Reconstruction and analysis of surface variation using photometric stereo

In many industrial applications, accurate and fast surface reconstruction is essential for quality control. Variation in surface finishing parameters, such as surface roughness, can reflect defects in a manufacturing process, non-optimal product operational efficiency, and reduced life expectancy of the product. This thesis considers reconstruction and analysis of high-frequency variation, that is roughness, on planar surfaces. Standard roughness measures in industry are calculated from surface topography. A fast and non-contact method to obtain surface topography is to apply photometric stereo in the estimation of surface gradients and to reconstruct the surface by integrating the gradient fields. Alternatively, visual methods, such as statistical measures, fractal dimension and distance transforms, can be used to characterize surface roughness directly from gray-scale images. In this thesis, the accuracy of distance transforms, statistical measures, and fractal dimension are evaluated in the estimation of surface roughness from gray-scale images and topographies. The results are contrasted to standard industry roughness measures. In distance transforms, the key idea is that distance values calculated along a highly varying surface are greater than distances calculated along a smoother surface. Statistical measures and fractal dimension are common surface roughness measures. In the experiments, skewness and variance of brightness distribution, fractal dimension, and distance transforms exhibited strong linear correlations to standard industry roughness measures. One of the key strengths of photometric stereo method is the acquisition of higher frequency variation of surfaces. In this thesis, the reconstruction of planar high-frequency varying surfaces is studied in the presence of imaging noise and blur. Two Wiener filterbased methods are proposed of which one is optimal in the sense of surface power spectral density given the spectral properties of the imaging noise and blur. Experiments show that the proposed methods preserve the inherent high-frequency variation in the reconstructed surfaces, whereas traditional reconstruction methods typically handle incorrect measurements by smoothing, which dampens the high-frequency variation.

A Closed-Form, Consistent and Robust Solution to Uncalibrated Photometric Stereo Via Local Diffuse Reflectance Maxima

Images of an object under different illumination are known to provide strong cues about the object surface. A mathematical formalization of how to recover the normal map of such a surface leads to the so-called uncalibrated photometric stereo problem. In the simplest instance, this problem can be reduced to the task of identifying only three parameters: the so-called generalized bas-relief (GBR) ambiguity. The challenge is to find additional general assumptions about the object, that identify these parameters uniquely. Current approaches are not consistent, i.e., they provide different solutions when run multiple times on the same data. To address this limitation, we propose exploiting local diffuse reflectance (LDR) maxima, i.e., points in the scene where the normal vector is parallel to the illumination direction (see Fig. 1). We demonstrate several noteworthy properties of these maxima: a closed-form solution, computational efficiency and GBR consistency. An LDR maximum yields a simple closed-form solution corresponding to a semi-circle in the GBR parameters space (see Fig. 2); because as few as two diffuse maxima in different images identify a unique solution, the identification of the GBR parameters can be achieved very efficiently; finally, the algorithm is consistent as it always returns the same solution given the same data. Our algorithm is also remarkably robust: It can obtain an accurate estimate of the GBR parameters even with extremely high levels of outliers in the detected maxima (up to 80 % of the observations). The method is validated on real data and achieves state-of-the-art results.

Uncalibrated Near-Light Photometric Stereo

In this work we solve the uncalibrated photometric stereo problem with lights placed near the scene. We investigate different image formation models and find the one that best fits our observations. Although the devised model is more complex than its far-light counterpart, we show that under a global linear ambiguity the reconstruction is possible up to a rotation and scaling, which can be easily fixed. We also propose a solution for reconstructing the normal map, the albedo, the light positions and the light intensities of a scene given only a sequence of near-light images. This is done in an alternating minimization framework which first estimates both the normals and the albedo, and then the light positions and intensities. We validate our method on real world experiments and show that a near-light model leads to a significant improvement in the surface reconstruction compared to the classic distant illumination case.

Overcoming shadows in 3-source photometric stereo

Light occlusions are one of the most significant difficulties of photometric stereo methods. When three or more images are available without occlusion, the local surface orientation is overdetermined so that shape can be computed and the shadowed pixels can be discarded. In this paper, we look at the challenging case when only two images are available without occlusion, leading to a one degree of freedom ambiguity per pixel in the local orientation. We show that, in the presence of noise, integrability alone cannot resolve this ambiguity and reconstruct the geometry in the shadowed regions. As the problem is ill-posed in the presence of noise, we describe two regularization schemes that improve the numerical performance of the algorithm while preserving the data. Finally, the paper describes how this theory applies in the framework of color photometric stereo where one is restricted to only three images and light occlusions are common. Experiments on synthetic and real image sequences are presented.

