A Survey on Computational Solutions for Reconstructing Complete Objects by Reassembling Their Fractured Parts

Reconstructing a complete object from its parts is a fundamental problem in many scientific domains. The purpose of this article is to provide a systematic survey on this topic. The reassembly problem requires understanding the attributes of individual pieces and establishing matches between different pieces. Many approaches also model priors of the underlying complete object. Existing approaches are tightly connected problems of shape segmentation, shape matching, and learning shape priors. We provide existing algorithms in this context and emphasize their similarities and differences to general-purpose approaches. We also survey the trends from early non-deep learning approaches to more recent deep learning approaches. In addition to algorithms, this survey will also describe existing datasets, open-source software packages, and applications. To the best of our knowledge, this is the first comprehensive survey on this topic in computer graphics.

Jigsaw++: Imagining Complete Shape Priors for Object Reassembly

The automatic assembly problem has attracted increasing interest due to its complex challenges that involve 3D representation. This paper introduces Jigsaw++, a novel generative method designed to tackle the multifaceted challenges of reconstruction for the reassembly problem. Existing approach focusing primarily on piecewise information for both part and fracture assembly, often overlooking the integration of complete object prior. Jigsaw++ distinguishes itself by learning a category-agnostic shape prior of complete objects. It employs the proposed "retargeting" strategy that effectively leverages the output of any existing assembly method to generate complete shape reconstructions. This capability allows it to function orthogonally to the current methods. Through extensive evaluations on Breaking Bad dataset and PartNet, Jigsaw++ has demonstrated its effectiveness, reducing reconstruction errors and enhancing the precision of shape reconstruction, which sets a new direction for future reassembly model developments.

PPLNs: Parametric Piecewise Linear Networks for Event-Based Temporal Modeling and Beyond

We present Parametric Piecewise Linear Networks (PPLNs) for temporal vision inference. Motivated by the neuromorphic principles that regulate biological neural behaviors, PPLNs are ideal for processing data captured by event cameras, which are built to simulate neural activities in the human retina. We discuss how to represent the membrane potential of an artificial neuron by a parametric piecewise linear function with learnable coefficients. This design echoes the idea of building deep models from learnable parametric functions recently popularized by Kolmogorov-Arnold Networks (KANs). Experiments demonstrate the state-of-the-art performance of PPLNs in event-based and image-based vision applications, including steering prediction, human pose estimation, and motion deblurring. The source code of our implementation is available at https://github.com/chensong1995/PPLN.

MoGenTS: Motion Generation based on Spatial-Temporal Joint Modeling

Motion generation from discrete quantization offers many advantages over continuous regression, but at the cost of inevitable approximation errors. Previous methods usually quantize the entire body pose into one code, which not only faces the difficulty in encoding all joints within one vector but also loses the spatial relationship between different joints. Differently, in this work we quantize each individual joint into one vector, which i) simplifies the quantization process as the complexity associated with a single joint is markedly lower than that of the entire pose; ii) maintains a spatial-temporal structure that preserves both the spatial relationships among joints and the temporal movement patterns; iii) yields a 2D token map, which enables the application of various 2D operations widely used in 2D images. Grounded in the 2D motion quantization, we build a spatial-temporal modeling framework, where 2D joint VQVAE, temporal-spatial 2D masking technique, and spatial-temporal 2D attention are proposed to take advantage of spatial-temporal signals among the 2D tokens. Extensive experiments demonstrate that our method significantly outperforms previous methods across different datasets, with a $26.6\%$ decrease of FID on HumanML3D and a $29.9\%$ decrease on KIT-ML.

Atlas Gaussians Diffusion for 3D Generation with Infinite Number of Points

Using the latent diffusion model has proven effective in developing novel 3D generation techniques. To harness the latent diffusion model, a key challenge is designing a high-fidelity and efficient representation that links the latent space and the 3D space. In this paper, we introduce Atlas Gaussians, a novel representation for feed-forward native 3D generation. Atlas Gaussians represent a shape as the union of local patches, and each patch can decode 3D Gaussians. We parameterize a patch as a sequence of feature vectors and design a learnable function to decode 3D Gaussians from the feature vectors. In this process, we incorporate UV-based sampling, enabling the generation of a sufficiently large, and theoretically infinite, number of 3D Gaussian points. The large amount of 3D Gaussians enables high-quality details of generation results. Moreover, due to local awareness of the representation, the transformer-based decoding procedure operates on a patch level, ensuring efficiency. We train a variational autoencoder to learn the Atlas Gaussians representation, and then apply a latent diffusion model on its latent space for learning 3D Generation. Experiments show that our approach outperforms the prior arts of feed-forward native 3D generation.

