the extraction of closed shapes from volume data. Master’s thesis, Rensselaer Polytechnic Institute, New York (1990)
Kass, M., Witkin, A., Terzopoulos, D.: Snakes: Active contour models. International Journal of Computer Vision 1, 321–331 (1988)
Cohen, L., Cohen, I.: Finite-element methods for active contour models and balloons for 2-D and 3-D images. IEEE Transactions on Pattern Analysis and Machine Intelligence 15(11), 1131–1147 (1993)
Szeliski, R., Terzopoulos, D.: Physically based and probabilistic models for computer vision. In: Geometric Methods in Computer Vision, vol. 1570, pp. 140–152 (1991)
Staib, L., Duncan, J.: Boundary finding with parametrically deformable models. IEEE Transactions on Pattern Analysis and Machine Intelligence 14(11), 1061–1075 (1992)
Delingette, H.: General object reconstruction based on simplex meshes. International Journal on Computer Vision 32, 111–146 (1999)
Cotin, S., Delingette, H., Ayache, N.: Real-time elastic deformations of soft tissues for surgery simulation. IEEE Transactions on Visualization and Computer Graphics 5, 62–73 (1999)
Lachaud, J., Montanvert, A.: Deformable meshes with automated topology changes for coarse-to-fine three-dimensional surface extraction. Medical Image Analysis 3(2), 187–207 (1999)
Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. Com. Pure App. Math. 42, 577–684 (1989)
Chan, T., Vese, L.: Active contours without edges. IEEE Transactions on Image Processing 10(2), 266–277 (2001)
Tsai, A., Yezzi, A., Willsky, A.: Curve Evolution Implementation of the Mumford Shah Functional for Image Segmentation, Denoising, Interpolation, and Magnification. IEEE Transactions on Image Processing 10(8), 1169–1186 (2001)
Cremers, D., Tischhauser, F., Weickert, J., Schnorr, C.: Diffusion snakes: introducing statistical shape knowledge into the Mumford-Shah functional. International Journal on Computer Vision 50, 295–313 (2002)
Zimmer, C., Olivo-Marin, J.C.: Coupled Parametric Active Contours. IEEE Transactions on Pattern Analysis and Machine Intelligence 27(11), 1838–1842 (2005)
Delingette, H.: Modelisation, Deformation et Reconnaissance d’Objets Tridimensionnels a l’Aide de Maillages Simplexes. PhD thesis, Ecole Centrale de Paris (1994)
Loop, C.: Smooth Subdivion Surfaces based on Triangles. PhD thesis, University of Utah (1987)
Ciofolo, C.: Segmentation des formes guidee par des modeles en neuro-imagerie. PhD thesis, Universite Rennes I (2005)
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Dufour, A., Vincent, N., Genovesio, A. (2006). 3D Mumford-Shah Based Active Mesh. In: Martínez-Trinidad, J.F., Carrasco Ochoa, J.A., Kittler, J. (eds) Progress in Pattern Recognition, Image Analysis and Applications. CIARP 2006. Lecture Notes in Computer Science, vol 4225. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11892755_21
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DOI: https://doi.org/10.1007/11892755_21
Publisher Name: Springer, Berlin, Heidelberg
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