Xinguo Liu

Large mesh deformation using the volumetric graph Laplacian

We present a novel technique for large deformations on 3D meshes using the volumetric graph Laplacian. We first construct a graph representing the volume inside the input mesh. The graph need not form a solid meshing of the input meshs interior; its edges simply connect nearby points in the volume. This graphs Laplacian encodes volumetric details as the difference between each point in the graph and the average of its neighbors. Preserving these volumetric details during deformation imposes a volumetric constraint that prevents unnatural changes in volume. We also include in the graph points a short distance outside the mesh to avoid local self-intersections. Volumetric detail preservation is represented by a quadric energy function. Minimizing it preserves details in a least-squares sense, distributing error uniformly over the whole deformed mesh. It can also be combined with conventional constraints involving surface positions, details or smoothness, and efficiently minimized by solving a sparse linear system.We apply this technique in a 2D curve-based deformation system allowing novice users to create pleasing deformations with little effort. A novel application of this system is to apply nonrigid and exaggerated deformations of 2D cartoon characters to 3D meshes. We demonstrate our systems potential with several examples.

Subspace gradient domain mesh deformation

In this paper we present a general framework for performing constrained mesh deformation tasks with gradient domain techniques. We present a gradient domain technique that works well with a wide variety of linear and nonlinear constraints. The constraints we introduce include the nonlinear volume constraint for volume preservation, the nonlinear skeleton constraint for maintaining the rigidity of limb segments of articulated figures, and the projection constraint for easy manipulation of the mesh without having to frequently switch between multiple viewpoints. To handle nonlinear constraints, we cast mesh deformation as a nonlinear energy minimization problem and solve the problem using an iterative algorithm. The main challenges in solving this nonlinear problem are the slow convergence and numerical instability of the iterative solver. To address these issues, we develop a subspace technique that builds a coarse control mesh around the original mesh and projects the deformation energy and constraints onto the control mesh vertices using the mean value interpolation. The energy minimization is then carried out in the subspace formed by the control mesh vertices. Running in this subspace, our energy minimization solver is both fast and stable and it provides interactive responses. We demonstrate our deformation constraints and subspace deformation technique with a variety of constrained deformation examples.

Synthesizing bidirectional texture functions for real-world surfaces

In this paper, we present a novel approach to synthetically generating bidirectional texture functions (BTFs) of real-world surfaces. Unlike a conventional two-dimensional texture, a BTF is a six-dimensional function that describes the appearance of texture as a function of illumination and viewing directions. The BTF captures the appearance change caused by visible small-scale geometric details on surfaces. From a sparse set of images under different viewing/lighting settings, our approach generates BTFs in three steps. First, it recovers approximate 3D geometry of surface details using a shape-from-shading method. Then, it generates a novel version of the geometric details that has the same statistical properties as the sample surface with a non-parametric sampling method. Finally, it employs an appearance preserving procedure to synthesize novel images for the recovered or generated geometric details under various viewing/lighting settings, which then define a BTF. Our experimental results demonstrate the effectiveness of our approach.

Spectral quadrangulation with orientation and alignment control

This paper presents a new quadrangulation algorithm, extending the spectral surface quadrangulation approach where the coarse quadrangular structure is derived from the Morse-Smale complex of an eigenfunction of the Laplacian operator on the input mesh. In contrast to the original scheme, we provide flexible explicit controls of the shape, size, orientation and feature alignment of the quadrangular faces. We achieve this by proper selection of the optimal eigenvalue (shape), by adaption of the area term in the Laplacian operator (size), and by adding special constraints to the Laplace eigenproblem (orientation and alignment). By solving a generalized eigen-problem we can generate a scalar field on the mesh whose Morse-Smale complex is of high quality and satisfies all the user requirements. The final quadrilateral mesh is generated from the Morse-Smale complex by computing a globally smooth parametrization. Here we additionally introduce edge constraints to preserve user specified feature lines accurately.

Real-time soft shadows in dynamic scenes using spherical harmonic exponentiation

Previous methods for soft shadows numerically integrate over many light directions at each receiver point, testing blocker visibility in each direction. We introduce a method for real-time soft shadows in dynamic scenes illuminated by large, low-frequency light sources where such integration is impractical. Our method operates on vectors representing low-frequency visibility of blockers in the spherical harmonic basis. Blocking geometry is modeled as a set of spheres; relatively few spheres capture the low-frequency blocking effect of complicated geometry. At each receiver point, we compute the product of visibility vectors for these blocker spheres as seen from the point. Instead of computing an expensive SH product per blocker as in previous work, we perform inexpensive vector sums to accumulate the log of blocker visibility. SH exponentiation then yields the product visibility vector over all blockers. We show how the SH exponentiation required can be approximated accurately and efficiently for low-order SH, accelerating previous CPU-based methods by a factor of 10 or more, depending on blocker complexity, and allowing real-time GPU implementation.

