Xiuping Liu

SMI 2013: Point cloud normal estimation via low-rank subspace clustering

In this paper, we present a robust normal estimation algorithm based on the low-rank subspace clustering technique. The main idea is based on the observation that compared with the points around sharp features, it is relatively easier to obtain accurate normals for the points within smooth regions. The points around sharp features and smooth regions are identified by covariance analysis of their neighborhoods. The neighborhood of a point in a smooth region can be well approximated by a plane. For a point around sharp features, some of its neighbors may be in smooth regions. These neighbor points normals are estimated by principal component analysis, and used as prior knowledge to carry out neighborhood clustering. An unsupervised learning process is designed to represent the prior knowledge as a guiding matrix. Then we segment the anisotropic neighborhood into several isotropic neighborhoods by low-rank subspace clustering with the guiding matrix, and identify a consistent subneighborhood for the current point. Hence the normal of the current point near sharp features is estimated as the normal of a plane fitting the consistent subneighborhood. Our method is capable of estimating normals accurately even in the presence of noise and anisotropic samplings, while preserving sharp features within the original point data. We demonstrate the effectiveness and robustness of the proposed method on a variety of examples.

Technical Section: Automatic hole-filling of CAD models with feature-preserving

In this paper, we propose an automatic hole-filling method, particularly for recovering missing feature curves and corners. We first extract the feature vertices around a hole of a CAD model and classify them into different feature sets. These feature sets are then automatically paired, using ordered double normals, Gaussian mapping and convex/concave analysis, to produce missing feature curves. Additionally, by minimizing a newly defined energy, the missing corners can be efficiently recovered as well. The hole is consequently divided into simple sub-holes according to the produced feature curves and recovered corners. Finally, each sub-hole is filled by a modified advancing front method individually. The experiments show that our approach is simple, efficient, and suitable for CAD systems.

Fabric defect inspection using prior knowledge guided least squares regression

This paper proposes an unsupervised model to inspect various detects in fabric images with diverse textures. A fabric image with defects is usually composed of a relatively consistent background texture and some sparse defects, which can be represented as a low-rank matrix plus a sparse matrix in a certain feature space. The process is formulated as a least squares regression based subspace segmentation model, which is convex, smooth and can be solved efficiently. A simple and effective prior is also learnt from local texture features of the image itself. Instead of considering only the feature space’ s global structure, the local prior is incorporated with it seamlessly by the proposed subspace segmentation model to guide and improve the segmentation. Experiments on a variety of fabric images demonstrate the effectiveness and robustness of the proposed method. Compared with existing methods, our method is more robust and locates various defects more precisely.

Least-squares images for edge-preserving smoothing

In this paper, we propose least-squares images (LS-images) as a basis for a novel edge-preserving image smoothing method. The LS-image requires the value of each pixel to be a convex linear combination of its neighbors, i.e., to have zero Laplacian, and to approximate the original image in a least-squares sense. The edge-preserving property inherits from the edge-aware weights for constructing the linear combination. Experimental results demonstrate that the proposed method achieves high quality results compared to previous state-of-the-art works. We also show diverse applications of LS-images, such as detail manipulation, edge enhancement, and clip-art JPEG artifact removal.

Short Communication to SMI 2011: Orienting raw point sets by global contraction and visibility voting

We present a global method for consistently orienting a defective raw point set with noise, non-uniformities and thin sharp features. Our method seamlessly combines two simple but effective techniques-constrained Laplacian smoothing and visibility voting-to tackle this challenge. First, we apply a Laplacian contraction to the given point cloud, which shrinks the shape a little bit. Each shrunk point corresponds to an input point and shares a visibility confidence assigned by voting from multiple viewpoints. The confidence is increased (resp. decreased) if the input point (resp. its corresponding shrunk point) is visible. Then, the initial normals estimated by principal component analysis are flipped according to the contraction vectors from shrunk points to the corresponding input points and the visibility confidence. Finally, we apply a Laplacian smoothing twice to correct the orientation of points with zero or low confidence. Our method is conceptually simple and easy to implement, without resorting to any complicated data structures and advanced solvers. Numerous experiments demonstrate that our method can orient the defective raw point clouds in a consistent manner. By taking advantage of our orientation information, the classical implicit surface reconstruction algorithms can faithfully generate the surface.

