Zhi-Quan Cheng

Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid

Three-dimensional surface registration transforms multiple three-dimensional data sets into the same coordinate system so as to align overlapping components of these sets. Recent surveys have covered different aspects of either rigid or nonrigid registration, but seldom discuss them as a whole. Our study serves two purposes: 1) To give a comprehensive survey of both types of registration, focusing on three-dimensional point clouds and meshes and 2) to provide a better understanding of registration from the perspective of data fitting. Registration is closely related to data fitting in which it comprises three core interwoven components: model selection, correspondences and constraints, and optimization. Study of these components 1) provides a basis for comparison of the novelties of different techniques, 2) reveals the similarity of rigid and nonrigid registration in terms of problem representations, and 3) shows how overfitting arises in nonrigid registration and the reasons for increasing interest in intrinsic techniques. We further summarize some practical issues of registration which include initializations and evaluations, and discuss some of our own observations, insights and foreseeable research trends.

Style-content separation by anisotropic part scales

We perform co-analysis of a set of man-made 3D objects to allow the creation of novel instances derived from the set. We analyze the objects at the part level and treat the anisotropic part scales as a shape style. The co-analysis then allows style transfer to synthesize new objects. The key to co-analysis is part correspondence, where a major challenge is the handling of large style variations and diverse geometric content in the shape set. We propose style-content separation as a means to address this challenge. Specifically, we define a correspondence-free style signature for style clustering. We show that confining analysis to within a style cluster facilitates tasks such as co-segmentation, content classification, and deformation-driven part correspondence. With part correspondence between each pair of shapes in the set, style transfer can be easily performed. We demonstrate our analysis and synthesis results on several sets of man-made objects with style and content variations.

Symmetry Hierarchy of Man-Made Objects

We introduce symmetry hierarchy of man‐made objects, a high‐level structural representation of a 3D model providing a symmetry‐induced, hierarchical organization of the models constituent parts. Given an input mesh, we segment it into primitive parts and build an initial graph which encodes inter‐part symmetries and connectivity relations, as well as self‐symmetries in individual parts. The symmetry hierarchy is constructed from the initial graph via recursive graph contraction which either groups parts by symmetry or assembles connected sets of parts. The order of graph contraction is dictated by a set of precedence rules designed primarily to respect the law of symmetry in perceptual grouping and the principle of compactness of representation. We show that symmetry hierarchy naturally implies a hierarchical segmentation that is more meaningful than those produced by local geometric considerations. We also develop an application of symmetry hierarchies for structural shape editing.

Technical Section: Robust normal estimation for point clouds with sharp features

This paper presents a novel technique for estimating normals on unorganized point clouds. Methods from robust statistics are used to detect the best local tangent plane for each point. Therefore the algorithm is capable to deal with points located in high curvature regions or near/on complex sharp features, while being highly robust with respect to noise and outliers. In particular, the presented method reliably recovers sharp features but does not require tedious manual parameter tuning as done by current methods. The key ingredients of our approach are a robust noise-scale estimator and a kernel density estimation (KDE) based objective function. In contrast to previous approaches the noise-scale estimation is not affected by sharp features and achieves high accuracy even in the presence of outliers. In addition, our normal estimation procedure allows detection and elimination of outliers. We confirm the validity and reliability of our approach on synthetic and measured data and demonstrate applications to point cloud denoising.

A survey of methods for moving least squares surfaces

Moving least squares (MLS) surfaces representation directly defines smooth surfaces from point cloud data, on which the differential geometric properties of point set can be conveniently estimated. Nowadays, the MLS surfaces have been widely applied in the processing and rendering of point-sampled models and increasingly adopted as the standard definition of point set surfaces. We classify the MLS surface algorithms into two types: projection MLS surfaces and implicit MLS surfaces, according to employing a stationary projection or a scalar field in their definitions. Then, the properties and constrains of the MLS surfaces are analyzed. After presenting its applications, we summarize the MLS surfaces definitions in a generic form and give the outlook of the future work at last.

Shape Retrieval of Non-rigid 3D Human Models

Abstract3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. We extend our recent paper which provided a benchmark for testing non-rigid 3D shape retrieval algorithms on 3D human models. This benchmark provided a far stricter challenge than previous shape benchmarks. We have added 145 new models for use as a separate training set, in order to standardise the training data used and provide a fairer comparison. We have also included experiments with the FAUST dataset of human scans. All participants of the previous benchmark study have taken part in the new tests reported here, many providing updated results using the new data. In addition, further participants have also taken part, and we provide extra analysis of the retrieval results. A total of 25 different shape retrieval methods are compared.

Multi-scale partial intrinsic symmetry detection

We present an algorithm for multi-scale partial intrinsic symmetry detection over 2D and 3D shapes, where the scale of a symmetric region is defined by intrinsic distances between symmetric points over the region. To identify prominent symmetric regions which overlap and vary in form and scale, we decouple scale extraction and symmetry extraction by performing two levels of clustering. First, significant symmetry scales are identified by clustering sample point pairs from an input shape. Since different point pairs can share a common point, shape regions covered by points in different scale clusters can overlap. We introduce the symmetry scale matrix (SSM), where each entry estimates the likelihood two point pairs belong to symmetries at the same scale. The pair-to-pair symmetry affinity is computed based on a pair signature which encodes scales. We perform spectral clustering using the SSM to obtain the scale clusters. Then for all points belonging to the same scale cluster, we perform the second-level spectral clustering, based on a novel point-to-point symmetry affinity measure, to extract partial symmetries at that scale. We demonstrate our algorithm on complex shapes possessing rich symmetries at multiple scales.

An incremental extremely random forest classifier for online learning and tracking

Decision trees have been widely used for online learning classification. Many approaches usually need large data stream to finish decision trees induction, as show notable limitations (even fail) with small data stream. In fact, there exist many real instances with small data stream. In the paper, we propose a novel incremental extremely random forest algorithm, dealing with online learning classification with small streaming data. In our method, arriving examples are stored at the leaf nodes and used to determine when to split the leaf nodes combined with Gini index, so the trees can be expanded efficiently with a few examples. Our algorithm has been applied to solve both online learning and video object tracking problems, and the results on UCI datasets and challenging video sequences demonstrate its effectiveness and robustness.

Shape retrieval of non-rigid 3D human models

We have created a new benchmarking dataset for testing non-rigid 3D shape retrieval algorithms, one that is much more challenging than existing datasets. Our dataset features exclusively human models, in a variety of body shapes and poses. 3D models of humans are commonly used within computer graphics and vision, and so the ability to distinguish between body shapes is an important shape retrieval problem. In this track nine groups have submitted the results of a total of 22 different methods which have been tested on our new dataset.

SuperMatching: Feature Matching Using Supersymmetric Geometric Constraints

Feature matching is a challenging problem at the heart of numerous computer graphics and computer vision applications. We present the SuperMatching algorithm for finding correspondences between two sets of features. It does so by considering triples or higher order tuples of points, going beyond the pointwise and pairwise approaches typically used. SuperMatching is formulated using a supersymmetric tensor representing an affinity metric that takes into account feature similarity and geometric constraints between features: Feature matching is cast as a higher order graph matching problem. SuperMatching takes advantage of supersymmetry to devise an efficient sampling strategy to estimate the affinity tensor, as well as to store the estimated tensor compactly. Matching is performed by an efficient higher order power iteration approach that takes advantage of this compact representation. Experiments on both synthetic and real data show that SuperMatching provides more accurate feature matching than other state-of-the-art approaches for a wide range of 2D and 3D features, with competitive computational cost.