Hujun Bao

Mesh editing with poisson-based gradient field manipulation

In this paper, we introduce a novel approach to mesh editing with the Poisson equation as the theoretical foundation. The most distinctive feature of this approach is that it modifies the original mesh geometry implicitly through gradient field manipulation. Our approach can produce desirable and pleasing results for both global and local editing operations, such as deformation, object merging, and smoothing. With the help from a few novel interactive tools, these operations can be performed conveniently with a small amount of user interaction. Our technique has three key components, a basic mesh solver based on the Poisson equation, a gradient field manipulation scheme using local transforms, and a generalized boundary condition representation based on local frames. Experimental results indicate that our framework can outperform previous related mesh editing techniques.

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.

Consistent Depth Maps Recovery from a Video Sequence

This paper presents a novel method for recovering consistent depth maps from a video sequence. We propose a bundle optimization framework to address the major difficulties in stereo reconstruction, such as dealing with image noise, occlusions, and outliers. Different from the typical multi-view stereo methods, our approach not only imposes the photo-consistency constraint, but also explicitly associates the geometric coherence with multiple frames in a statistical way. It thus can naturally maintain the temporal coherence of the recovered dense depth maps without over-smoothing. To make the inference tractable, we introduce an iterative optimization scheme by first initializing the disparity maps using a segmentation prior and then refining the disparities by means of bundle optimization. Instead of defining the visibility parameters, our method implicitly models the reconstruction noise as well as the probabilistic visibility. After bundle optimization, we introduce an efficient space-time fusion algorithm to further reduce the reconstruction noise. Our automatic depth recovery is evaluated using a variety of challenging video 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.

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.

Poisson shape interpolation

In this paper, we propose a novel shape interpolation approach based on Poisson equation. We formulate the trajectory problem of shape interpolation as solving Poisson equations defined on a domain mesh. A non-linear gradient field interpolation method is proposed to take both vertex coordinates and surface orientation into account. With proper boundary conditions, the in-between shapes are reconstructed implicitly from the interpolated gradient fields, while traditional methods usually manipulate vertex coordinates directly. Besides of global shape interpolation, our method is also applicable to local shape interpolation, and can be further enhanced by incorporating with deformation. Our approach can generate visual pleasing and physical plausible morphing sequences with stable area and volume changes. Experimental results demonstrate that our technique can avoid the shrinkage problem appeared in linear shape interpolation.

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.

Inverse texture synthesis

The quality and speed of most texture synthesis algorithms depend on a 2D input sample that is small and contains enough texture variations. However, little research exists on how to acquire such sample. For homogeneous patterns this can be achieved via manual cropping, but no adequate solution exists for inhomogeneous or globally varying textures, i.e. patterns that are local but not stationary, such as rusting over an iron statue with appearance conditioned on varying moisture levels. We present inverse texture synthesis to address this issue. Our inverse synthesis runs in the opposite direction with respect to traditional forward synthesis: given a large globally varying texture, our algorithm automatically produces a small texture compaction that best summarizes the original. This small compaction can be used to reconstruct the original texture or to re-synthesize new textures under user-supplied controls. More important, our technique allows real-time synthesis of globally varying textures on a GPU, where the texture memory is usually too small for large textures. We propose an optimization framework for inverse texture synthesis, ensuring that each input region is properly encoded in the output compaction. Our optimization process also automatically computes orientation fields for anisotropic textures containing both low- and high-frequency regions, a situation difficult to handle via existing techniques.

Laplacian Regularized Gaussian Mixture Model for Data Clustering

Gaussian Mixture Models (GMMs) are among the most statistically mature methods for clustering. Each cluster is represented by a Gaussian distribution. The clustering process thereby turns to estimate the parameters of the Gaussian mixture, usually by the Expectation-Maximization algorithm. In this paper, we consider the case where the probability distribution that generates the data is supported on a submanifold of the ambient space. It is natural to assume that if two points are close in the intrinsic geometry of the probability distribution, then their conditional probability distributions are similar. Specifically, we introduce a regularized probabilistic model based on manifold structure for data clustering, called Laplacian regularized Gaussian Mixture Model (LapGMM). The data manifold is modeled by a nearest neighbor graph, and the graph structure is incorporated in the maximum likelihood objective function. As a result, the obtained conditional probability distribution varies smoothly along the geodesics of the data manifold. Experimental results on real data sets demonstrate the effectiveness of the proposed approach.

An efficient GPU-based approach for interactive global illumination

This paper presents a GPU-based method for interactive global illumination that integrates complex effects such as multi-bounce indirect lighting, glossy reflections, caustics, and arbitrary specular paths. Our method builds upon scattered data sampling and interpolation on the GPU. We start with raytraced shading points and partition them into coherent shading clusters using adaptive seeding followed by k-means. At each cluster center we apply final gather to evaluate its incident irradiance using GPU-based photon mapping. We approximate the entire photon tree as a compact illumination cut, thus reducing the final gather cost for each ray. The sampled irradiance values are then interpolated at all shading points to produce rendering. Our method exploits the spatial coherence of illumination to reduce sampling cost. We sample sparsely and the distribution of sample points conforms with the underlying illumination changes. Therefore our method is both fast and preserves high rendering quality. Although the same property has been exploited by previous caching and adaptive sampling methods, these methods typically require sequential computation of sample points, making them ill-suited for the GPU. In contrast, we select sample points adaptively in a single pass, enabling parallel computation. As a result, our algorithm runs entirely on the GPU, achieving interactive rates for scenes with complex illumination effects.