Robust feature classification and editing

Neighbor Reweighted Local Centroid for Geometric Feature Identification

Identifying geometric features from sampled surfaces is a significant and fundamental task. The existing curvature-based methods that can identify ridge and valley features are generally sensitive to noise. Without requiring high-order differential operators, most statistics-based methods sacrifice certain extents of the feature descriptive powers in exchange for robustness. However, neither of these types of methods can treat the surface boundary features simultaneously. In this paper, we propose a novel neighbor reweighted local centroid (NRLC) computational algorithm to identify geometric features for point cloud models. It constructs a feature descriptor for the considered point via decomposing each of its neighboring vectors into two orthogonal directions. A neighboring vector starts from the considered point and ends with the corresponding neighbor. The decomposed neighboring vectors are then accumulated with different weights to generate the NRLC. With the defined NRLC, we design a probability set for each candidate feature point so that the convex, concave and surface boundary points can be recognized concurrently. In addition, we introduce a pair of feature operators, including assimilation and dissimilation, to further strengthen the identified geometric features. Finally, we test NRLC on a large body of point cloud models derived from different data sources. Several groups of the comparison experiments are conducted, and the results verify the validity and efficiency of our NRLC method.

Anisotropic elliptic PDEs for feature classification

The extraction and classification of multitype (point, curve, patch) features on manifolds are extremely challenging, due to the lack of rigorous definition for diverse feature forms. This paper seeks a novel solution of multitype features in a mathematically rigorous way and proposes an efficient method for feature classification on manifolds. We tackle this challenge by exploring a quasi-harmonic field (QHF) generated by elliptic PDEs, which is the stable state of heat diffusion governed by anisotropic diffusion tensor. Diffusion tensor locally encodes shape geometry and controls velocity and direction of the diffusion process. The global QHF weaves points into smooth regions separated by ridges and has superior performance in combating noise/holes. Our method's originality is highlighted by the integration of locally defined diffusion tensor and globally defined elliptic PDEs in an anisotropic manner. At the computational front, the heat diffusion PDE becomes a linear system with Dirichlet condition at heat sources (called seeds). Our new algorithms afford automatic seed selection, enhanced by a fast update procedure in a high-dimensional space. By employing diffusion probability, our method can handle both manufactured parts and organic objects. Various experiments demonstrate the flexibility and high performance of our method.

Mesh segmentation with concavity-aware fields

This paper presents a simple and efficient automatic mesh segmentation algorithm that solely exploits the shape concavity information. The method locates concave creases and seams using a set of concavity-sensitive scalar fields. These fields are computed by solving a Laplacian system with a novel concavity-sensitive weighting scheme. Isolines sampled from the concavity-aware fields naturally gather at concave seams, serving as good cutting boundary candidates. In addition, the fields provide sufficient information allowing efficient evaluation of the candidate cuts. We perform a summarization of all field gradient magnitudes to define a score for each isoline and employ a score-based greedy algorithm to select the best cuts. Extensive experiments and quantitative analysis have shown that the quality of our segmentations are better than or comparable with existing state-of-the-art more complex approaches.

A new watermarking method for 3D models based on integral invariants

In this paper, we propose a new semi-fragile watermarking algorithm for the authentication of 3D models based on integral invariants. A watermark image is embedded by modifying the integral invariants of some of the vertices. In order to modify the integral invariants, the positions of a vertex and its neighbors are shifted. To extract the watermark, all the vertices are tested for the embedded information, and this information is combined to recover the watermark image. The number of parts of the watermark image that can be recovered will determine the authentication decision. Experimental tests show that this method is robust against normal use modifications introduced by rigid transformations, format conversions, rounding errors, etc., and can be used to test for malicious attacks such as mesh editing and cropping. An additional contribution of this paper is a new algorithm for computing two kinds of integral invariants.

Optimal surface parameterization using inverse curvature map

Mesh parameterization is a fundamental technique in computer graphics. Our paper focuses on solving the problem of finding the best discrete conformal mapping that also minimizes area distortion. Firstly, we deduce an exact analytical differential formula to represent area distortion by curvature change in the discrete conformal mapping, giving a dynamic Poisson equation. Our result shows the curvature map is invertible. Furthermore, we give the explicit Jacobi matrix of the inverse curvature map. Secondly, we formulate the task of computing conformal parameterizations with least area distortions as a constrained nonlinear optimization problem in curvature space. We deduce explicit conditions for the optima. Thirdly, we give an energy form to measure the area distortions, and show it has a unique global minimum. We use this to design an efficient algorithm, called free boundary curvature diffusion, which is guaranteed to converge to the global minimum. This result proves the common belief that optimal parameterization with least area distortion has a unique solution and can be achieved by free boundary conformal mapping. Major theoretical results and practical algorithms are presented for optimal parameterization based on the inverse curvature map. Comparisons are conducted with existing methods and using different energies. Novel parameterization applications are also introduced.