Large transformer models are proving to be a powerful tool for 3D vision and novel view synthesis. However, the standard Transformer’s well-known quadratic complexity makes it difficult to scale these methods to large scenes. To address this challenge, we propose the Local View Transformer (LVT), a large-scale scene reconstruction and novel view synthesis architecture that circumvents the need for the quadratic attention operation. Motivated by the insight that spatially nearby views provide more useful signal about the local scene composition than distant views, our model processes all information in a local neighborhood around each view. To attend to tokens in nearby views, we leverage a novel positional encoding that conditions on the relative geometric transformation between the query and nearby views. We decode the output of our model into a 3D Gaussian Splat scene representation that includes both color and opacity view-dependence. Taken together, the Local View Transformer enables reconstruction of arbitrarily large, high-resolution scenes in a single forward pass. See our project page for results and interactive demos: https://toobaimt.github.io/lvt/.

We present a novel neural algorithm for performing high-quality, highresolution, real-time novel view synthesis. From a sparse set of input RGB images or videos streams, our network both reconstructs the 3D scene and renders novel views at 1080p resolution at 30fps on an NVIDIA A100. Our feed-forward network generalizes across a wide variety of datasets and scenes and produces state-of-the-art quality for a real-time method. Our quality approaches, and in some cases surpasses, the quality of some of the top offline methods. In order to achieve these results we use a novel combination of several key concepts, and tie them together into a cohesive and effective algorithm. We build on previous works that represent the scene using semi-transparent layers and use an iterative learned render-and-refine approach to improve those layers. Instead of flat layers, our method reconstructs layered depth maps (LDMs) that efficiently represent scenes with complex depth and occlusions. The iterative update steps are embedded in a multi-scale, UNet-style architecture to perform as much compute as possible at reduced resolution. Within each update step, to better aggregate the information from multiple input views, we use a specialized Transformer-based network component. This allows the majority of the per-input image processing to be performed in the input image space, as opposed to layer space, further increasing efficiency. Finally, due to the real-time nature of our reconstruction and rendering, we dynamically create and discard the internal 3D geometry for each frame, generating the LDM for each view. Taken together, this produces a novel and effective algorithm for view synthesis. Through extensive evaluation, we demonstrate that we achieve state-of-the-art quality at real-time rates.

Under the conventional diffuse shading model with unknown directional lighting, the set of quadratic surface shapes that are consistent with the spatial derivatives of intensity at a single image point is a two-dimensional algebraic variety embedded in the five-dimensional space of quadratic shapes. We describe the geometry of this variety, and we introduce a concise feedforward model that computes an explicit, differentiable approximation of the variety from the intensity and its derivatives at any single image point. The result is a parallelizable processor that operates at each image point and produces a lighting-invariant descriptor of the continuous set of compatible surface shapes at the point. We describe two applications of this processor: two-shot uncalibrated photometric stereo and quadratic-surface shape from shading.

We derive the tightest known bounds on η = 2ν, where ν is the growth rate of the logarithm of the number of independent sets on a hexagonal lattice. To obtain these bounds, we generalize a method proposed by Calkin and Wilf. Their original strategy cannot immediately be used to derive bounds for η, due to the difference in symmetry between square and hexagonal lattices, so we propose a modified method and an algorithm to derive rigorous bounds on η. In particular, we prove that 1.546440708536001 ≤ η ≤ 1.5513, which improves upon the best known bounds of 1.5463 ≤ η ≤ 1.5527 given by Nagy and Zeger. Our lower bound matches the numerical estimate of Baxter up to 9 digits after the decimal point, and our upper bound can be further improved by following our method.