P3P: Pseudo-3D Pre-training for Scaling 3D Masked Autoencoders

3D pre-training is crucial to 3D perception tasks. However, limited by the difficulties in collecting clean 3D data, 3D pre-training consistently faced data scaling challenges. Inspired by semi-supervised learning leveraging limited labeled data and a large amount of unlabeled data, in this work, we propose a novel self-supervised pre-training framework utilizing the real 3D data and the pseudo-3D data lifted from images by a large depth estimation model. Another challenge lies in the efficiency. Previous methods such as Point-BERT and Point-MAE, employ k nearest neighbors to embed 3D tokens, requiring quadratic time complexity. To efficiently pre-train on such a large amount of data, we propose a linear-time-complexity token embedding strategy and a training-efficient 2D reconstruction target. Our method achieves state-of-the-art performance in 3D classification and few-shot learning while maintaining high pre-training and downstream fine-tuning efficiency.

TutteNet: Injective 3D Deformations by Composition of 2D Mesh Deformations

This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method provides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.

4DRecons: 4D Neural Implicit Deformable Objects Reconstruction from a single RGB-D Camera with Geometrical and Topological Regularizations

This paper presents a novel approach 4DRecons that takes a single camera RGB-D sequence of a dynamic subject as input and outputs a complete textured deforming 3D model over time. 4DRecons encodes the output as a 4D neural implicit surface and presents an optimization procedure that combines a data term and two regularization terms. The data term fits the 4D implicit surface to the input partial observations. We address fundamental challenges in fitting a complete implicit surface to partial observations. The first regularization term enforces that the deformation among adjacent frames is as rigid as possible (ARAP). To this end, we introduce a novel approach to compute correspondences between adjacent textured implicit surfaces, which are used to define the ARAP regularization term. The second regularization term enforces that the topology of the underlying object remains fixed over time. This regularization is critical for avoiding self-intersections that are typical in implicit-based reconstructions. We have evaluated the performance of 4DRecons on a variety of datasets. Experimental results show that 4DRecons can handle large deformations and complex inter-part interactions and outperform state-of-the-art approaches considerably.

Real3D: Scaling Up Large Reconstruction Models with Real-World Images

The default strategy for training single-view Large Reconstruction Models (LRMs) follows the fully supervised route using large-scale datasets of synthetic 3D assets or multi-view captures. Although these resources simplify the training procedure, they are hard to scale up beyond the existing datasets and they are not necessarily representative of the real distribution of object shapes. To address these limitations, in this paper, we introduce Real3D, the first LRM system that can be trained using single-view real-world images. Real3D introduces a novel self-training framework that can benefit from both the existing synthetic data and diverse single-view real images. We propose two unsupervised losses that allow us to supervise LRMs at the pixel- and semantic-level, even for training examples without ground-truth 3D or novel views. To further improve performance and scale up the image data, we develop an automatic data curation approach to collect high-quality examples from in-the-wild images. Our experiments show that Real3D consistently outperforms prior work in four diverse evaluation settings that include real and synthetic data, as well as both in-domain and out-of-domain shapes. Code and model can be found here: https://hwjiang1510.github.io/Real3D/

CoFie: Learning Compact Neural Surface Representations with Coordinate Fields

This paper introduces CoFie, a novel local geometry-aware neural surface representation. CoFie is motivated by the theoretical analysis of local SDFs with quadratic approximation. We find that local shapes are highly compressive in an aligned coordinate frame defined by the normal and tangent directions of local shapes. Accordingly, we introduce Coordinate Field, which is a composition of coordinate frames of all local shapes. The Coordinate Field is optimizable and is used to transform the local shapes from the world coordinate frame to the aligned shape coordinate frame. It largely reduces the complexity of local shapes and benefits the learning of MLP-based implicit representations. Moreover, we introduce quadratic layers into the MLP to enhance expressiveness concerning local shape geometry. CoFie is a generalizable surface representation. It is trained on a curated set of 3D shapes and works on novel shape instances during testing. When using the same amount of parameters with prior works, CoFie reduces the shape error by 48% and 56% on novel instances of both training and unseen shape categories. Moreover, CoFie demonstrates comparable performance to prior works when using only 70% fewer parameters.