The bidirectional reflectance distribution function (BRDF) is an essential tool to capture the complex interaction of light and matter. Recently, several works have employed neural methods for BRDF modeling, following various strategies, ranging from utilizing existing parametric models to purely neural parametrizations. While all methods yield impressive results, a comprehensive comparison of the different approaches is missing in the literature. In this work, we present a thorough evaluation of several approaches, including results for qualitative and quantitative reconstruction quality and an analysis of reciprocity and energy conservation. Moreover, we propose two extensions that can be added to existing approaches: A novel additive combination strategy for neural BRDFs that split the reflectance into a diffuse and a specular part, and an input mapping that ensures reciprocity exactly by construction, while previous approaches only ensure it by soft constraints.

Neural approaches have shown a significant progress on camera-based reconstruction. But they require either a fairly dense sampling of the viewing sphere, or pre-training on an existing dataset, thereby limiting their generalizability. In contrast, photometric stereo (PS) approaches have shown great potential for achieving high-quality reconstruction under sparse viewpoints. Yet, they are impractical because they typically require tedious laboratory conditions, are restricted to dark rooms, and often multi-staged, making them subject to accumulated errors. To address these shortcomings, we propose an end-to-end uncalibrated multi-view PS frameworkfor reconstructing high-resolution shapes acquiredfrom sparse viewpoints in a real-world environment. We relax the dark room assumption, and allow a combination of static ambient lighting and dynamic near LED lighting, thereby enabling easy data capture outside the lab. Experimental validation confirms that it outperforms existing baseline approaches in the regime of sparse viewpoints by a large margin. This allows to bring high-accuracy 3D reconstruction from the dark room to the real world, while maintaining a reasonable data capture complexity.

We propose an end-to-end inverse rendering pipeline called SupeRVol that allows us to recover 3D shape and material parameters from a set of color images in a superresolution manner. To this end, we represent both the bidirectional reflectance distribution function’s (BRDF) parameters and the signed distance function (SDF) by multi-layer perceptrons (MLPs). In order to obtain both the surface shape and its reflectance properties, we revert to a differentiable volume renderer with a physically based illumination model that allows us to decouple reflectance and lighting. This physical model takes into account the effect of the camera’s point spread function thereby enabling a reconstruction of shape and material in a super-resolution quality. Experimental validation confirms that SupeRVol achieves state of the art performance in terms of inverse rendering quality. It generates reconstructions that are sharper than the individual input images, making this method ideally suited for 3D modeling from low-resolution imagery.

Fine-detailed reconstructions are in high demand in many applications. However, most of the existing RGB-D reconstruction methods rely on pre-calculated accurate camera poses to recover the detailed surface geometry, where the representation of a surface needs to be adapted when optimizing different quantities. In this paper, we present a novel multi-view RGB-D based reconstruction method that tackles camera pose, lighting, albedo, and surface normal estimation via the utilization of a gradient signed distance field (gradient-SDF). The proposed method formulates the image rendering process using specific physically-based model(s) and optimizes the surface’s quantities on the actual surface using its volumetric representation, as opposed to other works which estimate surface quantities only near the actual surface. To validate our method, we investigate two physically-based image formation models for natural light and point light source applications. The experimental results on synthetic and real-world datasets demonstrate that the proposed method can recover high-quality geometry of the surface more faithfully than the state-of-the-art and further improves the accuracy of estimated camera poses1.

Abstract Many problems in imaging and low-level vision can be formulated as nonconvex variational problems. A promising class of approaches to tackle such problems are convex relaxation methods, which consider a lifting of the energy functional to a higher-dimensional space. However, they come with increased memory requirements due to the lifting. The present paper is an extended version of the earlier conference paper by Ye et al. (in: DAGM German conference on pattern recognition (GCPR), 2021) which combined two recent approaches to make lifting more scalable: product-space relaxation and sublabel-accurate discretization. Furthermore, it is shown that a simple cutting-plane method can be used to solve the resulting semi-infinite optimization problem. This journal version extends the previous conference work with additional experiments, a more detailed outline of the complete algorithm and a user-friendly introduction to functional lifting methods.

