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12 May 2004 Curvature estimation of arbitrary discrete 3D surfaces using partial derivatives based on distance maps
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Abstract
This work investigates curvature estimation of level surfaces in 3D voxel images. We discuss features of a widely used curvature computation scheme developed by Thirion. It is shown that the locality of the implicit function theorem destroys the smoothness of the reference unit normal; the specialty of Monge patch restricts the derived curvature formulas. By explicitly choosing the normalized gradient of the level function as the reference unit normal, a curvature computation scheme is developed and reported here, in which consistent geometrical meaning of curvature sign is maintained. In order to estimate the curvature efficiently for arbitrary discrete surfaces, a scheme based on distance mapping is proposed. This method was tested on simple 2D objects. It was shown that our method gives accurate curvature estimation similar to Gaussian filtering method, but with much less computational cost.
© (2004) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Xiangwei Zhang and Milan Sonka "Curvature estimation of arbitrary discrete 3D surfaces using partial derivatives based on distance maps", Proc. SPIE 5370, Medical Imaging 2004: Image Processing, (12 May 2004); https://doi.org/10.1117/12.536179
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