A viscosity solutions approach to shape-from-shading
SIAM Journal on Numerical Analysis
International Journal of Computer Vision
Fast Surface Reconstruction Using the Level Set Method
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Flux-based level set method: A finite volume method for evolving interfaces
Applied Numerical Mathematics
Semi-Implicit Covolume Method in 3D Image Segmentation
SIAM Journal on Scientific Computing
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Cells segmentation from 3-D confocal images of early zebrafish embryogenesis
IEEE Transactions on Image Processing
Methods toward in vivo measurement of zebrafish epithelial and deep cell proliferation
Computer Methods and Programs in Biomedicine
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We present a set of techniques that enable us to segment objects from 3D cell membrane images. Particularly, we propose methods for detection of approximate cell nuclei centers, extraction of the inner cell boundaries, the surface of the organism and the intercellular borders-the so called intercellular skeleton. All methods are based on numerical solution of partial differential equations. The center detection problem is represented by a level set equation for advective motion in normal direction with curvature term. In case of the inner cell boundaries and the global surface, we use the generalized subjective surface model. The intercellular borders are segmented by the advective level set equation where the velocity field is given by the gradient of the signed distance function to the segmented inner cell boundaries. The distance function is computed by solving the time relaxed eikonal equation. We describe the mathematical models, explain their numerical approximation and finally we present various possible practical applications on the images of zebrafish embryogenesis-computation of important quantitative characteristics, evaluation of the cell shape, detection of cell divisions and others.