Abstract
In this contribution we develop a strategy for segmentation of evolving biological structures in image sequences. Our approach is based on combination of nonlinear tensor diffusion image smoothing and subjective surface based image segmentation. Since the fine cell structure would restrain the evolving segmentation function to achieve a shape of meaningful biological structures, we have to smooth properly the images in the sequence. To that goal we apply the nonlinear tensor diffusion which enhances the connectivity of bordering structure lines and smoothes their inner parts. For the numerical implementations we use semi-implicit diamond-cell finite volume methods both for filtering and segmentation. We show application of the method in image segmentation of early stages of zebrafish embryogenesis.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Corsaro, S., Mikula, K., Sarti, A., Sgallari, F.: Semi-implicit co-volume method in 3D image segmentation. SIAM J. Sci. Comput. 28(6), 2248–2265 (2006)
Coudiere, Y., Vila, J.P., Villedieu, P.: Convergence rate of a finite volume scheme for a two-dimensional convection-diffusion problem. M2AN Math. Model. Numer. Anal. 33, 493–516 (1999)
Drblíková, O., Mikula, K.: Convergence Analysis of Finite Volume Scheme for Nonlinear Tensor Anisotropic Diffusion in Image Processing. SIAM J. Numer. Anal. 46(1), 37–60 (2007)
Drblíková, O., Mikula, K.: Semi-implicit Diamond-cell Finite Volume Scheme for 3D Nonlinear Tensor Diffusion in Coherence Enhancing Image Filtering. In: Eymard, R., Herard, J.M. (eds.) Finite Volumes for Complex Applications V: Problems and Perspectives, ISTE and WILEY, London, pp. 343–350 (2008)
Eymard, R., Gallouët, T., Herbin, R.: Finite Volume Methods. In: Ciarlet, P., Lions, J.L. (eds.) Handbook for Numerical Analysis, vol. 7. Elsevier, Amsterdam (2000)
Frolkovič, P., Mikula, K., Peyriéras, N., Sarti, A.: A counting number of cells and cell segmentation using advection-diffusion equations. Kybernetika 43(6), 817–829 (2007)
Meijering, E., Niessen, W., Weickert, J., Viergever, M.: Diffusion-Enhanced Visualization and Quantification of Vascular Anomalies in Three-Dimensional Rotational Angiography: Results of an In-Vitro Evaluation. Medical Image Analysis 6(3), 217–235 (2002)
Mikula, K., Peyriéras, N., Remešíková, M., Sarti, A.: 3D embryogenesis image segmentation by the generalized subjective surface method using the finite volume technique. In: Eymard, R., Herard, J.M. (eds.) Finite Volumes for Complex Applications V: Problems and Perspectives, ISTE and WILEY, London, pp. 585–592 (2008)
Mikula, K., Sarti, A., Sgallari, F.: Co-volume level set method in subjective surface based medical image segmentation. In: Suri, J., et al. (eds.) Handbook of Medical Image Analysis: Segmentation and Registration Models, pp. 583–626. Springer, New York (2005)
Sarti, A., Malladi, R., Sethian, J.A.: Subjective Surfaces: A Method for Completing Missing Boundaries. Proceedings of the National Academy of Sciences of the United States of America 12(97), 6258–6263 (2000)
Weickert, J.: Coherence-enhancing diffusion filtering. Int. J. Comput. Vision 31, 111–127 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Drblíková, O., Mikula, K., Peyriéras, N. (2009). The Nonlinear Tensor Diffusion in Segmentation of Meaningful Biological Structures from Image Sequences of Zebrafish Embryogenesis. In: Tai, XC., Mørken, K., Lysaker, M., Lie, KA. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2009. Lecture Notes in Computer Science, vol 5567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02256-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-02256-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02255-5
Online ISBN: 978-3-642-02256-2
eBook Packages: Computer ScienceComputer Science (R0)