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Models for monocular shape reconstruction of surfaces with diffuse reflection -- shape from shading -- ought to produce distributions of outputs, because there are fundamental mathematical ambiguities of both continuous (e.g., bas-relief) and discrete (e.g., convex/concave) varieties which are also experienced by humans. Yet, the outputs of current models are limited to point estimates or tight distributions around single modes, which prevent them from capturing these effects. We introduce a model that reconstructs a multimodal distribution of shapes from a single shading image, which aligns with the human experience of multistable perception. We train a small denoising diffusion process to generate surface normal fields from $16\times 16$ patches of synthetic images of everyday 3D objects. We deploy this model patch-wise at multiple scales, with guidance from inter-patch shape consistency constraints. Despite its relatively small parameter count and predominantly bottom-up structure, we show that multistable shape explanations emerge from this model for ''ambiguous'' test images that humans experience as being multistable. At the same time, the model produces veridical shape estimates for object-like images that include distinctive occluding contours and appear less ambiguous. This may inspire new architectures for stochastic 3D shape perception that are more efficient and better aligned with human experience.

We present a differentiable model that infers explicit boundaries, including curves, corners and junctions, using a mechanism that we call boundary attention. Boundary attention is a boundary-aware local attention operation that, when applied densely and repeatedly, progressively refines a field of variables that specify an unrasterized description of the local boundary structure in every overlapping patch within an image. It operates in a bottom-up fashion, similar to classical methods for sub-pixel edge localization and edge-linking, but with a higher-dimensional description of local boundary structure, a notion of spatial consistency that is learned instead of designed, and a sequence of operations that is end-to-end differentiable. We train our model using simple synthetic data and then evaluate it using photographs that were captured under low-light conditions with variable amounts of noise. We find that our method generalizes to natural images corrupted by real sensor noise, and predicts consistent boundaries under increasingly noisy conditions where other state-of-the-art methods fail., Comment: Project website at boundaryattention.github.io: http://boundaryattention.github.io

Optical metasurfaces composed of precisely engineered nanostructures have gained significant attention for their ability to manipulate light and implement distinct functionalities based on the properties of the incident field. Computational imaging systems have started harnessing this capability to produce sets of coded measurements that benefit certain tasks when paired with digital post-processing. Inspired by these works, we introduce a new system that uses a birefringent metasurface with a polarizer-mosaicked photosensor to capture four optically-coded measurements in a single exposure. We apply this system to the task of incoherent opto-electronic filtering, where digital spatial-filtering operations are replaced by simpler, per-pixel sums across the four polarization channels, independent of the spatial filter size. In contrast to previous work on incoherent opto-electronic filtering that can realize only one spatial filter, our approach can realize a continuous family of filters from a single capture, with filters being selected from the family by adjusting the post-capture digital summation weights. To find a metasurface that can realize a set of user-specified spatial filters, we introduce a form of gradient descent with a novel regularizer that encourages light efficiency and a high signal-to-noise ratio. We demonstrate several examples in simulation and with fabricated prototypes, including some with spatial filters that have prescribed variations with respect to depth and wavelength. Visit the Project Page at https://deanhazineh.github.io/publications/Multi_Image_Synthesis/MIS_Home.html, Comment: Published in the Proceedings of the 2023 IEEE International Conference of Computational Photography

Decomposing an object's appearance into representations of its materials and the surrounding illumination is difficult, even when the object's 3D shape is known beforehand. This problem is especially challenging for diffuse objects: it is ill-conditioned because diffuse materials severely blur incoming light, and it is ill-posed because diffuse materials under high-frequency lighting can be indistinguishable from shiny materials under low-frequency lighting. We show that it is possible to recover precise materials and illumination -- even from diffuse objects -- by exploiting unintended shadows, like the ones cast onto an object by the photographer who moves around it. These shadows are a nuisance in most previous inverse rendering pipelines, but here we exploit them as signals that improve conditioning and help resolve material-lighting ambiguities. We present a method based on differentiable Monte Carlo ray tracing that uses images of an object to jointly recover its spatially-varying materials, the surrounding illumination environment, and the shapes of the unseen light occluders who inadvertently cast shadows upon it., Comment: Project page: https://dorverbin.github.io/eclipse/

Optical metasurfaces are planar substrates with custom-designed, nanoscale features that selectively modulate incident light with respect to direction, wavelength, and polarization. When coupled with photodetectors and appropriate post-capture processing, they provide a means to create computational imagers and sensors that are exceptionally small and have distinctive capabilities. We introduce D-Flat, a framework in TensorFlow that renders physically-accurate images induced by metasurface optical systems. This framework is fully differentiable with respect to metasurface shape and post-capture computational parameters and allows simultaneous optimization with respect to almost any measure of sensor performance. D-Flat enables simulation of millimeter to centimeter diameter metasurfaces on commodity computers, and it is modular in the sense of accommodating a variety of wave optics models for scattering at the metasurface and for propagation to photosensors. We validate D-Flat against symbolic calculations and previous experimental measurements, and we provide simulations that demonstrate its ability to discover novel computational sensor designs for two applications: single-shot depth sensing and single-shot spatial frequency filtering.

Neural Radiance Fields (NeRF) is a popular view synthesis technique that represents a scene as a continuous volumetric function, parameterized by multilayer perceptrons that provide the volume density and view-dependent emitted radiance at each location. While NeRF-based techniques excel at representing fine geometric structures with smoothly varying view-dependent appearance, they often fail to accurately capture and reproduce the appearance of glossy surfaces. We address this limitation by introducing Ref-NeRF, which replaces NeRF's parameterization of view-dependent outgoing radiance with a representation of reflected radiance and structures this function using a collection of spatially-varying scene properties. We show that together with a regularizer on normal vectors, our model significantly improves the realism and accuracy of specular reflections. Furthermore, we show that our model's internal representation of outgoing radiance is interpretable and useful for scene editing., Comment: Project page: https://dorverbin.github.io/refnerf/

Localizing stereo boundaries and predicting nearby disparities are difficult because stereo boundaries induce occluded regions where matching cues are absent. Most modern computer vision algorithms treat occlusions secondarily (e.g., via left-right consistency checks after matching) or rely on high-level cues to improve nearby disparities (e.g., via deep networks and large training sets). They ignore the geometry of stereo occlusions, which dictates that the spatial extent of occlusion must equal the amplitude of the disparity jump that causes it. This paper introduces an energy and level-set optimizer that improves boundaries by encoding occlusion geometry. Our model applies to two-layer, figure-ground scenes, and it can be implemented cooperatively using messages that pass predominantly between parents and children in an undecimated hierarchy of multi-scale image patches. In a small collection of figure-ground scenes curated from Middlebury and Falling Things stereo datasets, our model provides more accurate boundaries than previous occlusion-handling stereo techniques. This suggests new directions for creating cooperative stereo systems that incorporate occlusion cues in a human-like manner., Comment: extended journal version of arXiv:2006.16094