Abstract Non‐rigid iterative closest point (ICP) is a popular framework for shape alignment, typically formulated as alternating iteration of correspondence search and shape transformation. A common approach in the shape transformation stage is to solve a linear least squares problem to find a smoothness‐regularized transform that fits the target shape. However, completely solving the linear least squares problem to obtain a transform is wasteful because the correspondences used for constructing the problem are imperfect, especially at early iterations. In this work, we design a novel framework to compute a transform in single step without the exact linear solve. Our key idea is to use only a single step of an iterative linear system solver, conjugate gradient, at each shape transformation stage. For this single‐step scheme to be effective, appropriate preconditioning of the linear system is required. We design a novel adaptive Sobolev‐Jacobi preconditioning method for our single‐step transform to produce a large and regularized shape update suitable for correspondence search in the next iteration. We demonstrate that our preconditioned single‐step transform stably accelerates challenging 3D surface registration tasks.

Non-rigid registration of 3D shape collections using a template mesh is essential for constructing 3D datasets. Traditional non-rigid Iterative Closest Point (ICP) methods rely on manually selected template meshes, which can result in inconsistent registrations when applied to diverse shape collections. This inconsistency arises particularly when the template lacks common shape features with the input instances or when landmark annotations are sparse. To overcome this limitation, we propose a novel ICP framework that jointly optimizes a shared template shape and its instance-wise deformations. Our joint optimization framework assigns distinct roles to the shared template and instance-wise deformations: the template captures common shape features, while instance-wise deformations handle residual registration errors. We use stronger smoothness regularization on the instance-wise deformations in early iterations to prioritize the accumulation of common details on the template. Additionally, a distortion alignment energy minimizes interinstance map distortions, promoting consistent instance-wise deformations. On challenging 3D datasets with large shape variations, our method achieves state-of-the-art fitting accuracy and consistent results in shape averaging and deformation transfer. By removing the need for a carefully selected preset template, our method extends the capability of extrinsic non-rigid registration frameworks, offering a more robust and flexible solution for challenging registration scenarios.

Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To reconstruct an accurate depth map from the input normal map, hidden surface gradients occurring from the jumps must be handled. To model these jumps correctly, we design a novel discretization scheme for the domain of normal integration. Our key idea is to introduce auxiliary edges, which bridge between piecewise-smooth patches in the domain so that the magnitude of hidden jumps can be explicitly expressed. Using the auxiliary edges, we design a novel algorithm to optimize the discontinuity and the depth map from the input normal map. Our method optimizes dis-continuities by using a combination of iterative re-weighted least squares and iterative filtering of the jump magnitudes on auxiliary edges to provide strong sparsity regularization. Compared to previous discontinuity-preserving normal integration methods, which model the magnitudes of jumps only implicitly, our method reconstructs subtle disconti-nuities accurately thanks to our explicit representation of jumps allowing for strong sparsity regularization.

In this paper, we study hybrid neural representations for spherical data, a domain of increasing relevance in scientific research. In particular, our work focuses on weather and climate data as well as cosmic microwave background (CMB) data. Although previous studies have delved into coordinate-based neural representations for spherical signals, they often fail to capture the intricate details of highly nonlinear signals. To address this limitation, we introduce a novel approach named Hybrid Neural Representations for Spherical data (HNeR-S). Our main idea is to use spherical feature-grids to obtain positional features which are combined with a multi-layer perceptron to predict the target signal. We consider feature-grids with equirectangular and hierarchical equal area isolatitude pixelization structures that align with weather data and CMB data, respectively. We extensively verify the effectiveness of our HNeR-S for regression, super-resolution, temporal interpolation, and compression tasks.

In recent years, the neural stochastic differential equation (NSDE) has gained attention for modeling stochastic representations with great success in various types of applications. However, it typically loses expressivity when the data representation is manifold-valued. To address this issue, we suggest a principled method for expressing the stochastic representation with the Riemannian neural SDE (RNSDE), which extends the conventional Euclidean NSDE. Empirical results for various tasks demonstrate that the proposed method significantly outperforms baseline methods.

Three-dimensional (3D) reconstruction using an RGB-D camera has been widely adopted for realistic content creation. However, high-quality texture mapping onto the reconstructed geometry is often treated as an offline step that should run after geometric reconstruction. In this article, we propose TextureMe , a novel approach that jointly recovers 3D surface geometry and high-quality texture in real time. The key idea is to create triangular texture patches that correspond to zero-crossing triangles of truncated signed distance function (TSDF) progressively in a global texture atlas. Our approach integrates color details into the texture patches in parallel with the depth map integration to a TSDF. It also actively updates a pool of texture patches to adapt TSDF changes and minimizes misalignment artifacts that occur due to camera drift and image distortion. Our global texture atlas representation is fully compatible with conventional texture mapping. As a result, our approach produces high-quality textures without utilizing additional texture map optimization, mesh parameterization, or heavy post-processing. High-quality scenes produced by our real-time approach are even comparable to the results from state-of-the-art methods that run offline.

