Two Simple Yet Effective Strategies for Avoiding Over-Smoothing in SFS Problem

Minimization techniques are widely used for retrieving a 3D surface starting from a single shaded image i.e., for solving the shape from shading problem. Such techniques are based on the assumption that expected surface to be retrieved coincides with the one that minimize a properly developed functional, consisting of several contributions. Among the possible contributes defining the functional, the so called "smoothness constraint" is always used since it guides the convergence of the minimization process towards a more accurate solution. Unfortunately, in areas where actually brightness changes rapidly, it also introduces an undesired over-smoothing effect. The present work proposes two simple yet effective strategies for avoiding the typical over-smoothing effect, with regards to the image regions in which this effect is particularly undesired (e.g., areas where surface details are to be preserved in the reconstruction). Tested against a set of case studies the strategies prove to outperform traditional SFS-based methods

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

New constraints on data-closeness and needle map consistency for shape-from-shading

This paper makes two contributions to the problem of needle-map recovery using shape-from-shading. First, we provide a geometric update procedure which allows the image irradiance equation to be satisfied as a hard constraint. This not only improves the data closeness of the recovered needle-map, but also removes the necessity for extensive parameter tuning. Second, we exploit the improved ease of control of the new shape-from-shading process to investigate various types of needle-map consistency constraint. The first set of constraints are based on needle-map smoothness. The second avenue of investigation is to use curvature information to impose topographic constraints. Third, we explore ways in which the needle-map is recovered so as to be consistent with the image gradient field. In each case we explore a variety of robust error measures and consistency weighting schemes that can be used to impose the desired constraints on the recovered needle-map. We provide an experimental assessment of the new shape-from-shading framework on both real world images and synthetic images with known ground truth surface normals. The main conclusion drawn from our analysis is that the data-closeness constraint improves the efficiency of shape-from-shading and that both the topographic and gradient consistency constraints improve the fidelity of the recovered needle-map

Three-dimensional modeling of the human jaw/teeth using optics and statistics.

Object modeling is a fundamental problem in engineering, involving talents from computer-aided design, computational geometry, computer vision and advanced manufacturing. The process of object modeling takes three stages: sensing, representation, and analysis. Various sensors may be used to capture information about objects; optical cameras and laser scanners are common with rigid objects, while X-ray, CT and MRI are common with biological organs. These sensors may provide a direct or an indirect inference about the object, requiring a geometric representation in the computer that is suitable for subsequent usage. Geometric representations that are compact, i.e., capture the main features of the objects with a minimal number of data points or vertices, fall into the domain of computational geometry. Once a compact object representation is in the computer, various analysis steps can be conducted, including recognition, coding, transmission, etc. The subject matter of this dissertation is object reconstruction from a sequence of optical images using shape from shading (SFS) and SFS with shape priors. The application domain is dentistry. Most of the SFS approaches focus on the computational part of the SFS problem, i.e. the numerical solution. As a result, the imaging model in most conventional SFS algorithms has been simplified under three simple, but restrictive assumptions: (1) the camera performs an orthographic projection of the scene, (2) the surface has a Lambertian reflectance and (3) the light source is a single point source at infinity. Unfortunately, such assumptions are no longer held in the case of reconstruction of real objects as intra-oral imaging environment for human teeth. In this work, we introduce a more realistic formulation of the SFS problem by considering the image formation components: the camera, the light source, and the surface reflectance. This dissertation proposes a non-Lambertian SFS algorithm under perspective projection which benefits from camera calibration parameters. The attenuation of illumination is taken account due to near-field imaging. The surface reflectance is modeled using the Oren-Nayar-Wolff model which accounts for the retro-reflection case. In this context, a new variational formulation is proposed that relates an evolving surface model with image information, taking into consideration that the image is taken by a perspective camera with known parameters. A new energy functional is formulated to incorporate brightness, smoothness and integrability constraints. In addition, to further improve the accuracy and practicality of the results, 3D shape priors are incorporated in the proposed SFS formulation. This strategy is motivated by the fact that humans rely on strong prior information about the 3D world around us in order to perceive 3D shape information. Such information is statistically extracted from training 3D models of the human teeth. The proposed SFS algorithms have been used in two different frameworks in this dissertation: a) holistic, which stitches a sequence of images in order to cover the entire jaw, and then apply the SFS, and b) piece-wise, which focuses on a specific tooth or a segment of the human jaw, and applies SFS using physical teeth illumination characteristics. To augment the visible portion, and in order to have the entire jaw reconstructed without the use of CT or MRI or even X-rays, prior information were added which gathered from a database of human jaws. This database has been constructed from an adult population with variations in teeth size, degradation and alignments. The database contains both shape and albedo information for the population. Using this database, a novel statistical shape from shading (SSFS) approach has been created. Extending the work on human teeth analysis, Finite Element Analysis (FEA) is adapted for analyzing and calculating stresses and strains of dental structures. Previous Finite Element (FE) studies used approximate 2D models. In this dissertation, an accurate three-dimensional CAD model is proposed. 3D stress and displacements of different teeth type are successfully carried out. A newly developed open-source finite element solver, Finite Elements for Biomechanics (FEBio), has been used. The limitations of the experimental and analytical approaches used for stress and displacement analysis are overcome by using FEA tool benefits such as dealing with complex geometry and complex loading conditions

Height from Photometric Ratio with Model-based Light Source Selection

In this paper, we present a photometric stereo algorithm for estimating surface height. We follow recent work that uses photometric ratios to obtain a linear formulation relating surface gradients and image intensity. Using smoothed finite difference approximations for the surface gradient, we are able to express surface height recovery as a linear least squares problem that is large but sparse. In order to make the method practically useful, we combine it with a model-based approach that excludes observations which deviate from the assumptions made by the image formation model. Despite its simplicity, we show that our algorithm provides surface height estimates of a high quality even for objects with highly non-Lambertian appearance. We evaluate the method on both synthetic images with ground truth and challenging real images that contain strong specular reflections and cast shadows

Unifying diffuse and specular reflections for the photometric stereo problem

This is the author accepted manuscript. The final version is available from IEEE via http://dx.doi.org/10.1109/WACV.2016.7477643After 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.Experimental setups were provided by Toulouse Tech Transfer, and this collaboration was funded by CNRS GdR 2286 (MIA)

Video normals from colored lights

We present an algorithm and the associated single-view capture methodology to acquire the detailed 3D shape, bends, and wrinkles of deforming surfaces. Moving 3D data has been difficult to obtain by methods that rely on known surface features, structured light, or silhouettes. Multispectral photometric stereo is an attractive alternative because it can recover a dense normal field from an untextured surface. We show how to capture such data, which in turn allows us to demonstrate the strengths and limitations of our simple frame-to-frame registration over time. Experiments were performed on monocular video sequences of untextured cloth and faces with and without white makeup. Subjects were filmed under spatially separated red, green, and blue lights. Our first finding is that the color photometric stereo setup is able to produce smoothly varying per-frame reconstructions with high detail. Second, when these 3D reconstructions are augmented with 2D tracking results, one can register both the surfaces and relax the homogenous-color restriction of the single-hue subject. Quantitative and qualitative experiments explore both the practicality and limitations of this simple multispectral capture system