A single-lobe photometric stereo approach for heterogeneous material

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.Roberto Mecca is a Marie Curie fellow of the “Istituto Nazionale di Alta Matematica” (Italy) for a project shared with University of Cambridge, Department of Engineering and the Department of Mathematics, University of Bologna

Photometric stereo with only two images: A theoretical study and numerical resolution

This work tackles the problem of two-image photometric stereo. This problem constitutes the intermediate case between conventional photometric stereo with at least three images, which is well-posed, and shape-from-shading, which is ill-posed. We first provide a theoretical study of ambiguities arising in this intermediate case. Based on this study, we show that when the albedo is known, disambiguation can be formulated as a binary labeling problem, using integrability and a nonstationary Ising model. The resulting optimization problem is solved efficiently by resorting to the graph cut algorithm. These theoretical and numerical contributions are eventually validated in an application to three-image photometric stereo with shadows.Roberto Mecca was a Marie Curie Fellow of the Instituto Nazionale di Alta Matematic

On the well-posedness of uncalibrated photometric stereo under general lighting

Uncalibrated photometric stereo aims at estimating the 3D-shape of a surface, given a set of images captured from the same viewing angle, but under unknown, varying illumination. While the theoretical foundations of this inverse problem under directional lighting are well-established, there is a lack of mathematical evidence for the uniqueness of a solution under general lighting. On the other hand, stable and accurate heuristical solutions of uncalibrated photometric stereo under such general lighting have recently been proposed. The quality of the results demonstrated therein tends to indicate that the problem may actually be well-posed, but this still has to be established. The present paper addresses this theoretical issue, considering first-order spherical harmonics approximation of general lighting. Two important theoretical results are established. First, the orthographic integrability constraint ensures uniqueness of a solution up to a global concave-convex ambiguity , which had already been conjectured, yet not proven. Second, the perspective integrability constraint makes the problem well-posed, which generalizes a previous result limited to directional lighting. Eventually, a closed-form expression for the unique least-squares solution of the problem under perspective projection is provided , allowing numerical simulations on synthetic data to empirically validate our findings

Modèles ecologiques pour l'extrapolation des effets écotoxicologiques enregistrés lors de biotests in situ cheZ Gammarus

[Departement_IRSTEA]Eaux [TR1_IRSTEA]BELCAInternational audienceEvaluating the effects of chemical contamination on populations and ecological communities still constitutes a challenging necessity in environmental management. However the toxic effects of contaminants are commonly measured by means of organism-level responses. Linking such effects measures with ecological models is a promising way to apprehend population-level impacts. In this way, population models are currently increasingly used in predictive risk assessment procedures, but their use in environmental diagnostic framework remains limited due to their lack of ecological realism. The present study with the crustacean amphipod Gammarus fossarum, a sentinel species in freshwater monitoring, combines a dual field and laboratory experimental approach with a population modelling framework. In this way, we developed an ecologically-relevant periodic matrix population model for Gammarus. This model allowed us to capture the population dynamics in the field, and to understand the particular pattern of demographic sensitivities induced by Gammarus life-history phenology. The model we developed provided a robust population-level assessment of in situ-based effects measures recorded during a biomonitoring program on a French watershed impacted by past mining activities. Thus, our study illustrates the potential of population modelling when seeking to decipher the role of environmental toxic contamination in ecological perturbations

A single-lobe photometric stereo approach for heterogeneous material

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

On the well-posedness of uncalibrated photometric stereo under general lighting

International audienceUncalibrated photometric stereo aims at estimating the 3D-shape of a surface, given a set of images captured from the same viewing angle, but under unknown, varying illumination. While the theoretical foundations of this inverse problem under directional lighting are well-established, there is a lack of mathematical evidence for the uniqueness of a solution under general lighting. On the other hand, stable and accurate heuristical solutions of uncalibrated photometric stereo under such general lighting have recently been proposed. The quality of the results demonstrated therein tends to indicate that the problem may actually be well-posed, but this still has to be established. The present paper addresses this theoretical issue, considering first-order spherical harmonics approximation of general lighting. Two important theoretical results are established. First, the orthographic integrability constraint ensures uniqueness of a solution up to a global concave-convex ambiguity , which had already been conjectured, yet not proven. Second, the perspective integrability constraint makes the problem well-posed, which generalizes a previous result limited to directional lighting. Eventually, a closed-form expression for the unique least-squares solution of the problem under perspective projection is provided , allowing numerical simulations on synthetic data to empirically validate our findings

Combining Depth Fusion and Photometric Stereo for Fine-Detailed 3D Models

In recent years, great progress has been made on the problem of 3D scene reconstruction using depth sensors. On a large scale, these reconstructions look impressive, but often many fine details are lacking due to limitations in the sensor resolution. In this paper we combine two well-known principles for recovery of 3D models, namely fusion of depth images with photometric stereo to enhance the details of the reconstructions. We derive a simple and transparent objective functional that takes both the observed intensity images and depth information into account. The experimental results show that many details are captured that are not present in the input depth images. Moreover, we provide a quantitative evaluation that confirms the improvement of the resulting 3D reconstruction using a 3D printed model

Caractériser la toxicité des effluents de station de traitements 1. Expérimentations ex-situ et in-situ à la station d'épuration de Sophia-Antipolis : Réalisation de bio essais pour évaluer les performances épuratoires sur la toxicité du rejet et son impact sur le milieu récepteur.

National audienceLa caractérisation de la toxicité des différents effluents d'une chaine de traitements complémentaires de station d'épuration, et l'impact du rejet final sur le milieu récepteur ont été évalués à partir de deux méthodologies complémentaires. La caractérisation de la toxicité des effluents a été réalisée à partir de bioessais sur des organismes exposés en continu dans un laboratoire ex-situ dans lequel les eaux usées ont été amenés. L'impact du rejet a été mesuré à partir d'une exposition dans la rivière d'organismes encagés, et de la réalisation de ces mêmes bioessais