Junjie Cao

Point Cloud Skeletons via Laplacian Based Contraction

We present an algorithm for curve skeleton extraction via Laplacian-based contraction. Our algorithm can be applied to surfaces with boundaries, polygon soups, and point clouds. We develop a contraction operation that is designed to work on generalized discrete geometry data, particularly point clouds, via local Delaunay triangulation and topological thinning. Our approach is robust to noise and can handle moderate amounts of missing data, allowing skeleton-based manipulation of point clouds without explicit surface reconstruction. By avoiding explicit reconstruction, we are able to perform skeleton-driven topology repair of acquired point clouds in the presence of large amounts of missing data. In such cases, automatic surface reconstruction schemes tend to produce incorrect surface topology. We show that the curve skeletons we extract provide an intuitive and easy-to-manipulate structure for effective topology modification, leading to more faithful surface reconstruction.

Adaptive Partial Differential Equation Learning for Visual Saliency Detection

Partial Differential Equations (PDEs) have been successful in solving many low-level vision tasks. However, it is a challenging task to directly utilize PDEs for visual saliency detection due to the difficulty in incorporating human perception and high-level priors to a PDE system. Instead of designing PDEs with fixed formulation and boundary condition, this paper proposes a novel framework for adaptively learning a PDE system from an image for visual saliency detection. We assume that the saliency of image elements can be carried out from the relevances to the saliency seeds (i.e., the most representative salient elements). In this view, a general Linear Elliptic System with Dirichlet boundary (LESD) is introduced to model the diffusion from seeds to other relevant points. For a given image, we first learn a guidance map to fuse human prior knowledge to the diffusion system. Then by optimizing a discrete submodular function constrained with this LESD and a uniform matroid, the saliency seeds (i.e., boundary conditions) can be learnt for this image, thus achieving an optimal PDE system to model the evolution of visual saliency. Experimental results on various challenging image sets show the superiority of our proposed learning-based PDEs for visual saliency detection.

Topology-varying 3D shape creation via structural blending

We introduce an algorithm for generating novel 3D models via topology-varying shape blending. Given a source and a target shape, our method blends them topologically and geometrically, producing continuous series of in-betweens as new shape creations. The blending operations are defined on a spatio-structural graph composed of medial curves and sheets. Such a shape abstraction is structure-oriented, part-aware, and facilitates topology manipulations. Fundamental topological operations including split and merge are realized by allowing one-to-many correspondences between the source and the target. Multiple blending paths are sampled and presented in an interactive, exploratory tool for creative 3D modeling. We show a variety of topology-varying 3D shapes generated via continuous structural blending between man-made shapes exhibiting complex topological differences, in real time.

Consolidation of low-quality point clouds from outdoor scenes

The emergence of laser/LiDAR sensors, reliable multi‐view stereo techniques and more recently consumer depth cameras have brought point clouds to the forefront as a data format useful for a number of applications. Unfortunately, the point data from those channels often incur imperfection, frequently contaminated with severe outliers and noise. This paper presents a robust consolidation algorithm for low‐quality point data from outdoor scenes, which essentially consists of two steps: 1) outliers filtering and 2) noise smoothing. We first design a connectivity‐based scheme to evaluate outlierness and thereby detect sparse outliers. Meanwhile, a clustering method is used to further remove small dense outliers. Both outlier removal methods are insensitive to the choice of the neighborhood size and the levels of outliers. Subsequently, we propose a novel approach to estimate normals for noisy points based on robust partial rankings, which is the basis of noise smoothing. Accordingly, a fast approach is exploited to smooth noise, while preserving sharp features. We evaluate the effectiveness of the proposed method on the point clouds from a variety of outdoor scenes.

Curve Style Analysis in a Set of Shapes

The word ‘style’ can be interpreted in so many different ways in so many different contexts. To provide a general analysis and understanding of styles is a highly challenging problem. We pose the open question ‘how to extract styles from geometric shapes?’ and address one instance of the problem. Specifically, we present an unsupervised algorithm for identifying curve styles in a set of shapes. In our setting, a curve style is explicitly represented by a mode of curve features appearing along the 2D silhouettes of the shapes in the set. Unlike previous attempts, we do not rely on any preconceived conceptual characterisations, for example, via specific shape descriptors, to define what is or is not a style. Our definition of styles is data‐dependent; it depends on the input set but we do not require computing a shape correspondence across the set. We provide an operational definition of curve styles which focuses on separating curve features that represent styles from curve features that are content revealing. To this end, we develop a novel formulation and associated algorithm for style‐content separation. The analysis is based on a feature‐shape association matrix (FSM) whose rows correspond to modes of curve features, columns to shapes in the set, and each entry expresses the extent a feature mode is present in a shape. We make several assumptions to drive style‐content separation which only involve properties of, and relations between, rows of the FSM. Computationally, our algorithm only requires row‐wise correlation analysis in the FSM and a heuristic solution of an instance of the set cover problem. Results are demonstrated on several data sets showing the identification of curve styles. We also develop and demonstrate several style‐related applications including style exaggeration, removal, blending, and style transfer for 2D shape synthesis.