Multiview photometric stereo

This paper addresses the problem of obtaining complete, detailed reconstructions of textureless shiny objects. We present an algorithm which uses silhouettes of the object, as well as images obtained under changing illumination conditions. In contrast with previous photometric stereo techniques, ours is not limited to a single viewpoint but produces accurate reconstructions in full 3D. A number of images of the object are obtained from multiple viewpoints, under varying lighting conditions. Starting from the silhouettes, the algorithm recovers camera motion and constructs the object's visual hull. This is then used to recover the illumination and initialize a multiview photometric stereo scheme to obtain a closed surface reconstruction. There are two main contributions in this paper: First, we describe a robust technique to estimate light directions and intensities and, second, we introduce a novel formulation of photometric stereo which combines multiple viewpoints and, hence, allows closed surface reconstructions. The algorithm has been implemented as a practical model acquisition system. Here, a quantitative evaluation of the algorithm on synthetic data is presented together with complete reconstructions of challenging real objects. Finally, we show experimentally how, even in the case of highly textured objects, this technique can greatly improve on correspondence-based multiview stereo results.

Self-calibrated, multi-spectral photometric stereo for 3D face capture

This paper addresses the problem of obtaining 3d detailed reconstructions of human faces in real-time and with inexpensive hardware. We present an algorithm based on a monocular multi-spectral photometric-stereo setup. This system is known to capture high-detailed deforming 3d surfaces at high frame rates and without having to use any expensive hardware or synchronized light stage. However, the main challenge of such a setup is the calibration stage, which depends on the lights setup and how they interact with the specific material being captured, in this case, human faces. For this purpose we develop a self-calibration technique where the person being captured is asked to perform a rigid motion in front of the camera, maintaining a neutral expression. Rigidity constrains are then used to compute the head's motion with a structure-from-motion algorithm. Once the motion is obtained, a multi-view stereo algorithm reconstructs a coarse 3d model of the face. This coarse model is then used to estimate the lighting parameters with a stratified approach: In the first step we use a RANSAC search to identify purely diffuse points on the face and to simultaneously estimate this diffuse reflectance model. In the second step we apply non-linear optimization to fit a non-Lambertian reflectance model to the outliers of the previous step. The calibration procedure is validated with synthetic and real data.

Practical 3D reconstruction based on photometric stereo

Photometric Stereo is a powerful image based 3D reconstruction technique that has recently been used to obtain very high quality reconstructions. However, in its classic form, Photometric Stereo suffers from two main limitations: Firstly, one needs to obtain images of the 3D scene under multiple different illuminations. As a result the 3D scene needs to remain static during illumination changes, which prohibits the reconstruction of deforming objects. Secondly, the images obtained must be from a single viewpoint. This leads to depth-map based 2.5 reconstructions, instead of full 3D surfaces. The aim of this Chapter is to show how these limitations can be alleviated, leading to the derivation of two practical 3D acquisition systems: The first one, based on the powerful Coloured Light Photometric Stereo method can be used to reconstruct moving objects such as cloth or human faces. The second, permits the complete 3D reconstruction of challenging objects such as porcelain vases. In addition to algorithmic details, the Chapter pays attention to practical issues such as setup calibration, detection and correction of self and cast shadows. We provide several evaluation experiments as well as reconstruction results. © 2010 Springer-Verlag Berlin Heidelberg.

Classification of textures seen from different distances and under varying illumination direction

Changes in the angle of illumination incident upon a 3D surface texture can significantly alter its appearance, implying variations in the image texture. These texture variations produce displacements of class members in the feature space, increasing the failure rates of texture classifiers. To avoid this problem, a model-based texture recognition system which classifies textures seen from different distances and under different illumination directions is presented in this paper. The system works on the basis of a surface model obtained by means of 4-source colour photometric stereo, used to generate 2D image textures under different illumination directions. The recognition system combines coocurrence matrices for feature extraction with a Nearest Neighbour classifier. Moreover, the recognition allows one to guess the approximate direction of the illumination used to capture the test image

Classification of textures seen from different distances and under varying illumination direction

Changes in the angle of illumination incident upon a 3D surface texture can significantly alter its appearance, implying variations in the image texture. These texture variations produce displacements of class members in the feature space, increasing the failure rates of texture classifiers. To avoid this problem, a model-based texture recognition system which classifies textures seen from different distances and under different illumination directions is presented in this paper. The system works on the basis of a surface model obtained by means of 4-source colour photometric stereo, used to generate 2D image textures under different illumination directions. The recognition system combines coocurrence matrices for feature extraction with a Nearest Neighbour classifier. Moreover, the recognition allows one to guess the approximate direction of the illumination used to capture the test image

