A survey on deep geometry learning: from a representation perspective

Researchers have achieved great success in dealing with 2D images using deep learning. In recent years, 3D computer vision and geometry deep learning have gained ever more attention. Many advanced techniques for 3D shapes have been proposed for different applications. Unlike 2D images, which can be uniformly represented by a regular grid of pixels, 3D shapes have various representations, such as depth images, multi-view images, voxels, point clouds, meshes, implicit surfaces, etc. The performance achieved in different applications largely depends on the representation used, and there is no unique representation that works well for all applications. Therefore, in this survey, we review recent developments in deep learning for 3D geometry from a representation perspective, summarizing the advantages and disadvantages of different representations for different applications. We also present existing datasets in these representations and further discuss future research directions

3DShape2VecSet: A 3D Shape Representation for Neural Fields and Generative Diffusion Models

We introduce 3DShape2VecSet, a novel shape representation for neural fields designed for generative diffusion models. Our shape representation can encode 3D shapes given as surface models or point clouds, and represents them as neural fields. The concept of neural fields has previously been combined with a global latent vector, a regular grid of latent vectors, or an irregular grid of latent vectors. Our new representation encodes neural fields on top of a set of vectors. We draw from multiple concepts, such as the radial basis function representation and the cross attention and self-attention function, to design a learnable representation that is especially suitable for processing with transformers. Our results show improved performance in 3D shape encoding and 3D shape generative modeling tasks. We demonstrate a wide variety of generative applications: unconditioned generation, category-conditioned generation, text-conditioned generation, point-cloud completion, and image-conditioned generation.Comment: Accepted by SIGGRAPH 2023 (Journal Track), Project website: https://1zb.github.io/3DShape2VecSet/, Project demo: https://youtu.be/KKQsQccpBF

Implicit neural representations for unsupervised super-resolution and denoising of 4D flow MRI

4D flow MRI is a non-invasive imaging method that can measure blood flow velocities over time. However, the velocity fields detected by this technique have limitations due to low resolution and measurement noise. Coordinate-based neural networks have been researched to improve accuracy, with SIRENs being suitable for super-resolution tasks. Our study investigates SIRENs for time-varying 3-directional velocity fields measured in the aorta by 4D flow MRI, achieving denoising and super-resolution. We trained our method on voxel coordinates and benchmarked our approach using synthetic measurements and a real 4D flow MRI scan. Our optimized SIREN architecture outperformed state-of-the-art techniques, producing denoised and super-resolved velocity fields from clinical data. Our approach is quick to execute and straightforward to implement for novel cases, achieving 4D super-resolution

Observations on Cortical Mechanisms for Object Recognition andsLearning

This paper sketches a hypothetical cortical architecture for visual 3D object recognition based on a recent computational model. The view-centered scheme relies on modules for learning from examples, such as Hyperbf-like networks. Such models capture a class of explanations we call Memory-Based Models (MBM) that contains sparse population coding, memory-based recognition, and codebooks of prototypes. Unlike the sigmoidal units of some artificial neural networks, the units of MBMs are consistent with the description of cortical neurons. We describe how an example of MBM may be realized in terms of cortical circuitry and biophysical mechanisms, consistent with psychophysical and physiological data

PAPR: Proximity Attention Point Rendering

Learning accurate and parsimonious point cloud representations of scene surfaces from scratch remains a challenge in 3D representation learning. Existing point-based methods often suffer from the vanishing gradient problem or require a large number of points to accurately model scene geometry and texture. To address these limitations, we propose Proximity Attention Point Rendering (PAPR), a novel method that consists of a point-based scene representation and a differentiable renderer. Our scene representation uses a point cloud where each point is characterized by its spatial position, foreground score, and view-independent feature vector. The renderer selects the relevant points for each ray and produces accurate colours using their associated features. PAPR effectively learns point cloud positions to represent the correct scene geometry, even when the initialization drastically differs from the target geometry. Notably, our method captures fine texture details while using only a parsimonious set of points. We also demonstrate four practical applications of our method: geometry editing, object manipulation, texture transfer, and exposure control. More results and code are available on our project website at https://zvict.github.io/papr/