l;Fe present a new technique for extracting line-type features on point-sampled geometry. Given an unstructured point cloud as input, our method first applies principal component analysis on local neighborhoods to classiC points according to the likelihood that they belong to a feature. Using hysteresis threshoMing, we then compute a minimum spanning graph as an initial approximation of the feature lines. To smooth out the features while maintaining a close connection to the underlying surface, we use an adaptation of active contour models.

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.

3D scanners, iso-surface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit significant errors. The new Edge-Sharpener filter introduced here identifies the chamfer edges and subdivides them and their incident triangles by inserting new vertices and by forcing these vertices to lie on intersections of planes that locally approximate the smooth surfaces that meet at these sharp features.

We propose a fast and robust method for detecting crest lines on surfaces approximated by dense triangle meshes. The crest lines, salient surface features defined via first- and second-order curvature derivatives, are widely used for shape matching and interrogation purposes. Their practical extraction is difficult because it requires good estimation of high-order surface derivatives. Our approach to the crest line detection is based on estimating the curvature tensor and curvature derivatives via local polynomial fitting. Since the crest lines are not defined in the surface regions where the surface focal set (caustic) degenerates, we introduce a new thresholding scheme which exploits interesting relationships between curvature extrema, the so-called MVS functional of Moreton and Sequin, and Dupin cyclides, An application of the crest lines to adaptive mesh simplification is also considered.

In this paper, we propose a novel surface reconstruction technique based on Bayesian statistics: The measurement process as well as prior assumptions on the measured objects are modeled as probability distributions and Bayes ’ rule is used to infer a reconstruction of maximum probability. The key idea of this paper is to define both measurements and reconstructions as point clouds and describe all statistical assumptions in terms of this finite dimensional representation. This yields a discretization of the problem that can be solved using numerical optimization techniques. The resulting algorithm reconstructs both topology and geometry in form of a well-sampled point cloud with noise removed. In a final step, this representation is then converted into a triangle mesh. The proposed approach is conceptually simple and easy to extend. We apply the approach to reconstruct piecewise-smooth surfaces with sharp features and examine the performance of the algorithm on different synthetic and real-world data sets. Categories and Subject Descriptors (according to ACM CCS): I.5.1 [Models]: Statistical; I.3.5 [Computer Graphics]: Curve, surface, solid and object representations

This paper presents a novel approach for establishing vertex correspondences between two planar shapes. Correspondences are established between the perceptual feature points extracted from both source and target shapes. A similarity metric between two feature points is defined using the intrinsic properties of their local neighborhoods. The optimal correspondence is found by an efficient dynamic programming technique. Our approach treats shape noise by allowing discarding small feature points, which introduces skips in the traversal of the dynamic programming graph. Our method is fast, feature preserving, and invariant to geometric transformations. We demonstrate the superiority of our approach over other approaches by experimental results. 1.

This document is the extended version of the work published in [11]. Laser-based range sensors are commonly used on-board autonomous mobile robots for obstacle detection and scene understanding. A popular methodology for analyzing point cloud data from these sensors is to train Bayesian classifiers using locally computed features on labeled data and use them to compute class posteriors on-line at testing time. However, data from range sensors present a unique challenge for feature computation in the form of significant variation in spatial density of points, both across the field-of-view as well as within structures of interest. In particular, this poses the problem of choosing a scale for analysis and a support-region size for computing meaningful features reliably. While scale theory has been rigorously developed for 2-D images, no equivalent exists for unorganized 3-D point data. Choosing a satisfactory fixed scale over the entire dataset makes feature extraction sensitive to the presence of different manifolds in the data and varying data density. We adopt an approach inspired by recent developments in computational geometry [17] and investigate the problem of automatic data-driven scale selection to improve point cloud classification. The approach is validated with results using real data from different sensors in various environments (indoor, urban outdoor and natural outdoor) classified into different terrain types (vegetation, solid surface and linear structure).

A piecewise smooth surface, possibly with boundaries, sharp edges, corners, or other features is defined by a set of samples. The basic idea is to model surface patches, curve segments and points explicitly, and then to glue them together based on explicit connectivity information. The geometry is defined as the set of stationary points of a projection operator, which is generalized to allow modeling curves with samples, and extended to account for the connectivity information. Additional tangent constraints can be used to model shapes with continuous tangents across edges and corners.

Abstract—A variety of computer graphics applications sample surfaces of 3D shapes in a regular grid without making the sampling rate adaptive to the surface curvature or sharp features. Triangular meshes that interpolate or approximate these samples usually exhibit relative big error around the insensitive sampled sharp features. This paper presents a robust general approach conducting bilateral filters to recover sharp edges on such insensitive sampled triangular meshes. Motivated by the impressive results of bilateral filtering for mesh smoothing and denoising, we adopt it to govern the sharpening of triangular meshes. After recognizing the regions that embed sharp features, we recover the sharpness geometry through bilateral filtering, followed by iteratively modifying the given mesh’s connectivity to form singlewide sharp edges that can be easily detected by their dihedral angles. We show that the proposed method can robustly reconstruct sharp edges on feature-insensitive sampled meshes. Index Terms—Boundary representations, Geometric algorithms, languages, and systems. 1

In this paper, we describe a new algorithm for detecting structural redundancy in geometric data sets. Our algorithm computes rigid symmetries, i.e., subsets of a surface model that reoccur several times within the model differing only by translation, rotation or mirroring. Our algorithm is based on matching locally coherent constellations of feature lines on the object surfaces. In comparison to previous work, the new algorithm is able to detect a large number of symmetric parts without restrictions to regular patterns or nested hierarchies. In addition, working on relevant features only leads to a strong reduction in memory and processing costs such that very large data sets can be handled. We apply the algorithm to a number of real world 3D scanner data sets, demonstrating high recognition rates for general patterns of symmetry.