We provide additional qualitative comparative results on both ShapeNetandPix3DinFig8,9.

These authors contributed equally to this work. We now analyze a single layer of a neural network with conditioning via concatenation. Here, we provide exact specifications of the 2D experiments to ensure reproducibility. NP, 4-layer set encoder 101 .7/ 5. 1 154 . NP, 9-layer set encoder 92 .5 /2 .0

"motivation [...] very convincing and perfectly pitched to the reader" We believe that this will spur follow-up work benefitting both of these promising research directions. We have trained models on the ShapeNet "benches" class--please see qualitative We note that 2D results (Sec. Figure 1 of DeepSDF--see qualitative result in (c)--with no further fine-tuning or heuristics. We will add experiments and comparisons with further classes to the final manuscript. We will discuss DISN in-depth. We benchmark against this architecture (see submission Table 3, Figure 1).

Scene and object reconstruction is an important problem in robotics, in particular in planning collision-free trajectories or in object manipulation. This paper compares two strategies for the reconstruction of nonvisible parts of the object surface from a single RGB-D camera view. The first method, named DeepSDF predicts the Signed Distance Transform to the object surface for a given point in 3D space. The second method, named MirrorNet reconstructs the occluded objects' parts by generating images from the other side of the observed object. Experiments performed with objects from the ShapeNet dataset, show that the view-dependent MirrorNet is faster and has smaller reconstruction errors in most categories.

This work addresses the problem of \textit{shape completion}, i.e., the task of restoring incomplete shapes by predicting their missing parts. While previous works have often predicted the fractured and restored shape in one step, we approach the task by separately predicting the fractured and newly restored parts, but ensuring these predictions are interconnected. We use a decoder network motivated by related work on the prediction of signed distance functions (DeepSDF). In particular, our representation allows us to consider test-time-training, i.e., finetuning network parameters to match the given incomplete shape more accurately during inference. While previous works often have difficulties with artifacts around the fracture boundary, we demonstrate that our overfitting to the fractured parts leads to significant improvements in the restoration of eight different shape categories of the ShapeNet data set in terms of their chamfer distances.

Implicit neural representations have emerged as a powerful tool in learning 3D geometry, offering unparalleled advantages over conventional representations like mesh-based methods. A common type of INR implicitly encodes a shape's boundary as the zero-level set of the learned continuous function and learns a mapping from a low-dimensional latent space to the space of all possible shapes represented by its signed distance function. However, most INRs struggle to retain high-frequency details, which are crucial for accurate geometric depiction, and they are computationally expensive. To address these limitations, we present a novel approach that both reduces computational expenses and enhances the capture of fine details. Our method integrates periodic activation functions, positional encodings, and normals into the neural network architecture. This integration significantly enhances the model's ability to learn the entire space of 3D shapes while preserving intricate details and sharp features, areas where conventional representations often fall short.

A main challenge in mechanical design is to efficiently explore the design space while satisfying engineering constraints. This work explores the use of 3D generative models to explore the design space in the context of vehicle development, while estimating and enforcing engineering constraints. Specifically, we generate diverse 3D models of cars that meet a given set of geometric specifications, while also obtaining quick estimates of performance parameters such as aerodynamic drag. For this, we employ a data-driven approach (using the ShapeNet dataset) to train VehicleSDF, a DeepSDF based model that represents potential designs in a latent space witch can be decoded into a 3D model. We then train surrogate models to estimate engineering parameters from this latent space representation, enabling us to efficiently optimize latent vectors to match specifications. Our experiments show that we can generate diverse 3D models while matching the specified geometric parameters. Finally, we demonstrate that other performance parameters such as aerodynamic drag can be estimated in a differentiable pipeline.

Humans rely on their visual and tactile senses to develop a comprehensive 3D understanding of their physical environment. Recently, there has been a growing interest in exploring and manipulating objects using data-driven approaches that utilise high-resolution vision-based tactile sensors. However, 3D shape reconstruction using tactile sensing has lagged behind visual shape reconstruction because of limitations in existing techniques, including the inability to generalise over unseen shapes, the absence of real-world testing, and limited expressive capacity imposed by discrete representations. To address these challenges, we propose TouchSDF, a Deep Learning approach for tactile 3D shape reconstruction that leverages the rich information provided by a vision-based tactile sensor and the expressivity of the implicit neural representation DeepSDF. Our technique consists of two components: (1) a Convolutional Neural Network that maps tactile images into local meshes representing the surface at the touch location, and (2) an implicit neural function that predicts a signed distance function to extract the desired 3D shape. This combination allows TouchSDF to reconstruct smooth and continuous 3D shapes from tactile inputs in simulation and real-world settings, opening up research avenues for robust 3D-aware representations and improved multimodal perception in robotics. Code and supplementary material are available at: https://touchsdf.github.io/