In this work we present a novel multi-view photometric stereo (PS) method. Like many works in 3D reconstruction we are leveraging neural shape representations and learnt renderers. However, our work differs from the state-of-the-art multi-view PS methods such as PS-NeRF or SuperNormal we explicity leverage per-pixel intensity renderings rather than relying mainly on estimated normals. We model point light attenuation and explicitly raytrace cast shadows in order to best approximate each points incoming radiance. This is used as input to a fully neural material renderer that uses minimal prior assumptions and it is jointly optimised with the surface. Finally, estimated normal and segmentation maps can also incorporated in order to maximise the surface accuracy. Our method is among the first to outperform the classical approach of DiLiGenT-MV and achieves average 0.2mm Chamfer distance for objects imaged at approx 1.5m distance away with approximate 400x400 resolution. Moreover, we show robustness to poor normals in low light count scenario, achieving 0.27mm Chamfer distance when pixel rendering is used instead of estimated normals.

In this work we propose a novel, highly practical, binocular photometric stereo (PS) framework, which has same acquisition speed as single view PS, however significantly improves the quality of the estimated geometry. As in recent neural multi-view shape estimation frameworks such as NeRF, SIREN and inverse graphics approaches to multi-view photometric stereo (e.g. PS-NeRF) we formulate shape estimation task as learning of a differentiable surface and texture representation by minimising surface normal discrepancy for normals estimated from multiple varying light images for two views as well as discrepancy between rendered surface intensity and observed images. Our method differs from typical multi-view shape estimation approaches in two key ways. First, our surface is represented not as a volume but as a neural heightmap where heights of points on a surface are computed by a deep neural network. Second, instead of predicting an average intensity as PS-NeRF or introducing lambertian material assumptions as Guo et al., we use a learnt BRDF and perform near-field per point intensity rendering. Our method achieves the state-of-the-art performance on the DiLiGenT-MV dataset adapted to binocular stereo setup as well as a new binocular photometric stereo dataset - LUCES-ST.

The biggest improvements in Photometric Stereo (PS) field has recently come from adoption of differentiable volumetric rendering techniques such as NeRF or Neural SDF achieving impressive reconstruction error of 0.2mm on DiLiGenT-MV benchmark. However, while there are sizeable datasets for environment lit objects such as Digital Twin Catalogue (DTS), there are only several small Photometric Stereo datasets which often lack challenging objects (simple, smooth, untextured) and practical, small form factor (near-field) light setup. To address this, we propose LUCES-MV, the first real-world, multi-view dataset designed for near-field point light source photometric stereo. Our dataset includes 15 objects with diverse materials, each imaged under varying light conditions from an array of 15 LEDs positioned 30 to 40 centimeters from the camera center. To facilitate transparent end-to-end evaluation, our dataset provides not only ground truth normals and ground truth object meshes and poses but also light and camera calibration images. We evaluate state-of-the-art near-field photometric stereo algorithms, highlighting their strengths and limitations across different material and shape complexities. LUCES-MV dataset offers an important benchmark for developing more robust, accurate and scalable real-world Photometric Stereo based 3D reconstruction methods.

Reconstructing the 3D shape of an object using several images under different light sources is a very challenging task, especially when realistic assumptions such as light propagation and attenuation, perspective viewing geometry and specular light reflection are considered. Many of works tackling Photometric Stereo (PS) problems often relax most of the aforementioned assumptions. Especially they ignore specular reflection and global illumination effects. In this work, we propose a CNN-based approach capable of handling these realistic assumptions by leveraging recent improvements of deep neural networks for far-field Photometric Stereo and adapt them to the point light setup. We achieve this by employing an iterative procedure of point-light PS for shape estimation which has two main steps. Firstly we train a per-pixel CNN to predict surface normals from reflectance samples. Secondly, we compute the depth by integrating the normal field in order to iteratively estimate light directions and attenuation which is used to compensate the input images to compute reflectance samples for the next iteration. Our approach sigificantly outperforms the state-of-the-art on the DiLiGenT real world dataset. Furthermore, in order to measure the performance of our approach for near-field point-light source PS data, we introduce LUCES the first real-world 'dataset for near-fieLd point light soUrCe photomEtric Stereo' of 14 objects of different materials were the effects of point light sources and perspective viewing are a lot more significant. Our approach also outperforms the competition on this dataset as well. Data and test code are available at the project page.

