The process of aligning a pair of shapes is a fundamental operation in computer graphics. Traditional alignment methods rely heavily on matching corresponding points or features, a paradigm that falters when significant shape portions are missing. In this paper, we present a novel alignment technique between two 2D shapes that is robust to shape incompleteness. We take an unsupervised learning approach, and train a neural network on the task of shape alignment using pairs of shapes for self-supervision. Our network, called FFDnet, learns the space of warping transformations between two shapes by performing a free-form deformation on a source shape such that it aligns well with a potentially geometrically distinct partial target shape. With this extensive training, we aim for the network to form a specialized expertise over the common characteristics of the shapes in each dataset, supporting a higher-level understanding of the expected shape space that a local approach is oblivious to. Specifically, the network is trained to warp complete source shapes to incomplete targets generated from full shapes, as if the target shapes were complete, thus essentially rendering the alignment partial-shape agnostic. We constrain FFDnet through an anisotropic total variation identity regularization to promote piecewise smooth deformation fields,

Most recent garment capturing techniques rely on acquiring multiple views of clothing, which may not always be readily available, especially in the case of pre-existing photographs from the web. As an alternative, we propose a method that is able to compute a rich and realistic 3D model of a human body and its outfits from a single photograph with little human interaction. Our algorithm is not only able to capture the global shape and geometry of the clothing, it can also extract small but important details of cloth, such as occluded wrinkles and folds. Unlike previous methods using full 3D information (i.e. depth, multi-view images, or sampled 3D geometry), our approach achieves detailed garment recovery from a single-view image by using statistical, geometric, and physical priors and a combination of parameter estimation, semantic parsing, shape recovery, and physics-based cloth simulation. We demonstrate the effectiveness of our algorithm by re-purposing the reconstructed garments for virtual try-on and garment transfer applications, as well as cloth animation for digital characters.

Simulating (elastically) deformable models that can collide with each other and with the environment remains a challenging task. The resulting contact problems can be elegantly approached using Lagrange multipliers to represent the unknown magnitude of the response forces. Typical methods construct and solve a Linear Complementarity Problem (LCP) to obtain the response forces. This requires the inverse of the generalized mass matrix, which is in general hard to obtain for deformable-body problems. In this paper we tackle such contact problems by directly solving the Mixed Linear Complementarity Problem (MLCP) and omitting the construction of an LCP matrix. Since the MLCP is equivalent to a convex quadratic program subject to inequality constraints, we propose to use a Conjugate Residual (CR) solver as the backbone of our collision-response system. We also propose a simple yet efficient preconditioner that ensures faster convergence. Finally, our approach is faster than existing methods (at the same accuracy), and it allows accurate treatment of friction.

Synthesizing motions for legged characters in arbitrary environments is a long-standing problem that has recently received a lot of attention from the computer graphics community. We tackle this problem with a procedural approach that is generic, fully automatic and independent from motion capture data. The main contribution of this paper is a point-mass-model-based method to synthesize Center Of Mass trajectories. These trajectories are then used to generate the whole-body motion of the character. The use of a point mass model often results in physically inconsistent motions and joint limit violations. We mitigate these issues through the use of a novel formulation of the kinematic constraints which allows us to generate a quasi-static Center Of Mass trajectory, in a way that is both user-friendly and computationally efficient. We also show that the quasi-static constraint can be relaxed to generate motions usable for applications of computer graphics (on average 83% of a given trajectory remain physically consistent). Our method was integrated in an open-source contact planner and tested with different scenarios - some never addressed before- featuring legged characters performing motions in cluttered environments. The computational efficiency of our trajectory generation algorithm enables us to synthesize motions in a few seconds.

We exploit the permutation creation ability of genetic optimization to find the permutation of one point set that puts it into correspondence with another one. To this effect, we provide the first, to our knowledge, genetic algorithm for 3D shape correspondence, which is the main contribution of this paper. As another significant contribution, we present an adaptive sampling approach that relocates the matched points based on the currently available correspondence via an alternating optimization. The point sets to be matched are sampled from two isometric (or nearly isometric) shapes. The sparse one-to-one correspondence, i.e., bijection, that we produce is validated both in terms of timing and accuracy in a comprehensive evaluation suite that includes three standard shape benchmarks and state-of-the-art techniques.

In this paper, we introduce a novel method that can generate a sequence of physical transformations between 3D models with different shape and topology. Feasible transformations are realized on a chain structure with connected components that are 3D printed. Collision-free motions are computed to transform between different configurations of the 3D printed chain structure. To realize the transformation between different 3D models, we first voxelize these input models into similar number of voxels. The challenging part of our approach is to generate a simple path --- as a chain configuration to connect most voxels. A layer-based algorithm is developed with theoretical guarantee of the existence and the path length. We find that collision-free motion sequence can always be generated when using a straight line as the intermediate configuration of transformation. The effectiveness of our method is demonstrated by both the simulation and the experimental tests taken on 3D printed chains.

