Lin Gao

An optimization approach for extracting and encoding consistent maps in a shape collection

We introduce a novel approach for computing high quality point-to-point maps among a collection of related shapes. The proposed approach takes as input a sparse set of imperfect initial maps between pairs of shapes and builds a compact data structure which implicitly encodes an improved set of maps between all pairs of shapes. These maps align well with point correspondences selected from initial maps; they map neighboring points to neighboring points; and they provide cycle-consistency, so that map compositions along cycles approximate the identity map. The proposed approach is motivated by the fact that a complete set of maps between all pairs of shapes that admits nearly perfect cycle-consistency are highly redundant and can be represented by compositions of maps through a single base shape. In general, multiple base shapes are needed to adequately cover a diverse collection. Our algorithm sequentially extracts such a small collection of base shapes and creates correspondences from each of these base shapes to all other shapes. These correspondences are found by global optimization on candidate correspondences obtained by diffusing initial maps. These are then used to create a compact graphical data structure from which globally optimal cycle-consistent maps can be extracted using simple graph algorithms. Experimental results on benchmark datasets show that the proposed approach yields significantly better results than state-of-the-art data-driven shape matching methods.

A Data-Driven Approach to Realistic Shape Morphing

Morphing between 3D objects is a fundamental technique in computer graphics. Traditional methods of shape morphing focus on establishing meaningful correspondences and finding smooth interpolation between shapes. Such methods however only take geometric information as input and thus cannot in general avoid producing unnatural interpolation, in particular for large‐scale deformations. This paper proposes a novel data‐driven approach for shape morphing. Given a database with various models belonging to the same category, we treat them as data samples in the plausible deformation space. These models are then clustered to form local shape spaces of plausible deformations. We use a simple metric to reasonably represent the closeness between pairs of models. Given source and target models, the morphing problem is casted as a global optimization problem of finding a minimal distance path within the local shape spaces connecting these models. Under the guidance of intermediate models in the path, an extended as‐rigid‐as‐possible interpolation is used to produce the final morphing. By exploiting the knowledge of plausible models, our approach produces realistic morphing for challenging cases as demonstrated by various examples in the paper.

L p shape deformation

Shape deformation is a fundamental tool in geometric modeling. Existing methods consider preserving local details by minimizing some energy functional measuring local distortions in the L2 norm. This strategy distributes distortions quite uniformly to all the vertices and penalizes outliers. However, there is no unique answer for a natural deformation as it depends on the nature of the objects. Inspired by recent sparse signal reconstruction work with non L2 norm, we introduce general Lp norms to shape deformation; the positive parameter p provides the user with a flexible control over the distribution of unavoidable distortions. Compared with the traditional L2 norm, using smaller p, distortions tend to be distributed to a sparse set of vertices, typically in feature regions, thus making most areas less distorted and structures better preserved. On the other hand, using larger p tends to distribute distortions more evenly across the whole model. This flexibility is often desirable as it mimics objects made up with different materials. By specifying varying p over the shape, more flexible control can be achieved. We demonstrate the effectiveness of the proposed algorithm with various examples.

Active Exploration of Large 3D Model Repositories

With broader availability of large-scale 3D model repositories, the need for efficient and effective exploration becomes more and more urgent. Existing model retrieval techniques do not scale well with the size of the database since often a large number of very similar objects are returned for a query, and the possibilities to refine the search are quite limited. We propose an interactive approach where the user feeds an active learning procedure by labeling either entire models or parts of them as “like” or “dislike” such that the system can automatically update an active set of recommended models. To provide an intuitive user interface, candidate models are presented based on their estimated relevance for the current query. From the methodological point of view, our main contribution is to exploit not only the similarity between a query and the database models but also the similarities among the database models themselves. We achieve this by an offline pre-processing stage, where global and local shape descriptors are computed for each model and a sparse distance metric is derived that can be evaluated efficiently even for very large databases. We demonstrate the effectiveness of our method by interactively exploring a repository containing over 100 K models.