Feature detection of triangular meshes via neighbor supporting

We propose a robust method for detecting features on triangular meshes by combining normal tensor voting with neighbor supporting. Our method contains two stages: feature detection and feature refinement. First, the normal tensor voting method is modified to detect the initial features, which may include some pseudo features. Then, at the feature refinement stage, a novel salient measure deriving from the idea of neighbor supporting is developed. Benefiting from the integrated reliable salient measure feature, pseudo features can be effectively discriminated from the initially detected features and removed. Compared to previous methods based on the differential geometric property, the main advantage of our method is that it can detect both sharp and weak features. Numerical experiments show that our algorithm is robust, effective, and can produce more accurate results. We also discuss how detected features are incorporated into applications, such as feature-preserving mesh denoising and hole-filling, and present visually appealing results by integrating feature information.

Mendable consistent orientation of point clouds

Consistent normal orientation is challenging in the presence of noise, non-uniformities and thin sharp features. None of any existing local or global methods is capable of orienting all point cloud models consistently, and none of them offers a mechanism to rectify the inconsistent normals. In this paper, we present a new normal orientation method based on the multi-source propagation technique with two insights: faithful normals respecting sharp features tend to cause incorrect orientation propagation, and propagation orientation just using one source is problematic. It includes a novel orientation-benefit normal estimation algorithm for reducing wrong normal propagation near sharp features, and a multi-source orientation propagation algorithm for orientation improvement. The results of any orientation methods can be corrected by adding more credible sources, interactively or automatically, then propagating. To alleviate the manual work of interactive orientation, we devise an automatic propagation source extraction method by visibility voting. It can be applied directly to find multiple credible sources, combining with our orientation-benefit normals and multi-source propagation technique, to generate a consistent orientation, or to rectify an inconsistent orientation. The experimental results show that our methods generate consistent orientation more or as faithful as those global methods with far less computational cost. Hence it is more pragmatic and suitable to handle large point cloud models.

3D shape segmentation using multiple random walkers

Abstract Recently, 3D shapes are widely available in many ways, and the demand for shape analysis and understanding is increasing in the field of computer graphics. Shape segmentation is a significant step towards shape analysis. In this paper, we propose an interactive shape segmentation algorithm based on multiple random walkers (MRW). In the MRW system, a restart rule is designed among multiple agents on a single graph to achieve desired interactions. The process of our algorithm is different from conventional random walk. Restart distribution of each agent is computed according to the probability distributions of all agents. The experimental results demonstrate the accuracy and stability of our approach. Furthermore, our method can well handle the complex 3D shapes. In addition, we expand this MRW to the field of co-segmentation, and the results yielded by our approach are comparable to state-of-the-art co-segmentation techniques.

Normal estimation via shifted neighborhood for point cloud

Abstract For accurately estimating the normal of a point, the structure of its neighborhood has to be analyzed. All the previous methods use some neighborhood centering at the point, which is prone to be sampled from different surface patches when the point is near sharp features. Then more inaccurate normals or higher computation cost may be unavoidable. To conquer this problem, we present a fast and quality normal estimator based on neighborhood shift. Instead of using the neighborhood centered at the point, we wish to locate a neighborhood containing the point but clear of sharp features, which is usually not centering at the point. Two specific neighborhood shift techniques are designed in view of the complex structure of sharp features and the characteristic of raw point clouds. The experiments show that our method out-performs previous normal estimators in either quality or running time, even in the presence of noise and anisotropic sampling.

Locality-constrained nonnegative robust shape interaction subspace clustering and its applications☆

Abstract In this paper, we present a locality-constrained nonnegative robust shape interaction (LNRSI) subspace clustering method. LNRSI integrates the local manifold structure of data into the robust shape interaction (RSI) in a unified formulation, which guarantees the locality and the low-rank property of the optimal affinity graph. Compared with traditional low-rank representation (LRR) learning method, LNRSI can not only pursuit the global structure of data space by low-rank regularization, but also keep the locality manifold, which leads to a sparse and low-rank affinity graph. Due to the clear block-diagonal effect of the affinity graph, LNRSI is robust to noise and occlusions, and achieves a higher rate of correct clustering. The theoretical analysis of the clustering effect is also discussed. An efficient solution based on linearized alternating direction method with adaptive penalty (LADMAP) is built for our method. Finally, we evaluate the performance of LNRSI on both synthetic data and real computer vision tasks, i.e., motion segmentation and handwritten digit clustering. The experimental results show that our LNRSI outperforms several state-of-the-art algorithms.