We introduce Multiresolution Deep Implicit Functions (MDIF), a hierarchical representation that can recover fine geometry detail, while being able to perform global operations such as shape completion. Our model represents a complex 3D shape with a h
ierarchy of latent grids, which can be decoded into different levels of detail and also achieve better accuracy. For shape completion, we propose latent grid dropout to simulate partial data in the latent space and therefore defer the completing functionality to the decoder side. This along with our multires design significantly improves the shape completion quality under decoder-only latent optimization. To the best of our knowledge, MDIF is the first deep implicit function model that can at the same time (1) represent different levels of detail and allow progressive decoding; (2) support both encoder-decoder inference and decoder-only latent optimization, and fulfill multiple applications; (3) perform detailed decoder-only shape completion. Experiments demonstrate its superior performance against prior art in various 3D reconstruction tasks.
We present a method for differentiable rendering of 3D surfaces that supports both explicit and implicit representations, provides derivatives at occlusion boundaries, and is fast and simple to implement. The method first samples the surface using no
n-differentiable rasterization, then applies differentiable, depth-aware point splatting to produce the final image. Our approach requires no differentiable meshing or rasterization steps, making it efficient for large 3D models and applicable to isosurfaces extracted from implicit surface definitions. We demonstrate the effectiveness of our method for implicit-, mesh-, and parametric-surface-based inverse rendering and neural-network training applications. In particular, we show for the first time efficient, differentiable rendering of an isosurface extracted from a neural radiance field (NeRF), and demonstrate surface-based, rather than volume-based, rendering of a NeRF.
We present a method that synthesizes novel views of complex scenes by interpolating a sparse set of nearby views. The core of our method is a network architecture that includes a multilayer perceptron and a ray transformer that estimates radiance and
volume density at continuous 5D locations (3D spatial locations and 2D viewing directions), drawing appearance information on the fly from multiple source views. By drawing on source views at render time, our method hearkens back to classic work on image-based rendering (IBR), and allows us to render high-resolution imagery. Unlike neural scene representation work that optimizes per-scene functions for rendering, we learn a generic view interpolation function that generalizes to novel scenes. We render images using classic volume rendering, which is fully differentiable and allows us to train using only multi-view posed images as supervision. Experiments show that our method outperforms recent novel view synthesis methods that also seek to generalize to novel scenes. Further, if fine-tuned on each scene, our method is competitive with state-of-the-art single-scene neural rendering methods. Project page: https://ibrnet.github.io/
The goal of this project is to learn a 3D shape representation that enables accurate surface reconstruction, compact storage, efficient computation, consistency for similar shapes, generalization across diverse shape categories, and inference from de
pth camera observations. Towards this end, we introduce Local Deep Implicit Functions (LDIF), a 3D shape representation that decomposes space into a structured set of learned implicit functions. We provide networks that infer the space decomposition and local deep implicit functions from a 3D mesh or posed depth image. During experiments, we find that it provides 10.3 points higher surface reconstruction accuracy (F-Score) than the state-of-the-art (OccNet), while requiring fewer than 1 percent of the network parameters. Experiments on posed depth image completion and generalization to unseen classes show 15.8 and 17.8 point improvements over the state-of-the-art, while producing a structured 3D representation for each input with consistency across diverse shape collections.
Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is funda
mental in computer graphics, where it provides one of the most common ways to approximate geometry, for example, in real-time physics simulation. A convex object also has the property of being simultaneously an explicit and implicit representation: one can interpret it explicitly as a mesh derived by computing the vertices of a convex hull, or implicitly as the collection of half-space constraints or support functions. Their implicit representation makes them particularly well suited for neural network training, as they abstract away from the topology of the geometry they need to represent. However, at testing time, convexes can also generate explicit representations -- polygonal meshes -- which can then be used in any downstream application. We introduce a network architecture to represent a low dimensional family of convexes. This family is automatically derived via an auto-encoding process. We investigate the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.
Template 3D shapes are useful for many tasks in graphics and vision, including fitting observation data, analyzing shape collections, and transferring shape attributes. Because of the variety of geometry and topology of real-world shapes, previous me
thods generally use a library of hand-made templates. In this paper, we investigate learning a general shape template from data. To allow for widely varying geometry and topology, we choose an implicit surface representation based on composition of local shape elements. While long known to computer graphics, this representation has not yet been explored in the context of machine learning for vision. We show that structured implicit functions are suitable for learning and allow a network to smoothly and simultaneously fit multiple classes of shapes. The learned shape template supports applications such as shape exploration, correspondence, abstraction, interpolation, and semantic segmentation from an RGB image.
We present a method for training a regression network from image pixels to 3D morphable model coordinates using only unlabeled photographs. The training loss is based on features from a facial recognition network, computed on-the-fly by rendering the
predicted faces with a differentiable renderer. To make training from features feasible and avoid network fooling effects, we introduce three objectives: a batch distribution loss that encourages the output distribution to match the distribution of the morphable model, a loopback loss that ensures the network can correctly reinterpret its own output, and a multi-view identity loss that compares the features of the predicted 3D face and the input photograph from multiple viewing angles. We train a regression network using these objectives, a set of unlabeled photographs, and the morphable model itself, and demonstrate state-of-the-art results.
The use of rendered images, whether from completely synthetic datasets or from 3D reconstructions, is increasingly prevalent in vision tasks. However, little attention has been given to how the selection of viewpoints affects the performance of rende
red training sets. In this paper, we propose a data-driven approach to view set selection. Given a set of example images, we extract statistics describing their contents and generate a set of views matching the distribution of those statistics. Motivated by semantic segmentation tasks, we model the spatial distribution of each semantic object category within an image view volume. We provide a search algorithm that generates a sampling of likely candidate views according to the example distribution, and a set selection algorithm that chooses a subset of the candidates that jointly cover the example distribution. Results of experiments with these algorithms on SUNCG indicate that they are indeed able to produce view distributions similar to an example set from NYUDv2 according to the earth movers distance. Furthermore, the selected views improve performance on semantic segmentation compared to alternative view selection algorithms.
Recent papers on approximation algorithms for the traveling salesman problem (TSP) have given a new variant on the well-known Christofides algorithm for the TSP, called the Best-of-Many Christofides algorithm. The algorithm involves sampling a spanni
ng tree from the solution the standard LP relaxation of the TSP, subject to the condition that each edge is sampled with probability at most its value in the LP relaxation. One then runs Christofides algorithm on the tree by computing a minimum-cost matching on the odd-degree vertices in the tree, and shortcutting the resulting Eulerian graph to a tour. In this paper we perform an experimental evaluation of the Best-of-Many Christofides algorithm to see if there are empirical reasons to believe its performance is better than that of Christofides algorithm. Furthermore, several different sampling schemes have been proposed; we implement several different schemes to determine which ones might be the most promising for obtaining improved performance guarantees over that of Christofides algorithm. In our experiments, all of the implemented methods perform significantly better than the Christofides algorithm; an algorithm that samples from a maximum entropy distribution over spanning trees seems to be particularly good, though there are others that perform almost as well.