A survey on human performance capture and animation

With the rapid development of computing technology, three-dimensional (3D) human body models and their dynamic motions are widely used in the digital entertainment industry. Human performance mainly involves human body shapes and motions. Key research problems in human performance animation include how to capture and analyze static geometric appearance and dynamic movement of human bodies, and how to simulate human body motions with physical effects. In this survey, according to the main research directions of human body performance capture and animation, we summarize recent advances in key research topics, namely human body surface reconstruction, motion capture and synthesis, as well as physics-based motion simulation, and further discuss future research problems and directions. We hope this will be helpful for readers to have a comprehensive understanding of human performance capture and animation.

Efficient and Flexible Deformation Representation for Data-Driven Surface Modeling

Effectively characterizing the behavior of deformable objects has wide applicability but remains challenging. We present a new rotation-invariant deformation representation and a novel reconstruction algorithm to accurately reconstruct the positions and local rotations simultaneously. Meshes can be very efficiently reconstructed from our representation by matrix pre-decomposition, while, at the same time, hard or soft constraints can be flexibly specified with only positions of handles needed. Our approach is thus particularly suitable for constrained deformations guided by examples, providing significant benefits over state-of-the-art methods. Based on this, we further propose novel data-driven approaches to mesh deformation and non-rigid registration of deformable objects. Both problems are formulated consistently as finding an optimized model in the shape space that satisfies boundary constraints, either specified by the user, or according to the scan. By effectively exploiting the knowledge in the shape space, our method produces realistic deformation results in real-time and produces high quality registrations from a template model to a single noisy scan captured using a low-quality depth camera, outperforming state-of-the-art methods.

Rigidity controllable as-rigid-as-possible shape deformation

Shape deformation is one of the fundamental techniques in geometric processing. One principle of deformation is to preserve the geometric details while distributing the necessary distortions uniformly. To achieve this, state-of-the-art techniques deform shapes in a locally as-rigid-as-possible (ARAP) manner. Existing ARAP deformation methods optimize rigid transformations in the 1-ring neighborhoods and maintain the consistency between adjacent pairs of rigid transformations by single overlapping edges. In this paper, we make one step further and propose to use larger local neighborhoods to enhance the consistency of adjacent rigid transformations. This is helpful to keep the geometric details better and distribute the distortions more uniformly. Moreover, the size of the expanded local neighborhoods provides an intuitive parameter to adjust physical stiffness. The larger the neighborhood is, the more rigid the material is. Based on these, we propose a novel rigidity controllable mesh deformation method where shape rigidity can be flexibly adjusted. The size of the local neighborhoods can be learned from datasets of deforming objects automatically or specified by the user, and may vary over the surface to simulate shapes composed of mixed materials. Various examples are provided to demonstrate the effectiveness of our method.

Data-driven shape interpolation and morphing editing

Shape interpolation has many applications in computer graphics such as morphing for computer animation. In this paper, we propose a novel data‐driven mesh interpolation method. We adapt patch‐based linear rotational invariant coordinates to effectively represent deformations of models in a shape collection, and utilize this information to guide the synthesis of interpolated shapes. Unlike previous data‐driven approaches, we use a rotation/translation invariant representation which defines the plausible deformations in a global continuous space. By effectively exploiting the knowledge in the shape space, our method produces realistic interpolation results at interactive rates, outperforming state‐of‐the‐art methods for challenging cases. We further propose a novel approach to interactive editing of shape morphing according to the shape distribution. The user can explore the morphing path and select example models intuitively and adjust the path with simple interactions to edit the morphing sequences. This provides a useful tool to allow users to generate desired morphing with little effort. We demonstrate the effectiveness of our approach using various examples.

Biharmonic deformation transfer with automatic key point selection

Deformation transfer is an important research problem in geometry processing and computer animation.A fundamental problem for existing deformation transfer methods is to build reliable correspondences. This is challenging, especially when the source and target shapes differ significantly and manual labeling is typically used. We propose a novel deformation transfer method that aims at minimizing user effort. We adapt a biharmonic weight deformation framework which is able to produce plausible deformation even with only a few key points. We then develop an automatic algorithm to identify a minimum set of key points on the source model that characterizes the deformation well. While minimal user effort is still needed to specify corresponding points on the target model for the selected key points, our approach avoids the difficult problem of choosing key points. Experimental results demonstrate that our method, despite requiring little user effort, produces better deformation results than alternative solutions. Keywords: shape deformation; biharmonic weights; key point selection; deformation transfer