We propose LaplacianFusion , a novel approach that reconstructs detailed and controllable 3D clothed-human body shapes from an input depth or 3D point cloud sequence. The key idea of our approach is to use Laplacian coordinates, well-known differential coordinates that have been used for mesh editing, for representing the local structures contained in the input scans, instead of implicit 3D functions or vertex displacements used previously. Our approach reconstructs a controllable base mesh using SMPL, and learns a surface function that predicts Laplacian coordinates representing surface details on the base mesh. For a given pose, we first build and subdivide a base mesh, which is a deformed SMPL template, and then estimate Laplacian coordinates for the mesh vertices using the surface function. The final reconstruction for the pose is obtained by integrating the estimated Laplacian coordinates as a whole. Experimental results show that our approach based on Laplacian coordinates successfully reconstructs more visually pleasing shape details than previous methods. The approach also enables various surface detail manipulations, such as detail transfer and enhancement.

We propose deep virtual markers, a framework for estimating dense and accurate positional information for various types of 3D data. We design a concept and construct a framework that maps 3D points of 3D articulated models, like humans, into virtual marker labels. To realize the framework, we adopt a sparse convolutional neural network and classify 3D points of an articulated model into virtual marker labels. We propose to use soft labels for the classifier to learn rich and dense interclass relationships based on geodesic distance. To measure the localization accuracy of the virtual markers, we test FAUST challenge, and our result outperforms the state-of-the-art. We also observe outstanding performance on the generalizability test, unseen data evaluation, and different 3D data types (meshes and depth maps). We show additional applications using the estimated virtual markers, such as non-rigid registration, texture transfer, and realtime dense marker prediction from depth maps.

Abstract This paper presents an effective method for generating a spatiotemporal (time‐varying) texture map for a dynamic object using a single RGB‐D camera. The input of our framework is a 3D template model and an RGB‐D image sequence. Since there are invisible areas of the object at a frame in a single‐camera setup, textures of such areas need to be borrowed from other frames. We formulate the problem as an MRF optimization and define cost functions to reconstruct a plausible spatiotemporal texture for a dynamic object. Experimental results demonstrate that our spatiotemporal textures can reproduce the active appearances of captured objects better than approaches using a single texture map.

Abstract We propose a novel framework to generate a global texture atlas for a deforming geometry. Our approach distinguishes from prior arts in two aspects. First, instead of generating a texture map for each timestamp to color a dynamic scene, our framework reconstructs a global texture atlas that can be consistently mapped to a deforming object. Second, our approach is based on a single RGB‐D camera, without the need of a multiple‐camera setup surrounding a scene. In our framework, the input is a 3D template model with an RGB‐D image sequence, and geometric warping fields are found using a state‐of‐the‐art non‐rigid registration method [GXW*15] to align the template mesh to noisy and incomplete input depth images. With these warping fields, our multi‐scale approach for texture coordinate optimization generates a sharp and clear texture atlas that is consistent with multiple color observations over time. Our approach is accelerated by graphical hardware and provides a handy configuration to capture a dynamic geometry along with a clean texture atlas. We demonstrate our approach with practical scenarios, particularly human performance capture. We also show that our approach is resilient on misalignment issues caused by imperfect estimation of warping fields and inaccurate camera parameters.

In a human-robot interaction (HRI) device that performs physical collaboration operations in constant contact with the user, admittance control and impedance control are generally used. Since the two controllers exhibit opposite performances depending on the stiffness condition, controllers capable of dealing with various magnitudes of stiffness are required. As such, this study proposes hybrid control that adjusts the control distribution ratios of admittance control and impedance control based on the operating frequency analysis to react to the user intention and various stiffness conditions in real time. The proposed controller algorithm exhibited lower overshoot than impedance control in the step input response simulation, faster response speed compared to admittance control in the response simulation for 0-5 Hz input frequencies, and the smallest vibration magnitude and number of vibrations in the case of a virtual wall collision, resulting in improved performance compared to existing control methods.

Spatial Magnetic Field Visualization is an interactive kinetic art installation driven by magnetic field data from Nature. It is a physical space that emulates the electromagnetic connection between the Sun and Earth, the invisible yet ubiquitous forces in nature, which has a profound effect on us residing on the earth. One purpose behind this project is to create conversations about this scientific topic in the realm of media art through a three dimensional physical visualization. The Earth's magnetic field is like a living organism that goes between ups and downs. The geomagnetic field is ever-changing and requires constant observation. The impact of what is now called "space weather" on the human life and technology (e.g., GPS, radio communication, power transmission, etc) is substantial, significant enough for former president Obama to call for an executive order in preparation for space weather-related disasters. This project uses painted magnetic balls as pixels in the spatial dimension and attempts to visualize the effect of this scientific phenomenon in the three dimensional space.