Texture recognition under varying imaging geometries

La visió és probablement el nostre sentit més dominant a partir del qual derivem la majoria d'informació del món que ens envolta. A través de la visió podem percebre com són les coses, on són i com es mouen. En les imatges que percebem amb el nostre sistema de visió podem extreure'n característiques com el color, la textura i la forma, i gràcies a aquesta informació som capaços de reconèixer objectes fins i tot quan s'observen sota unes condicions totalment diferents. Per exemple, som capaços de distingir un mateix objecte si l'observem des de diferents punts de vista, distància, condicions d'il·luminació, etc. La Visió per Computador intenta emular el sistema de visió humà mitjançant un sistema de captura d'imatges, un ordinador, i un conjunt de programes. L'objectiu desitjat no és altre que desenvolupar un sistema que pugui entendre una imatge d'una manera similar com ho realitzaria una persona. Aquesta tesi es centra en l'anàlisi de la textura per tal de realitzar el reconeixement de superfícies. La motivació principal és resoldre el problema de la classificació de superfícies texturades quan han estat capturades sota diferents condicions, com ara distància de la càmera o direcció de la il·luminació. D'aquesta forma s'aconsegueix reduir els errors de classificació provocats per aquests canvis en les condicions de captura. En aquest treball es presenta detalladament un sistema de reconeixement de textures que ens permet classificar imatges de diferents superfícies capturades en diferents condicions. El sistema proposat es basa en un model 3D de la superfície (que inclou informació de color i forma) obtingut mitjançant la tècnica coneguda com a 4-Source Colour Photometric Stereo (CPS). Aquesta informació és utilitzada posteriorment per un mètode de predicció de textures amb l'objectiu de generar noves imatges 2D de les textures sota unes noves condicions. Aquestes imatges virtuals que es generen seran la base del nostre sistema de reconeixement, ja que seran utilitzades com a models de referència per al nostre classificador de textures. El sistema de reconeixement proposat combina les Matrius de Co-ocurrència per a l'extracció de característiques de textura, amb la utilització del Classificador del veí més proper. Aquest classificador ens permet al mateix temps aproximar la direcció d'il·luminació present en les imatges que s'utilitzen per testejar el sistema de reconeixement. És a dir, serem capaços de predir l'angle d'il·luminació sota el qual han estat capturades les imatges de test. Els resultats obtinguts en els diferents experiments que s'han realitzat demostren la viabilitat del sistema de predicció de textures, així com del sistema de reconeixement.

Reflectance Transfer for Material Editing and Relighting

We present a new approach to diffuse reflectance estimation for dynamic scenes. Non-parametric image statistics are used to transfer reflectance properties from a static example set to a dynamic image sequence. The approach allows diffuse reflectance estimation for surface materials with inhomogeneous appearance, such as those which commonly occur with patterned or textured clothing. Material editing is also possible by transferring edited reflectance properties. Material reflectance properties are initially estimated from static images of the subject under multiple directional illuminations using photometric stereo. The estimated reflectance together with the corresponding image under uniform ambient illumination form a prior set of reference material observations. Material reflectance properties are then estimated for video sequences of a moving person captured under uniform ambient illumination by matching the observed local image statistics to the reference observations. Results demonstrate that the transfer of reflectance properties enables estimation of the dynamic surface normals and subsequent relighting combined with material editing. This approach overcomes limitations of previous work on material transfer and relighting of dynamic scenes which was limited to surfaces with regions of homogeneous reflectance. We evaluate our approach for relighting 3D model sequences reconstructed from multiple view video. Comparison to previous model relighting demonstrates improved reproduction of detailed texture and shape dynamics.

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.

Variational Stereo Imaging of Oceanic Waves with Statistical Constraints

An image processing observational technique for the stereoscopic reconstruction of the wave form of oceanic sea states is developed. The technique incorporates the enforcement of any given statistical wave law modeling the quasi Gaussianity of oceanic waves observed in nature. The problem is posed in a variational optimization framework, where the desired wave form is obtained as the minimizer of a cost functional that combines image observations, smoothness priors and a weak statistical constraint. The minimizer is obtained combining gradient descent and multigrid methods on the necessary optimality equations of the cost functional. Robust photometric error criteria and a spatial intensity compensation model are also developed to improve the performance of the presented image matching strategy. The weak statistical constraint is thoroughly evaluated in combination with other elements presented to reconstruct and enforce constraints on experimental stereo data, demonstrating the improvement in the estimation of the observed ocean surface.