Recovering a 4D motion from sparse visual information (such as two temporal frames of a subject) is a significant challenge. While humans are able to hallucinate the missing information in a plausible way, generative AI struggles due to a lack of high-quality training data and heavy computing requirements. To overcome these limitations, we propose TwoSquared, a method that obtains a 4D plausible sequence from just two 2D RGB images corresponding to the beginning and the end of the action. We propose to solve the problem in two steps: 1) first, obtaining a 3D reconstruction of the initial and final status, and 2) model the intermediate sequence as a physically plausible deformation. Our method does not require templates or class-specific prior knowledge, and can operate with arbitrary in-the-wild examples. We demonstrate our capabilities in a number of different objects, diverse in terms of nature, class, and deformation, surpassing video-based alternatives, which cannot achieve the same level of consistency.

Generating realistic intermediate shapes between non-rigidly deformed shapes is a challenging task in computer vision, especially with unstructured data (e.g., point clouds) where temporal consistency across frames is lacking, and topologies are changing. Most interpolation methods are designed for structured data (i.e., meshes) and do not apply to real-world point clouds. In contrast, our approach, 4Deform, leverages neural implicit representation (NIR) to enable free topology changing shape deformation. Unlike previous mesh-based methods that learn vertex-based deformation fields, our method learns a continuous velocity field in Euclidean space. Thus, it is suitable for less structured data such as point clouds. Additionally, our method does not require intermediate-shape supervision during training; instead, we incorporate physical and geometrical constraints to regularize the velocity field. We reconstruct intermediate surfaces using a modified level-set equation, directly linking our NIR with the velocity field. Experiments show that our method significantly outperforms previous NIR approaches across various scenarios (e.g., noisy, partial, topology-changing, non-isometric shapes) and, for the first time, enables new applications like 4D Kinect sequence upsampling and real-world high-resolution mesh deformation.

In this work, we introduce the first unsupervised method that simultaneously predicts time-varying neural implicit surfaces and deformations between pairs of point clouds. We propose to model the point movement using an explicit velocity field and directly deform a time-varying implicit field using the modified level-set equation. This equation utilizes an iso-surface evolution with Eikonal constraints in a compact formulation, ensuring the integrity of the signed distance field. By applying a smooth, volume-preserving constraint to the velocity field, our method successfully recovers physically plausible intermediate shapes. Our method is able to handle both rigid and non-rigid deformations without any intermediate shape supervision. Our experimental results demonstrate that our method significantly outperforms existing works, delivering superior results in both quality and efficiency.

Abstract Finding correspondences between 3D deformable shapes is an important and long‐standing problem in geometry processing, computer vision, graphics, and beyond. While various shape matching datasets exist, they are mostly static or limited in size, restricting their adaptation to different problem settings, including both full and partial shape matching. In particular the existing partial shape matching datasets are small (fewer than 100 shapes) and thus unsuitable for data‐hungry machine learning approaches. Moreover, the type of partiality present in existing datasets is often artificial and far from realistic. To address these limitations, we introduce a generic and flexible framework for the procedural generation of challenging full and partial shape matching datasets. Our framework allows the propagation of custom annotations across shapes, making it useful for various applications. By utilising our framework and manually creating cross‐dataset correspondences between seven existing (complete geometry) shape matching datasets, we propose a new large benchmark BeCoS with a total of 2543 shapes. Based on this, we offer several challenging benchmark settings, covering both full and partial matching, for which we evaluate respective state‐of‐the‐art methods as baselines. Visualisations and code of our benchmark can be found at: https://nafieamrani.github.io/BeCoS/ .

Fine-detailed reconstructions are in high demand in many applications. However, most of the existing RGB-D reconstruction methods rely on pre-calculated accurate camera poses to recover the detailed surface geometry, where the representation of a surface needs to be adapted when optimizing different quantities. In this paper, we present a novel multi-view RGB-D based reconstruction method that tackles camera pose, lighting, albedo, and surface normal estimation via the utilization of a gradient signed distance field (gradient-SDF). The proposed method formulates the image rendering process using specific physically-based model(s) and optimizes the surface’s quantities on the actual surface using its volumetric representation, as opposed to other works which estimate surface quantities only near the actual surface. To validate our method, we investigate two physically-based image formation models for natural light and point light source applications. The experimental results on synthetic and real-world datasets demonstrate that the proposed method can recover high-quality geometry of the surface more faithfully than the state-of-the-art and further improves the accuracy of estimated camera poses1.

We present Gradient-SDF, a novel representation for 3D geometry that combines the advantages of implict and explicit representations. By storing at every voxel both the signed distance field as well as its gradient vector field, we enhance the capability of implicit representations with approaches originally formulated for explicit surfaces. As concrete examples, we show that (1) the Gradient-SDF allows us to perform direct SDF tracking from depth images, using efficient storage schemes like hash maps, and that (2) the Gradient-SDF representation enables us to perform photometric bundle adjustment directly in a voxel representation (without transforming into a point cloud or mesh), naturally a fully implicit optimization of geometry and camera poses and easy geometry upsampling. Experimental results confirm that this leads to significantly sharper reconstructions. Since the overall SDF voxel structure is still respected, the proposed Gradient-SDF is equally suited for (GPU) parallelization as related approaches.

A novel approach towards depth map super-resolution using multi-view uncalibrated photometric stereo is presented. Practically, an LED light source is attached to a commodity RGB-D sensor and is used to capture objects from multiple viewpoints with unknown motion. This non-static camera-to-object setup is described with a nonconvex variational approach such that no calibration on lighting or camera motion is required due to the formulation of an end-to-end joint optimization problem. Solving the proposed variational model results in high resolution depth, reflectance and camera pose estimates, as we show on challenging synthetic and real-world datasets.