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3D image segmentation supported by a point cloud. (English) Zbl 1471.65148

Summary: Here, we report a novel method of 3D image segmentation, using surface reconstruction from 3D point cloud data and 3D digital image information. For this task, we apply a mathematical model and numerical method based on the level set algorithm. This method solves surface reconstruction by the application of advection equation with a curvature term, which gives the evolution of an initial condition to the final state. This is done by defining the advective velocity in the level set equation as the weighted sum of distance function and edge detector function gradients. The distance function to the shape, represented by the point cloud, is computed using the fast sweeping method. The edge detector function is applied to the presmoothed 3D image. A crucial point for efficiency is the construction of an initial condition by a simple tagging algorithm, which allows us also to highly speed up the numerical scheme when solving PDEs. For the numerical discretization, we use a semi-implicit co-volume scheme in the curvature part and implicit upwind scheme in the advective part. The method was tested on representative examples and applied to real data representing 3D biological microscopic images of developing mammalian embryo.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65Y20 Complexity and performance of numerical algorithms
68U10 Computing methodologies for image processing
92C55 Biomedical imaging and signal processing
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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