A wave-based anisotropic quadrangulation method

This paper proposes a new method for remeshing a surface into anisotropically sized quads. The basic idea is to construct a special standing wave on the surface to generate the global quadrilateral structure. This wave based quadrangulation method is capable of controlling the quad size in two directions and precisely aligning the quads with feature lines. Similar to the previous methods, we augment the input surface with a vector field to guide the quad orientation. The anisotropic size control is achieved by using two size fields on the surface. In order to reduce singularity points, the size fields are optimized by a new curl minimization method. The experimental results show that the proposed method can successfully handle various quadrangulation requirements and complex shapes, which is difficult for the existing state-of-the-art methods.

Octree-based fusion for realtime 3D reconstruction

This paper proposes an octree-based surface representation for KinectFusion, a realtime reconstruction technique of in-door scenes using a low-cost moving depth camera and a commodity graphics hardware. In KinectFusion, the scene is represented as a signed distance function (SDF) and stored as an uniform grid of voxels. Though the grid-based SDF is suitable for parallel computation in graphics hardware, most of the storage are wasted, because the geometry is very sparse in the scene volume. In order to reduce the memory cost and save the computation time, we represent the SDF in an octree, and developed several octree-based algorithms for reconstruction update and surface prediction that are suitable for parallel computation in graphics hardware. In the reconstruction update step, the octree nodes are adaptively split in breath-first order. To handle scenes with moving objects, the corresponding nodes are automatically detected and removed to avoid storage overflow. In the surface prediction step, an octree-based ray tracing method is adopted and parallelized for graphic hardware. To further reduce the computation time, the octree is organized into four layers, called top layer, branch layer, middle layer and data layer. The experiments showed that, the proposed method consumes only less than 10% memory of original KinectFusion method, and achieves faster performance. Consequently, it can reconstruct scenes with more than 10 times larger size than the original KinectFusion on the same hardware setup.

Synthesis and rendering of bidirectional texture functions on arbitrary surfaces

The bidirectional texture function (BTF) is a 6D function that describes the appearance of a real-world surface as a function of lighting and viewing directions. The BTF can model the fine-scale shadows, occlusions, and specularities caused by surface mesostructures. We present algorithms for efficient synthesis of BTFs on arbitrary surfaces and for hardware-accelerated rendering. For both synthesis and rendering, a main challenge is handling the large amount of data in a BTF sample. To addresses this challenge, we approximate the BTF sample by a small number of 4D point appearance functions (PAFs) multiplied by 2D geometry maps. The geometry maps and PAFs lead to efficient synthesis and fast rendering of BTFs on arbitrary surfaces. For synthesis, a surface BTF can be generated by applying a texton-based synthesis algorithm to a small set of 2D geometry maps while leaving the companion 4D PAFs untouched. As for rendering, a surface BTF synthesized using geometry maps is well-suited for leveraging the programmable vertex and pixel shaders on the graphics hardware. We present a real-time BTF rendering algorithm that runs at the speed of about 30 frames/second on a mid-level PC with an ATI Radeon 8500 graphics card. We demonstrate the effectiveness of our synthesis and rendering algorithms using both real and synthetic BTF samples.

Templateless Quasi-rigid Shape Modeling with Implicit Loop-Closure

This paper presents a method for quasi-rigid objects modeling from a sequence of depth scans captured at different time instances. As quasi-rigid objects, such as human bodies, usually have shape motions during the capture procedure, it is difficult to reconstruct their geometries. We represent the shape motion by a deformation graph, and propose a model-to-part method to gradually integrate sampled points of depth scans into the deformation graph. Under an as-rigid-as-possible assumption, the model-to-part method can adjust the deformation graph non-rigidly, so as to avoid error accumulation in alignment, which also implicitly achieves loop-closure. To handle the drift and topological error for the deformation graph, two algorithms are introduced. First, we use a two-stage registration to largely keep the rigid motion part. Second, in the step of graph integration, we topology-adaptively integrate new parts and dynamically control the regularization effect of the deformation graph. We demonstrate the effectiveness and robustness of our method by several depth sequences of quasi-rigid objects, and an application in human shape modeling.

Variational sphere set approximation for solid objects

We approximate a solid object represented as a triangle mesh by a bounding set of spheres having minimal summed volume outside the object. We show how outside volume for a single sphere can be computed using a simple integration over the object’s triangles. We then minimize the total outside volume over all spheres in the set using a variant of iterative Lloyd clustering that splits the mesh points into sets and bounds each with an outside volume-minimizing sphere. The resulting sphere sets are tighter than those of previous methods. In experiments comparing against a state-of-the-art alternative (adaptive medial axis), our method often requires half as many spheres, or fewer, to obtain the same error, under a variety of error metrics including total outside volume, shadowing fidelity, and proximity measurement.