Probabilistic Directed Distance Fields for Ray-Based Shape Representations

In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning frameworks. Standard explicit shape representations (voxels, point clouds, or meshes) are often easily rendered, but can suffer from limited geometric fidelity, among other issues. On the other hand, implicit representations (occupancy, distance, or radiance fields) preserve greater fidelity, but suffer from complex or inefficient rendering processes, limiting scalability. In this work, we devise Directed Distance Fields (DDFs), a novel neural shape representation that builds upon classical distance fields. The fundamental operation in a DDF maps an oriented point (position and direction) to surface visibility and depth. This enables efficient differentiable rendering, obtaining depth with a single forward pass per pixel, as well as differential geometric quantity extraction (e.g., surface normals), with only additional backward passes. Using probabilistic DDFs (PDDFs), we show how to model inherent discontinuities in the underlying field. We then apply DDFs to several applications, including single-shape fitting, generative modelling, and single-image 3D reconstruction, showcasing strong performance with simple architectural components via the versatility of our representation. Finally, since the dimensionality of DDFs permits view-dependent geometric artifacts, we conduct a theoretical investigation of the constraints necessary for view consistency. We find a small set of field properties that are sufficient to guarantee a DDF is consistent, without knowing, for instance, which shape the field is expressing.

PolyOculus: Simultaneous Multi-view Image-based Novel View Synthesis

This paper considers the problem of generative novel view synthesis (GNVS), generating novel, plausible views of a scene given a limited number of known views. Here, we propose a set-based generative model that can simultaneously generate multiple, self-consistent new views, conditioned on any number of known views. Our approach is not limited to generating a single image at a time and can condition on zero, one, or more views. As a result, when generating a large number of views, our method is not restricted to a low-order autoregressive generation approach and is better able to maintain generated image quality over large sets of images. We evaluate the proposed model on standard NVS datasets and show that it outperforms the state-of-the-art image-based GNVS baselines. Further, we show that the model is capable of generating sets of camera views that have no natural sequential ordering, like loops and binocular trajectories, and significantly outperforms other methods on such tasks.

Reconstructive Latent-Space Neural Radiance Fields for Efficient 3D Scene Representations

Neural Radiance Fields (NeRFs) have proven to be powerful 3D representations, capable of high quality novel view synthesis of complex scenes. While NeRFs have been applied to graphics, vision, and robotics, problems with slow rendering speed and characteristic visual artifacts prevent adoption in many use cases. In this work, we investigate combining an autoencoder (AE) with a NeRF, in which latent features (instead of colours) are rendered and then convolutionally decoded. The resulting latent-space NeRF can produce novel views with higher quality than standard colour-space NeRFs, as the AE can correct certain visual artifacts, while rendering over three times faster. Our work is orthogonal to other techniques for improving NeRF efficiency. Further, we can control the tradeoff between efficiency and image quality by shrinking the AE architecture, achieving over 13 times faster rendering with only a small drop in performance. We hope that our approach can form the basis of an efficient, yet high-fidelity, 3D scene representation for downstream tasks, especially when retaining differentiability is useful, as in many robotics scenarios requiring continual learning.

Watch Your Steps: Local Image and Scene Editing by Text Instructions

Denoising diffusion models have enabled high-quality image generation and editing. We present a method to localize the desired edit region implicit in a text instruction. We leverage InstructPix2Pix (IP2P) and identify the discrepancy between IP2P predictions with and without the instruction. This discrepancy is referred to as the relevance map. The relevance map conveys the importance of changing each pixel to achieve the edits, and is used to to guide the modifications. This guidance ensures that the irrelevant pixels remain unchanged. Relevance maps are further used to enhance the quality of text-guided editing of 3D scenes in the form of neural radiance fields. A field is trained on relevance maps of training views, denoted as the relevance field, defining the 3D region within which modifications should be made. We perform iterative updates on the training views guided by rendered relevance maps from the relevance field. Our method achieves state-of-the-art performance on both image and NeRF editing tasks. Project page: https://ashmrz.github.io/WatchYourSteps/

Reference-guided Controllable Inpainting of Neural Radiance Fields

The popularity of Neural Radiance Fields (NeRFs) for view synthesis has led to a desire for NeRF editing tools. Here, we focus on inpainting regions in a view-consistent and controllable manner. In addition to the typical NeRF inputs and masks delineating the unwanted region in each view, we require only a single inpainted view of the scene, i.e., a reference view. We use monocular depth estimators to back-project the inpainted view to the correct 3D positions. Then, via a novel rendering technique, a bilateral solver can construct view-dependent effects in non-reference views, making the inpainted region appear consistent from any view. For non-reference disoccluded regions, which cannot be supervised by the single reference view, we devise a method based on image inpainters to guide both the geometry and appearance. Our approach shows superior performance to NeRF inpainting baselines, with the additional advantage that a user can control the generated scene via a single inpainted image. Project page: https://ashmrz.github.io/reference-guided-3d

SPIn-NeRF: Multiview Segmentation and Perceptual Inpainting with Neural Radiance Fields