Many strategies exist for optimizing non-linear distortion energies in geometry and physics applications, but devising an approach that achieves the convergence promised by Newton-type methods remains challenging. In order to guarantee the positive semi-definiteness required by these methods, a numerical eigendecomposition or approximate regularization is usually needed. In this paper, we present analytic expressions for the eigensystems at each quadrature point of a wide range of isotropic distortion energies. These systems can then be used to project energy Hessians to positive semi-definiteness analytically. Unlike previous attempts, our formulation provides compact expressions that are valid both in 2D and 3D, and does not introduce spurious degeneracies. At its core, our approach utilizes the invariants of the stretch tensor that arises from the polar decomposition of the deformation gradient. We provide closed-form expressions for the eigensystems for all these invariants, and use them to systematically derive the eigensystems of any isotropic energy. Our results are suitable for geometry optimization over flat surfaces or volumes, and agnostic to both the choice of discretization and basis function. To demonstrate the efficiency of our approach, we include comparisons against existing methods on common graphics tasks such as surface parameterization and volume deformation.

A large number of imaging and computer graphics applications require localized information on the visibility of image distortions. Existing image quality metrics are not suitable for this task as they provide a single quality value per image. Existing visibility metrics produce visual difference maps, and are specifically designed for detecting just noticeable distortions but their predictions are often inaccurate. In this work, we argue that the key reason for this problem is the lack of large image collections with a good coverage of possible distortions that occur in different applications. To address the problem, we collect an extensive dataset of reference and distorted image pairs together with user markings indicating whether distortions are visible or not. We propose a statistical model that is designed for the meaningful interpretation of such data, which is affected by visual search and imprecision of manual marking. We use our dataset for training existing metrics and we demonstrate that their performance significantly improves. We show that our dataset with the proposed statistical model can be used to train a new CNN-based metric, which outperforms the existing solutions. We demonstrate the utility of such a metric in visually lossless JPEG compression, super-resolution and watermarking.

Subtractive manufacturing technologies, such as 3-axis milling, add a useful tool to the digital manufacturing arsenal. However, each milling pass using such machines can only carve a single height-field, defined with respect to the machine tray. We enable fabrication of general shapes using 3-axis milling, providing a robust algorithm to decompose any shape into a few height-field blocks. Such blocks can be manufactured with a single milling pass and then assembled to form the target geometry. Computing such decompositions requires solving a complex discrete optimization problem, variants of which are known to be NP-hard. We propose a two-step process, based on the observation that if the height-field directions are constrained to the major axes we can guarantee a valid decomposition starting from a suitable surface segmentation. Our method first produces a compact set of large, possibly overlapping, height-field blocks that jointly cover the model surface. We then compute an overlap-free decomposition via a combination of cycle elimination and topological sorting on a graph. The algorithm produces a compact set of height-field blocks that jointly describe the input model and satisfy all manufacturing constraints. We demonstrate our method on a range of inputs, and showcase several real life models manufactured using our technique.

Imaging objects obscured by occluders is a significant challenge for many applications. A camera that could ``see around corners'' could help improve navigation and mapping capabilities of autonomous vehicles or make search and rescue missions more effective. Time-resolved single-photon imaging systems have recently been demonstrated to record optical information of a scene that can lead to an estimation of the shape and reflectance of objects hidden from the line of sight of a camera. However, existing non-line-of-sight (NLOS) reconstruction algorithms have been constrained in the types of light transport effects they model for the hidden scene parts. We introduce a factored NLOS light transport representation that accounts for partial occlusions and surface normals. Based on this model, we develop a factorization approach for inverse time-resolved light transport and demonstrate high-fidelity NLOS reconstructions for challenging scenes both in simulation and with an experimental NLOS imaging system.

In this paper, we introduce a surface reconstruction method that can perform gracefully with non-uniformly-distributed, noisy, and even sparse data. We reconstruct the surface by estimating an implicit function and then obtain a triangle mesh by extracting an iso-surface from it. Our implicit function takes advantage of both the indicator function and the signed distance function. It is dominated by the indicator function at the regions away from the surface and approximates the signed distance function near the surface. On one hand, it is well defined over the entire space so that the extracted iso-surface must lie near the underlying true surface and is free of spurious sheets. On the other hand, thanks to the nice properties of the signed distance function, a smooth iso-surface can be extracted using the approach of marching cubes with simple linear interpolations. More importantly, our implicit function can be estimated directly from an explicit integral formula without solving any linear system. This direct approach leads to a simple, accurate and robust reconstruction method, which can be paralleled with little overhead. We apply our method to both synthetic and real-world scanned data and demonstrate the accuracy, robustness and efficiency of our method.

Everyone uses the sense of touch to explore the world, and roughness is one of the most important qualities in tactile perception. Roughness is a major identifier for judgments of material composition, comfort and friction, and it is tied closely to manual dexterity. The advent of high-resolution 3D printing technology provides the ability to fabricate arbitrary 3D textures with surface geometry that confers haptic properties. In this work, we address the problem of mapping object geometry to tactile roughness. We fabricate a set of carefully designed stimuli and use them in experiments with human subjects to build a perceptual space for roughness. We then match this space to a quantitative model obtained from strain fields derived from elasticity simulations of the human skin contacting the texture geometry, drawing from past research in neuroscience and psychophysics. We demonstrate how this model can be applied to predict and alter surface roughness, and we show several applications in the context of fabrication.