International audience

International audience

This paper introduces a versatile paradigm for integrating multi-view reflectance (optional) and normal maps acquired through photometric stereo. Our approach employs a pixel-wise joint reparameterization of reflectance and normal, considering them as a vector of radiances rendered under simulated, varying illumination. This re-parameterization enables the seamless integration of reflectance and normal maps as input data in neural volume rendering-based 3D reconstruction while preserving a single optimization objective. In contrast, recent multi-view photometric stereo (MVPS) methods depend on multiple, potentially conflicting objectives. Despite its apparent simplicity, our proposed approach outperforms state-of-the-art approaches in MVPS benchmarks across F-score, Chamfer distance, and mean angular error metrics. Notably, it significantly improves the detailed 3D reconstruction of areas with high curvature or low visibility.

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.

Read Your Voice is a playful interactive multimedia system that allows the user to record a sound, encode it as an image, and then play it back using his smartphone, while controlling the speed and direction of playback.

In this article we show how to extend the multi-view stereo technique when the object to be reconstructed is inside a transparent - but refractive - material, which causes distortions in the images. We provide a theoretical formulation of the problem accounting for a general, non-planar shape of the refractive interface, then a discrete solving method, which are validated by tests on synthetic and real data.

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.

Macrogroove is an interactive and playful multimedia system that allows the user to play a sound coded in the form of a 3D-sonagram. The user is invited to manually move a laser sheet over this "pseudo-relief", in order to playback the original sound in real time.

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.

This paper tackles the photometric stereo problem in the presence of inaccurate lighting, obtained either by calibration or by an uncalibrated photometric stereo method. Based on a precise modeling of noise and outliers, a robust variational approach is introduced. It explicitly accounts for self-shadows, and enforces robustness to cast-shadows and specularities by resorting to redescending M-estimators. The resulting non-convex model is solved by means of a computationally efficient alternating reweighted least-squares algorithm. Since it implicitly enforces integrability, the new variational approach can refine both the intensities and the directions of the lighting.

The integration of surface normals for the purpose of computing the shape of a surface in 3D space is a classic problem in computer vision. However, even nowadays it is still a challenging task to devise a method that is flexible enough to work on non-trivial computational domains with high accuracy, robustness, and computational efficiency. By uniting a classic approach for surface normal integration with modern computational techniques, we construct a solver that fulfils these requirements. Building upon the Poisson integration model, we use an iterative Krylov subspace solver as a core step in tackling the task. While such a method can be very efficient, it may only show its full potential when combined with suitable numerical preconditioning and problem-specific initialisation. We perform a thorough numerical study in order to identify an appropriate preconditioner for this purpose. To provide suitable initialisation, we compute this initial state using a recently developed fast marching integrator. Detailed numerical experiments illustrate the benefits of this novel combination. In addition, we show on real-world photometric stereo datasets that the developed numerical framework is flexible enough to tackle modern computer vision applications.

3D shape recovery using photometric stereo (PS) gained increasing attention in the computer vision community in the last three decades due to its ability to recover the thinnest geometric structures. Yet, the reliability of PS for color images is difficult to guarantee, because existing methods are usually formulated as the sequential estimation of the colored albedos, the normals and the depth. Hence, the overall reliability depends on that of each subtask. In this work we propose a new formulation of color photometric stereo, based on image ratios, that makes the technique independent from the albedos. This allows the unbiased 3D-reconstruction of colored surfaces in a single step, by solving a system of linear PDEs using a variational approach.

After thirty years of researching, the photometric stereo technique for 3D shape recovery still does not provide reliable results if it is not constrained into very well-controlled scenarios. In fact, dealing with realistic materials and lightings yields a non-linear bidirectional reflectance distribution function which is primarily difficult to parametrize and then arduous to solve. With the aim to let the photometric stereo approach face more realistic assumptions, in this work we firstly introduce a unified irradiance equation describing both diffuse and specular reflection components in a general lighting setting. After that, we define a new equation we call unifying due to its basic features modeling the photometric stereo problem for heterogeneous materials. It is provided by making the ratio of irradiance equations holding both diffuse and specular reflections as well as non-linear light propagation features simultaneously. Performing a wide range of experiments, we show that this new approach overcomes state-of-the-art since it leads to a system of unifying equations which can be solved in a very robust manner using an efficient variational approach.

Shape from shading with multiple light sources is an active research area, and a diverse range of approaches have been proposed in recent decades. However, devising a robust reconstruction technique still remains a challenging goal, as the image acquisition process is highly nonlinear. Recent Photometric Stereo variants rely on simplifying assumptions in order to make the problem solvable: light propagation is still commonly assumed to be uniform, and the Bidirectional Reflectance Distribution Function is assumed to be diffuse, with limited interest for specular materials. In this work, we introduce a well-posed formulation based on partial differential equations (PDEs) for a unified reflectance function that can model both diffuse and specular reflections. We base our derivation on ratio of images, which makes the model independent from photometric invariants and yields a well-posed differential problem based on a system of quasi-linear PDEs with discontinuous coefficients. In addition, we directly solve a differential problem for the unknown depth, thus avoiding the intermediate step of approximating the normal field. A variational approach is presented ensuring robustness to noise and outliers (such as black shadows), and this is confirmed with a wide range of experiments on both synthetic and real data, where we compare favorably to the state of the art.