Neural Radiance Fields (NeRFs) have emerged as a popular approach for novel view synthesis. While NeRFs are quickly being adapted for a wider set of applications, intuitively editing NeRF scenes is still an open challenge. One important editing task is the removal of unwanted objects from a 3D scene, such that the replaced region is visually plausible and consistent with its context. We refer to this task as 3D inpainting. In 3D, solutions must be both consistent across multiple views and geometrically valid. In this paper, we propose a novel 3D inpainting method that addresses these challenges. Given a small set of posed images and sparse annotations in a single input image, our framework first rapidly obtains a 3D segmentation mask for a target object. Using the mask, a perceptual optimizationbased approach is then introduced that leverages learned 2D image inpainters, distilling their information into 3D space, while ensuring view consistency. We also address the lack of a diverse benchmark for evaluating 3D scene inpainting methods by introducing a dataset comprised of challenging real-world scenes. In particular, our dataset contains views of the same scene with and without a target object, enabling more principled benchmarking of the 3D inpainting task. We first demonstrate the superiority of our approach on multiview segmentation, comparing to NeRFbased methods and 2D segmentation approaches. We then evaluate on the task of 3D inpainting, establishing state-ofthe-art performance against other NeRF manipulation algorithms, as well as a strong 2D image inpainter baseline

Representing 3D Shapes with Probabilistic Directed Distance Fields

Differentiable rendering is an essential operation in modern vision, allowing inverse graphics approaches to 3D understanding to be utilized in modern machine learning frameworks. Explicit shape representations (voxels, point clouds, or meshes), while relatively easily rendered, often suffer from limited geometric fidelity or topological constraints. On the other hand, implicit representations (occupancy, distance, or radiance fields) preserve greater fidelity, but suffer from complex or inefficient rendering processes, limiting scalability. In this work, we endeavour to address both shortcomings with a novel shape representation that allows fast differentiable rendering within an implicit architecture. Building on implicit distance representations, we define Directed Distance Fields (DDFs), which map an oriented point (position and direction) to surface visibility and depth. Such a field can render a depth map with a single forward pass per pixel, enable differential surface geometry extraction (e.g., surface normals and curvatures) via network derivatives, be easily composed, and permit extraction of classical unsigned distance fields. Using probabilistic DDFs (PDDFs), we show how to model inherent discontinuities in the underlying field. Finally, we apply our method to fitting single shapes, unpaired 3D-aware generative image modelling, and single-image 3D reconstruction tasks, showcasing strong performance with simple architectural components via the versatility of our representation.

GraN-GAN: Piecewise Gradient Normalization for Generative Adversarial Networks

Modern generative adversarial networks (GANs) predominantly use piecewise linear activation functions in discriminators (or critics), including ReLU and LeakyReLU. Such models learn piecewise linear mappings, where each piece handles a subset of the input space, and the gradients per subset are piecewise constant. Under such a class of discriminator (or critic) functions, we present Gradient Normalization (GraN), a novel input-dependent normalization method, which guarantees a piecewise K-Lipschitz constraint in the input space. In contrast to spectral normalization, GraN does not constrain processing at the individual network layers, and, unlike gradient penalties, strictly enforces a piecewise Lipschitz constraint almost everywhere. Empirically, we demonstrate improved image generation performance across multiple datasets (incl. CIFAR-10/100, STL-10, LSUN bedrooms, and CelebA), GAN loss functions, and metrics. Further, we analyze altering the often untuned Lipschitz constant K in several standard GANs, not only attaining significant performance gains, but also finding connections between K and training dynamics, particularly in low-gradient loss plateaus, with the common Adam optimizer.

Towards Robust Bisimulation Metric Learning

Learned representations in deep reinforcement learning (DRL) have to extract task-relevant information from complex observations, balancing between robustness to distraction and informativeness to the policy. Such stable and rich representations, often learned via modern function approximation techniques, can enable practical application of the policy improvement theorem, even in high-dimensional continuous state-action spaces. Bisimulation metrics offer one solution to this representation learning problem, by collapsing functionally similar states together in representation space, which promotes invariance to noise and distractors. In this work, we generalize value function approximation bounds for on-policy bisimulation metrics to non-optimal policies and approximate environment dynamics. Our theoretical results help us identify embedding pathologies that may occur in practical use. In particular, we find that these issues stem from an underconstrained dynamics model and an unstable dependence of the embedding norm on the reward signal in environments with sparse rewards. Further, we propose a set of practical remedies: (i) a norm constraint on the representation space, and (ii) an extension of prior approaches with intrinsic rewards and latent space regularization. Finally, we provide evidence that the resulting method is not only more robust to sparse reward functions, but also able to solve challenging continuous control tasks with observational distractions, where prior methods fail.

Disentangling Geometric Deformation Spaces in Generative Latent Shape Models

A complete representation of 3D objects requires characterizing the space of deformations in an interpretable manner, from articulations of a single instance to changes in shape across categories. In this work, we improve on a prior generative model of geometric disentanglement for 3D shapes, wherein the space of object geometry is factorized into rigid orientation, non-rigid pose, and intrinsic shape. The resulting model can be trained from raw 3D shapes, without correspondences, labels, or even rigid alignment, using a combination of classical spectral geometry and probabilistic disentanglement of a structured latent representation space. Our improvements include more sophisticated handling of rotational invariance and the use of a diffeomorphic flow network to bridge latent and spectral space. The geometric structuring of the latent space imparts an interpretable characterization of the deformation space of an object. Furthermore, it enables tasks like pose transfer and pose-aware retrieval without requiring supervision. We evaluate our model on its generative modelling, representation learning, and disentanglement performance, showing improved rotation invariance and intrinsic-extrinsic factorization quality over the prior model.