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.

Mesh saliency via ranking unsalient patches in a descriptor space

This paper presents a novel mesh saliency detection approach based on manifold ranking in a descriptor space. Starting from the over-segmented patches of a mesh, we compute a descriptor vector for each patch based on Zernike coefficients, and the local distinctness of each patch by a center-surround operator. Patches with small or high local distinctness are named as background or foreground patches, respectively. Unlike existing mesh saliency methods which focus on local or global contrast, we estimate the saliency of patches based on their relevances to some of the most unsalient background patches, i.e. background patches with the smallest local distinctness, via manifold ranking. Compared with ranking with some of the most salient foreground patches as queries, this improves the robustness of our method and contributes to make our method insensitive to the queries estimated. The ranking is performed in the descriptor space of the patches by incorporating the manifold structure of the shape descriptors, which therefore is more applicable for mesh saliency since the salient regions of a mesh are often scattered in spatial domain. Finally, a Laplacian smoothing procedure is applied to spread the patch saliency to each vertex. Comparisons with the state-of-the-art methods on a wide range of models show the effectiveness and robustness of our approach. Graphical abstractDisplay Omitted HighlightsA simple mesh saliency detection method via manifold ranking is proposed.We select some unsalient background patches as queries to achieve more robust results.Ranking in the descriptor space of the patches reveals the saliency patches independent of their locations and cardinality.Our method achieves faithful results using only single scale descriptor.Our algorithm is comparable with state-of-the-art methods.

Empirical mode decomposition on surfaces

Empirical Mode Decomposition (EMD) is a powerful tool for analysing non-linear and non-stationary signals, and has drawn a great deal of attentions in various areas. In this paper, we generalize the classical EMD from Euclidean space to the setting of surfaces represented as triangular meshes. Inspired by the EMD, we also propose a feature-preserving smoothing method based on extremal envelopes. The core of our generalized EMD on surfaces is an envelope computation method that solves a bi-harmonic field with Dirichlet boundary conditions. Experimental results show that the proposed generalization of EMD on surfaces works well. We also demonstrate that the generalized EMD can be effectively utilized in filtering scalar functions defined over surfaces and surfaces themselves.

Deformation-driven topology-varying 3D shape correspondence

We present a deformation-driven approach to topology-varying 3D shape correspondence. In this paradigm, the best correspondence between two shapes is the one that results in a minimal-energy, possibly topology-varying, deformation that transforms one shape to conform to the other while respecting the correspondence. Our deformation model, called GeoTopo transform, allows both geometric and topological operations such as part split, duplication, and merging, leading to fine-grained and piecewise continuous correspondence results. The key ingredient of our correspondence scheme is a deformation energy that penalizes geometric distortion, encourages structure preservation, and simultaneously allows topology changes. This is accomplished by connecting shape parts using structural rods, which behave similarly to virtual springs but simultaneously allow the encoding of energies arising from geometric, structural, and topological shape variations. Driven by the combined deformation energy, an optimal shape correspondence is obtained via a pruned beam search. We demonstrate our deformation-driven correspondence scheme on extensive sets of man-made models with rich geometric and topological variation and compare the results to state-of-the-art approaches.

Feature-Preserving Surface Reconstruction From Unoriented, Noisy Point Data

We propose a robust method for surface mesh reconstruction from unorganized, unoriented, noisy and outlier‐ridden 3D point data. A kernel‐based scale estimator is introduced to estimate the scale of inliers of the input data. The best tangent planes are computed for all points based on mean shift clustering and adaptive scale sample consensus, followed by detecting and removing outliers. Subsequently, we estimate the normals for the remaining points and smooth the noise using a surface fitting and projection strategy. As a result, the outliers and noise are removed and filtered, while the original sharp features are well preserved. We then adopt an existing method to reconstruct surface meshes from the processed point data. To preserve sharp features of the generated meshes that are often blurred during reconstruction, we describe a two‐step approach to effectively recover original sharp features. A number of examples are presented to demonstrate the effectiveness and robustness of our method.