Voronoi-based feature curves extraction for sampled singular surfaces

Abstract

The detection and reconstruction of feature curves in surfaces from a point cloud data is a challenging problem because most of the known theories for smooth surfaces break down at these places. The features such as boundaries, sharp ridges and corners, and curves where multiple surface patches intersect creating non-manifold points are often considered important geometries for further processing. As a result, they need to be preserved in a reconstruction of the sampled surface from its point sample. The problem becomes harder in presence of noise. We propose a robust Voronoi-based pipeline that engages several sub steps consisting of approaches proposed originally for smooth case. We modify or enhance them to handle features in singular surfaces. The experimental results provide the evidence that the method is effective.

Surface-reconstructing growing neural gas: A method for online construction of textured triangle meshes

“…15 right) concentrate at q % 0:98. Since SPSR uses Marching Cubes that is known to construct a considerable amount of irregular triangles, the angle distributions of SGNG are compared to the results presented by Xiong et al [24]: the peak in the angle distribution created by SGNG is located at a slightly smaller angle than in both the dictionary learning approach by Xiong et al and in Singular Cocone reconstruction by Dey and Wang [49]. However, the distribution achievable with SGNG is much steeper, thus considerably fewer acute or obtuse triangles are created.…”

Functional Surface Reconstruction from Unorganized Noisy Point Clouds

“…In [3] feature points are detected by Gaussian-weighted graph Laplacian and feature curves are constructed by Reeb graph. In [4] the authors first detect feature points by voronoi-based method. The feature direction information is then determined by PCA and corner points are simultaneously distinguished.…”

Automatic extraction of 3D anatomical feature curves of hip bone models reconstructed from CT images

“…Furthermore, AFC of known individuals are also used to segment CT images or construct statistical models [2,16,17]. AFC are extremely curved regions that are also called ridge-valley lines, crest lines or feature curves in computer graphics [18][19][20]. Automatically or semi-automatically extracting them from discrete data, such as bone surface data reconstructed from CT images, is a challenging task, because of noises and sampling errors [18][19][20][21].…”

“…AFC are extremely curved regions that are also called ridge-valley lines, crest lines or feature curves in computer graphics [18][19][20]. Automatically or semi-automatically extracting them from discrete data, such as bone surface data reconstructed from CT images, is a challenging task, because of noises and sampling errors [18][19][20][21]. The task of the present work is to automatically extract AFC of hip bones using a computer graphics technique (DCSS-direct curvature scale space) [22,23] and the anatomical structure of the hip bone as prior knowledge.…”

“…It is kind of typical for feature extraction methods to separate extreme curvature points/curves from surfaces using classical geometrical variables, such as normal vectors, dihedral angles, curvatures, distances [18][19][20][24][25][26][27][28][29], etc. Such methods have been used to locate anatomical landmarks such as the ones on the distal femur and on the proximal tibia [1], lumbar dimples [30], ridge-valley lines on brains [31], etc.…”