Computation of Surface Geometry and Segmentation Using Covariance Techniques
By J. Berkmann, Terry M. Caelli. 1994
In this correspondence, the application of covariance techniques to surface representation of 3-D objects is discussed and such ways of computing surface geometry are compared with traditional methods using differential geometry. It is shown how the covariance method provides surface descriptors that are invariant to rigid motions without explicitly using surface parameterizations or derivatives. Analogous covariance operators for both the Gauss and Weingarten maps are defined and a range image segmentation technique is presented that labels pixels as jump or crease discontinuities or planar, parabolic or curved region types. >
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- Leonidas J. Guibas
- Niloy J. Mitra
Citations in the corpus
- PCPNet Learning Local Shape Properties from Raw Point Clouds (2017, background): “In a similar spirit, curvatures can be computed by considering normal variation in a local neighborhood [BC94, KNSS09].”
- Scale Space Meshing of Raw Data Point Sets (2011, background): “In [BC94] the principal curvatures are computed from an oriented raw data set without surface fitting by expressing the fundamental forms of a 3D surface as covariance matrices.”
- Voronoi-Based Curvature and Feature Estimation from Point Clouds (2011, methodology): “[13] propose a method that relies on computing the covariance matrices of normal vectors to approximate the shape operator.”
- Hierarchical face clustering on polygonal surfaces (2001, methodology): “This method, which is identical to the least squares method of normal equations, is frequently used to estimate or define local tangent planes [16, 22, 5] when reconstructing surfaces from sets of points.”
- Anisotropic Diffusion Descriptors (2016, methodology): “The directions of principal curvature are computed as eigenvectors of the covariance matrix of neighboring normals, which provides an approximation to the shape operator [BC94].”