Retrieving accurate 3D reconstructions of objects from the way they reflect light is a very challenging task in computer vision. Despite more than four decades since the definition of the Photometric Stereo problem, most of the literature has had limited success when global illumination effects such as cast shadows, self-reflections and ambient light come into play, especially for specular surfaces. Recent approaches have leveraged the capabilities of deep learning in conjunction with computer graphics in order to cope with the need of a vast number of training data to invert the image irradiance equation and retrieve the geometry of the object. However, rendering global illumination effects is a slow process which can limit the amount of training data that can be generated. In this work we propose a novel pixel-wise training procedure for normal prediction by replacing the training data (observation maps) of globally rendered images with independent per-pixel generated data. We show that global physical effects can be approximated on the observation map domain and this simplifies and speeds up the data creation procedure. Our network, PX-NET, achieves state-of-the-art performance compared to other pixelwise methods on synthetic datasets, as well as the DiLiGenT real dataset on both dense and sparse light settings.

Three-dimensional reconstruction of objects from shading information is a challenging task in computer vision. As most of the approaches facing the Photometric Stereo problem use simplified far-field assumptions, real-world scenarios have essentially more complex physical effects that need to be handled for accurately reconstructing the 3D shape. An increasing number of methods have been proposed to address the problem when point light sources are assumed to be nearby the target object. The proximity of the light sources complicates the modeling of the image formation as the light behaviour requires non-linear parameterisation to describe its propagation and attenuation. To understand the capability of the approaches dealing with this near-field scenario, the literature till now has used synthetically rendered photometric images or minimal and very customised real-world data. In order to fill the gap in evaluating near-field photometric stereo methods, we introduce LUCES the first real-world 'dataset for near-fieLd point light soUrCe photomEtric Stereo' of 14 objects of a varying of materials. A device counting 52 LEDs has been designed to lit each object positioned 10 to 30 centimeters away from the camera. Together with the raw images, in order to evaluate the 3D reconstructions, the dataset includes both normal and depth maps for comparing different features of the retrieved 3D geometry. Furthermore, we evaluate the performance of the latest near-field Photometric Stereo algorithms on the proposed dataset to assess the SOTA method with respect to actual close range effects and object materials.

Reconstructing the 3D shape of an object using several images under different light sources is a very challenging task, especially when realistic assumptions such as light propagation and attenuation, perspective viewing geometry and specular light reflection are considered. Many of works tackling Photometric Stereo (PS) problems often relax most of the aforementioned assumptions. Especially they ignore specular reflection and global illumination effects. In this work, we propose the first CNN based approach capable of handling these realistic assumptions in Photometric Stereo. We leverage recent improvements of deep neural networks for far-field Photometric Stereo and adapt them to near field setup. We achieve this by employing an iterative procedure for shape estimation which has two main steps. Firstly we train a per-pixel CNN to predict surface normals from reflectance samples. Secondly, we compute the depth by integrating the normal field in order to iteratively estimate light directions and attenuation which is used to compensate the input images to compute reflectance samples for the next iteration. To the best of our knowledge this is the first near-field framework which is able to accurately predict 3D shape from highly specular objects. Our method outperforms competing state-of-the-art near-field Photometric Stereo approaches on both synthetic and real experiments.

Highly accurate 3D volumetric reconstruction is still an open research topic where the main difficulty is usually related to merging some rough estimations with high frequency details. One of the most promising methods is the fusion between multi-view stereo and photometric stereo images. Beside the intrinsic difficulties that multi-view stereo and photometric stereo in order to work reliably, supplementary problems arise when considered together. In this work, we present a volumetric approach to the multi-view photometric stereo problem. The key point of our method is the signed distance field parameterisation and its relation to the surface normal. This is exploited in order to obtain a linear partial differential equation which is solved in a variational framework, that combines multiple images from multiple points of view in a single system. In addition, the volumetric approach is naturally implemented on an octree, which allows for fast ray-tracing that reliably alleviates occlusions and cast shadows. Our approach is evaluated on synthetic and real data-sets and achieves state-of-the-art results.

