Decoupling local geometric features from the spatial location of a mesh is crucial for feature-preserving mesh denoising. This paper focuses on first order features, i.e., facet normals, and presents a simple yet effective anisotropic mesh denoising framework via normal field denoising. Unlike previous denoising methods based on normal filtering, which process normals defined on the Gauss sphere, our method considers normals as a surface signal defined over the original mesh. This allows the design of a novel bilateral normal filter that depends on both spatial distance and signal distance. Our bilateral filter is a more natural extension of the elegant bilateral filter for image denoising than those used in previous bilateral mesh denoising methods. Besides applying this bilateral normal filter in a local, iterative scheme, as common in most of previous works, we present for the first time a global, noniterative scheme for an isotropic denoising. We show that the former scheme is faster and more effective for denoising extremely noisy meshes while the latter scheme is more robust to irregular surface sampling. We demonstrate that both our feature-preserving schemes generally produce visually and numerically better denoising results than previous methods, especially at challenging regions with sharp features or irregular sampling.

Curve-skeleton is a very useful 1D structure to abstract the geometry and topology of a 3D object. Extraction of curve-skeletons is a fundamental problem in computer graphics, visualization, image processing and computer vision.There many useful applications including virtual colonoscopies, collision detection, computer animation, surface reconstruction and shape matching etc. In the literature [1][2], most previous methods require a volumetric discrete representation of the input model. However, transforming them into volumetric representations may raise discretization error in both geometry and connectivity.In this work [3], we propose a novel technique to extract skeletons directly from the mesh domain without requirement of volumetric discretization. Our approach (Figure 1) consists of three main steps: 1) mesh contraction, 2) connectivity surgery and 3) centeredness refinement. First, we contract a given mesh into a zero-volume skeletal shape by applying an iterative Laplacian smoothing procedure [4] with global positional constraints. Second, we execute a connectivity surgery procedure to progressively convert the contracted mesh into a 1D curve skeleton. Finally, to ensure its centeredness within the mesh, we refine the skeleton by moving each skeletal node to the center of its corresponding mesh region. In contrast to previous work, our approach has the following advantages: 1) our extracted skeleton is ensured to be homotopic to the original object, 2) it is inherently robust against noise disturbance (see Figure 2) and avoids volumetric discretization errors, and 3) the method is very fast and it is rotation invariant, and pose insensitive (Figure 3).

Curve-skeleton is a very useful 1D structure to abstract the geometry and topology of a 3D object. Extraction of curve-skeletons is a fundamental problem in computer graphics, visualization, image processing and computer vision.There many useful applications including virtual colonoscopies, collision detection, computer animation, surface reconstruction and shape matching etc. In the literature [1][2], most previous methods require a volumetric discrete representation of the input model. However, transforming them into volumetric representations may raise discretization error in both geometry and connectivity.In this work [3], we propose a novel technique to extract skeletons directly from the mesh domain without requirement of volumetric discretization. Our approach (Figure 1) consists of three main steps: 1) mesh contraction, 2) connectivity surgery and 3) centeredness refinement. First, we contract a given mesh into a zero-volume skeletal shape by applying an iterative Laplacian smoothing procedure [4] with global positional constraints. Second, we execute a connectivity surgery procedure to progressively convert the contracted mesh into a 1D curve skeleton. Finally, to ensure its centeredness within the mesh, we refine the skeleton by moving each skeletal node to the center of its corresponding mesh region. In contrast to previous work, our approach has the following advantages: 1) our extracted skeleton is ensured to be homotopic to the original object, 2) it is inherently robust against noise disturbance (see Figure 2) and avoids volumetric discretization errors, and 3) the method is very fast and it is rotation invariant, and pose insensitive (Figure 3).

Recent shape editing techniques, especially for man-made models, have gradually shifted focus from maintaining local, low-level geometric features to preserving structural, high-level characteristics like symmetry and parallelism. Such new editing goals typically require a pre-processing shape analysis step to enable subsequent shape editing. Observing that most editing of shapes involves manipulating their constituent components, we introduce component-wise controllers that are adapted to the component characteristics inferred from shape analysis. The controllers capture the natural degrees of freedom of individual components and thus provide an intuitive user interface for editing. A typical model usually results in a moderate number of controllers, allowing easy establishment of semantic relations among them by automatic shape analysis supplemented with user interaction. We propose a component-wise propagation algorithm to automatically preserve the established inter-relations while maintaining the defining characteristics of individual controllers and respecting the user-specified modeling constraints. We extend these ideas to a hierarchical setup, allowing the user to adjust the tool complexity with respect to the desired modeling complexity. We demonstrate the effectiveness of our technique on a wide range of manmade models with structural features, often containing multiple connected pieces.

Abstract-Recently, differential information as local intrinsic feature descriptors has been used for mesh editing. Given certain user input as constraints, a deformed mesh is reconstructed by minimizing the changes in the differential information. Since the differential information is encoded in a global coordinate system, it must somehow be transformed to fit the orientations of details in the deformed surface, otherwise distortion will appear. We observe that visually pleasing deformed meshes should preserve both local parameterization and geometry details. We propose to encode these two types of information in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Both sets of information are nondirectional and nonlinearly dependent on the vertex positions. Thus, we present a novel editing framework that iteratively updates both the primal vertex positions and the dual Laplacian coordinates to progressively reduce distortion in parametrization and geometry. Unlike previous related work, our method can produce visually pleasing deformations with simple user interaction, requiring only the handle positions, not local frames at the handles.