We propose a method to estimate the bidirectional reflectance distribution function (BRDF) and shading of complete scenes under static illumination given the 3D scene geometry and a corresponding high dynamic range (HDR) video. By splitting the BRDF into its diffuse and non-diffuse parts we solve the estimation of each component separately. For the diffuse component, we sample the incident illumination at each point in the scene using Monte Carlo ray tracing, allowing us to factor the captured surface color into albedo and shading. We then use a novel ray tracing-based optimization strategy to estimate the non-diffuse parameters of the BRDF. In a variety of experiments, we demonstrate that our method efficiently generates realistic copies of the observed scenes.

A novel approach towards depth map super-resolution using multi-view uncalibrated photometric stereo is presented. Practically, an LED light source is attached to a commodity RGB-D sensor and is used to capture objects from multiple viewpoints with unknown motion. This non-static camera-to-object setup is described with a nonconvex variational approach such that no calibration on lighting or camera motion is required due to the formulation of an end-to-end joint optimization problem. Solving the proposed variational model results in high resolution depth, reflectance and camera pose estimates, as we show on challenging synthetic and real-world datasets.

This study explores the use of photometric techniques (shape-from-shading and uncalibrated photometric stereo) for upsampling the low-resolution depth map from an RGB-D sensor to the higher resolution of the companion RGB image. A single-shot variational approach is first put forward, which is effective as long as the target's reflectance is piecewise-constant. It is then shown that this dependency upon a specific reflectance model can be relaxed by focusing on a specific class of objects (e.g., faces), and delegate reflectance estimation to a deep neural network. A multi-shot strategy based on randomly varying lighting conditions is eventually discussed. It requires no training or prior on the reflectance, yet this comes at the price of a dedicated acquisition setup. Both quantitative and qualitative evaluations illustrate the effectiveness of the proposed methods on synthetic and real-world scenarios.

This work is concerned with both the 3D-reconstruction of an object using photometric stereo, and its 2D-segmentation from the background. In contrast with previous works on photometric stereo which assume that a mask of the area of interest has been computed beforehand, we formulate 3D-reconstruction and 2D-segmentation as a joint problem. The proposed variational solution combines a differential formulation of photometric stereo with the classic Chan-Vese model for active contours. Given a set of photometric stereo images, this solution simultaneously infers a binary mask of the object of interest and a depth map representing its 3D-shape. Experiments on real-world datasets confirm the soundness of simultaneously solving both these classic computer vision problems, as the joint approach considerably simplifies the overall 3D-scanning process for the end-user.

Photometric stereo (PS) techniques nowadays remain constrained to an ideal laboratory setup where modeling and calibration of lighting is amenable. To eliminate such restrictions, we propose an efficient principled variational approach to uncalibrated PS under general illumination. To this end, the Lambertian reflectance model is approximated through a spherical harmonic expansion, which preserves the spatial invariance of the lighting. The joint recovery of shape, reflectance and illumination is then formulated as a single variational problem. There the shape estimation is carried out directly in terms of the underlying perspective depth map, thus implicitly ensuring integrability and bypassing the need for a subsequent normal integration. To tackle the resulting nonconvex problem numerically, we undertake a two-phase procedure to initialize a balloon-like perspective depth map, followed by a “lagged” block coordinate descent scheme. The experiments validate efficiency and robustness of this approach. Across a variety of evaluations, we are able to reduce the mean angular error consistently by a factor of 2-3 compared to the state-of-the-art.

We put forward a principled variational approach for up-sampling a single depth map to the resolution of the companion color image provided by an RGB-D sensor. We combine heterogeneous depth and color data in order to jointly solve the ill-posed depth super-resolution and shape-from-shading problems. The low-frequency geometric information necessary to disambiguate shape-from-shading is extracted from the low-resolution depth measurements and, symmetrically, the high-resolution photometric clues in the RGB image provide the high-frequency information required to disambiguate depth super-resolution.