Despite the longtime research aimed at retrieving geometrical information of an object from polarimetric imaging, physical limitations in the polarisation phenomena constrain current approaches to provide ambiguous depth estimation. As an additional constraint, polarimetric imaging formulation differs when light is reflected off the object specularly or diffusively. This introduces another source of ambiguity that current formulations cannot overcome. With the aim of deriving a formulation capable of dealing with as many heterogeneous effects as possible, we propose a differential formulation of the Shape from Polarisation problem that depends only on polarimetric images. This allows the direct geometrical characterisation of the level-set of the object keeping consistent mathematical formulation for diffuse and specular reflection. We show via synthetic and real-world experiments that diffuse and specular reflection can be easily distinguished in order to extract meaningful geometrical features from just polarimetric imaging. The inherent ambiguity of the Shape from Polarization problem becomes evident through the impossibility of reconstructing the whole surface with this differential approach. To overcome this limitation, we consider shading information elegantly embedding this new formulation into a two-light calibrated photometric stereo approach..

3D Reconstruction from shading information through Photometric Stereo is considered a very challenging problem in Computer Vision. Although this technique can potentially provide highly detailed shape recovery, its accuracy is critically dependent on a numerous set of factors among them the reliability of the light sources in emitting a constant amount of light. In this work, we propose a novel variational approach to solve the so called semi-calibrated near field Photometric Stereo problem, where the positions but not the brightness of the light sources are known. Additionally, we take into account realistic modeling features such as perspective viewing geometry and heterogeneous scene composition, containing both diffuse and specular objects. Furthermore, we also relax the point light source assumption that usually constraints the near field formulation by explicitly calculating the light attenuation maps. Synthetic experiments are performed for quantitative evaluation for a wide range of cases whilst real experiments provide comparisons, qualitatively outperforming the state of the art.

State-of-the-art formulations of the Shape from Polarisation problem consist of several steps based on merging physical principles that prevent this problem being described by a single mathematical framework. In addition, specular and diffuse reflections need to be separately considered, making the three-dimensional shape reconstruction not easily applicable to heterogeneous scenes consisting of different materials. In this work we derive a unified specular/diffuse reflection parametrisation of the Shape from Polarisation problem based on a linear partial differential equation capable of recovering the level-set of the surface. The inherent ambiguity of the Shape from Polarization problem becomes evident through the impossibility of reconstructing the whole surface with this differential approach. To overcome this limitation, we consider shading information elegantly embedding this new formulation into a two-lights calibrated photometric stereo approach. Thus we derive an albedo independent and well-posed differential model based on a system of hyperbolic PDEs capable of reconstructing the shape with no ambiguity. We validate the geometrical properties of the new differential model for the Shape from Polarisation problem using synthetic and real data by computing the isocontours of the shape under observation. Lastly, we show the suitability of this new model to elegantly fit into a variational solver that is able to provide 3D shape reconstructions from synthetic and real data. Acknowledgments Roberto Mecca was supported through a Marie Curie fellowship of the “Istituto Nazionale di Alta Matematica”, Italy.

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.

Shape recovery from shading information has recently regained importance due to the improvement towards making the Photometric Stereo technique more reliable in terms of appearance of reflective objects. However, although more advanced models have been lately proposed, 3D scanners based on this technology do not provide reliable reconstructions as long as the considered irradiance equation neglects any additive bias. Depending on the context, such bias assumes different physical meanings. For example, in murky water it is known as saturated backscattered effect or for acquisition in pure air medium it is known as ambient light. Although the theoretical part covers both cases, this work mostly focuses on the pure air acquisition case. Indeed, we present a new approach based on ratios of differences of images where an exhaustive set of physical features are tackled while dealing with Photometric Stereo acquisition with considerable importance for the ambient light. To the best of our knowledge, this is the first attempt to recover the shape from Photometric Stereo considering simultaneously perspective viewing geometry, non-linear light propagation, both specular and diffuse reflectance plus the additive bias of the ambient light. Proof of concept is provided by showing experimental results on synthetic and real data.