Multistable Shape from Shading Emerges from Patch Diffusion

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.

Boundary Attention: Learning to Find Faint Boundaries at Any Resolution

We present a differentiable model that explicitly models boundaries -- including contours, corners and junctions -- using a new mechanism that we call boundary attention. We show that our model provides accurate results even when the boundary signal is very weak or is swamped by noise. Compared to previous classical methods for finding faint boundaries, our model has the advantages of being differentiable; being scalable to larger images; and automatically adapting to an appropriate level of geometric detail in each part of an image. Compared to previous deep methods for finding boundaries via end-to-end training, it has the advantages of providing sub-pixel precision, being more resilient to noise, and being able to process any image at its native resolution and aspect ratio.

Polarization Multi-Image Synthesis with Birefringent Metasurfaces

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.

Eclipse: Disambiguating Illumination and Materials using Unintended Shadows

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 ill-conditioned because diffuse materials severely blur incoming light, and 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.

Ref-NeRF: Structured View-Dependent Appearance for Neural Radiance Fields

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.

Level Set Binocular Stereo with Occlusions

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.

StegaPos: Preventing Crops and Splices with Imperceptible Positional Encodings

We present a model for differentiating between images that are authentic copies of ones published by photographers, and images that have been manipulated by cropping, splicing or downsampling after publication. The model comprises an encoder that resides with the photographer and a matching decoder that is available to observers. The encoder learns to embed imperceptible positional signatures into image values prior to publication. The decoder learns to use these steganographic positional ("stegapos") signatures to determine, for each small image patch, the 2D positional coordinates that were held by the patch in its originally-published image. Crop, splice and downsample edits become detectable by the inconsistencies they cause in the hidden positional signatures. We find that training the encoder and decoder together produces a model that imperceptibly encodes position, and that enables superior performance on established benchmarks for splice detection and high accuracy on a new benchmark for crop detection.

Field of Junctions

We introduce a bottom-up model for jointly finding many boundary elements in an image, including edges, curves, corners and junctions. The model explains boundary shape in each small patch using a junction with M angles and a freely-moving vertex. Images are analyzed by solving a non-convex optimization problem using purposefully-designed algorithms, cooperatively finding M+2 junction values at every pixel. The resulting field of junctions is simultaneously an edge detector, a corner/junction detector, and a boundary-aware smoothing of regional appearance. We demonstrate how it behaves at different scales, and for both single-channel and multi-channel input. Notably, we find it has unprecedented resilience to noise: It succeeds at high noise levels where previous methods for segmentation and for edge, corner and junction detection fail.

Layered Stereo by Cooperative Grouping with Occlusion

Human stereo vision uses occlusions as a prominent cue, sometimes the only cue, to localize object boundaries and recover depth relationships between surfaces adjacent to these boundaries. However, many modern computer vision systems treat occlusions as a secondary cue or ignore them as outliers, leading to imprecise boundaries, especially when matching cues are weak. In this work, we introduce a layered approach to stereo that explicitly incorporates occlusions. Unlike previous layer-based methods, our model is cooperative, involving local computations among units that have overlapping receptive fields at multiple scales, and sparse lateral and vertical connections between the computational units. Focusing on bi-layer scenes, we demonstrate our model's ability to localize boundaries between figure and ground in a wide variety of cases, including images from Middlebury and Falling Things datasets, as well as perceptual stimuli that lack matching cues and have yet to be well explained by previous computational stereo systems. Our model suggests new directions for creating cooperative stereo systems that incorporate occlusion cues in a human-like manner.

Unique Geometry and Texture from Corresponding Image Patches

We present a sufficient condition for the recovery of a unique texture process and a unique set of viewpoints from a set of image patches that are generated by observing a flat texture process from unknown directions and orientations. We show that four image patches are sufficient in general, and we characterize the ambiguities that arise when this condition is not satisfied. The results are applicable to the perception of shape from texture and to texture-based structure from motion.