Ridge-valley lines on meshes via implicit surface fitting

Abstract

We propose a simple and effective method for detecting view-and scale-independent ridge-valley lines defined via first-and secondorder curvature derivatives on shapes approximated by dense triangle meshes. A high-quality estimation of high-order surface derivatives is achieved by combining multi-level implicit surface fitting and finite difference approximations. We demonstrate that the ridges and valleys are geometrically and perceptually salient surface features and, therefore, can be potentially used for shape recognition, coding, and quality evaluation purposes.

Feature Line Based Building Detection and Reconstruction From Oblique Airborne Imagery

“…In this step, we follow the method of [Ohtake et al 2004] to extract the feature curves. In this work, compactly supported radial basis functions (CS-RBFs) is employed for global smoothing purposes.…”

Principal curvatures from the integral invariant viewpoint

“…These curves proved to be useful for the detection of special shapes, and also for such diverse applications as the work on nonisotropic remeshing by Alliez et al (2003), and on line-art rendering of smooth surfaces by Hertzmann and Zorin (2000). Global features whose definition relies on even higher order differential invariants (like derivatives of principal curvatures) also carry important shape information: For instance, the curves known as feature lines and crest lines received a lot of attention in the geometry processing community (see Cazals and Pouget (2005), Clarenz et al (2004b), Hildebrandt et al (2005), Ohtake et al (2004), Pauly et al (2003), and Yoshizawa et al (2005)). …”

“…Also the global understanding of shapes benefits from differential entities, as exemplified by the network of principal curvature lines, and by the crest lines of a surface. References on these topics include Alliez et al (2003), Cazals and Pouget (2005), Hildebrandt et al (2005), Ohtake et al (2004), and Yoshizawa et al (2005). Real-world data, which are e.g.…”

“…the work by Bajaj and Xu (2003), Clarenz et al (2004b), and Osher and Fedkiw (2002)). Local methods, using smooth approximations of the data in an appropriate neighbourhood, are presented by Cazals and Pouget (2003), Goldfeather and Interrante (2004), Ohtake et al (2004), Taubin (1995), and Tong and Tang (2005). In either case, the preservation of features which may not be considered as noise is not an easy task and requires especially adapted algorithms.…”

Surface-from-Gradients with Incomplete Data for Single View Modeling

“…Finally, to generate a 3D surface mesh for visualization, we use the solved f (Eqn. 1) to find the 3D point for every image location, and then generate the surface by applying [14], for instance.…”