Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
Geometric surface smoothing via anisotropic diffusion of normals
Proceedings of the conference on Visualization '02
Smooth surface reconstruction from noisy range data
Proceedings of the 1st international conference on Computer graphics and interactive techniques in Australasia and South East Asia
Saliency sequential surface organization for free-form object recognition
Computer Vision and Image Understanding
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
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A position and direction is a fundamental information for U-Business as an anywhere service. A mobile device camera image can increase an accuracy of the positioning, and a range image provides significant information in an occlusion scene. U-Business service queries the information with the range image for a precision position or a target object. We present a method for smoothing heavy noisy surfaces acquired by mobile 3D imaging devices to obtain the stable curvature. The smoothing is performed in a way that finds centers of probability distributions, which maximizes the likelihood of observed points with smooth constraints. The smooth constraints are derived from the unit tangent vector equality. This provides a way of obtaining smooth surfaces and stable curvatures. We achieve the smoothing by solving the regularized linear system. The unit tangent vector equality involves consideration of geometric symmetry, and it minimizes the variation of differential values that are a factor of curvatures. The proposed algorithm has two apparent advantages. The first thing is that the surfaces in a scene with various signals-to-noise ratio are smoothed, and then they can earn suitable curvatures. The second is that the proposed method works on heavy noisy surfaces, for example, a stereo camera image. Experiments on range images demonstrate that the proposed method yields the smooth surfaces from the input with various signals-to-noise ratio and the stable curvatures obtained from the smooth surfaces.