Photometric Stereo with General,Unknown Lighting

Work on photometric stereo has shown how to recover the shape and reflectance properties of an object using multiple images taken with a fixed viewpoint and variable lighting conditions. This work has primarily relied on known lighting conditions or the presence of a single point source of light in each image. In this paper we show how to perform photometric stereo assuming that all lights in a scene are distant from the object but otherwise unconstrained. Lighting in each image may be an unknown and may include arbitrary combination of diffuse, point and extended sources. Our work is based on recent results showing that for Lambertian objects, general lighting conditions can be represented using low order spherical harmonics. Using this representation we can recover shape by performing a simple optimization in a low-dimensional space. We also analyze the shape ambiguities that arise in such a representation. We demonstrate our method by reconstructing the shape of objects from images obtained under a variety of lightings. We further compare the reconstructed shapes against shapes obtained with a laser scanner.     

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 initialise a multi-view photometric stereo scheme to obtain a closed surface reconstruction. There are two main contributions in this paper: Firstly we describe a robust technique to estimate light directions and intensities and secondly, 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 multi-view stereo results.     

Translational photometric alignment of single-view image sequences

Photometric stereo is a well-established method to estimate surface normals of an object. When coupled with depth-map estimation, it can be used to reconstruct an object’s height field. Typically, photometric stereo requires an image sequence of an object under the same viewpoint but with differing illumination directions. One crucial assumption of this configuration is perfect pixel correspondence across images in the sequence. While this assumption is often satisfied, certain setups are susceptible to translational errors or misalignments across images. Current methods to align image sequences were not designed specifically for single-view photometric stereo. Thus, they either struggle to account for changing illumination across images, require training sets, or are overly complex for these conditions. However, the unique nature of single-view photometric stereo allows one to model misaligned image sequences using the underlying image formation model and a set of translational shifts. This paper introduces such a technique, entitled translational photometric alignment, that employs the Lambertian model of image formation. This reduces the alignment problem to minimizing a nonlinear sum-squared error function in order to best reconcile the observed images with the generative model. Thus, the end goal of translational photometric alignment is not only to align image sequences, but also to produce the best surface-normal estimates given the observed images. Controlled experiments on the Yale Face Database B demonstrate the high accuracy of translational photometric alignment. The utility and benefits of the technique are further illustrated by additional experiments on image sequences suffering from uncontrolled real-world misalignments.     

Three-dimensional shape from color photometric stereo

Computer vision systems can be used to determine the shapes of real three-dimensional objects for purposes of object recognition and pose estimation or for CAD applications. One method that has been developed is photometric stereo. This method uses several images taken from the same viewpoint, but with different lightings, to determine the three-dimensional shape of an object. Most previous work in photometric stereo has been with gray-tone images; color images have only been used for dielectric materials. In this paper we describe a procedure for color photometric stereo, which recovers the shape of a colored object from two or more color images of the object under white illumination. This method can handle different types of materials, such as composites and metals, and can employ various reflection models such as the Lambertian, dichromatic, and Torrance-Sparrow models. For composite materials, colored metals, and dielectrics, there are two advantages of utilizing color information: at each pixel, there are more constraints on the orientation, and the result is less sensitive to noise. Consequently, the shape can be found more accurately. The method has been tested on both artificial and real images of objects of various materials, and on real images of a multi-colored object.     

基于形变模型由立体序列图象恢复物体的3D形状

结合立体视觉和形变模型提出了一种新的物体3D形状的恢复方法。采用立体视觉方法导出物体表面的3D坐标;利用光流模型估计物体的3D运动,根据此运动移动形变模型,使其对准物体的表面块;由形变模型将由各幅图象得到的离散的3D点融为一起,得到物体的表面形状。实验结果表明该方法能用于形状复杂的物体恢复。     

3D Shape Recovery of Smooth Surfaces: Dropping the Fixed-Viewpoint Assumption

We present a new method for recovering the 3D shape of a featureless smooth surface from three or more calibrated images illuminated by different light sources (three of them are independent). This method is unique in its ability to handle images taken from unconstrained perspective viewpoints and unconstrained illumination directions. The correspondence between such images is hard to compute and no other known method can handle this problem locally from a small number of images. Our method combines geometric and photometric information in order to recover dense correspondence between the images and accurately computes the 3D shape. Only a single pass starting at one point and local computation are used. This is in contrast to methods that use the occluding contours recovered from many images to initialize and constrain an optimization process. The output of our method can be used to initialize such processes. In the special case of fixed viewpoint, the proposed method becomes a new perspective photometric stereo algorithm. Nevertheless, the introduction of the multiview setup, self-occlusions, and regions close to the occluding boundaries are better handled, and the method is more robust to noise than photometric stereo. Experimental results are presented for simulated and real images.     

Stereo Image Analysis of Non-Lambertian Surfaces

Stereo image analysis is based on establishing correspondences between a pair of images by determining similarity measures for potentially corresponding image parts. Such similarity criteria are only strictly valid for surfaces with Lambertian (diffuse) reflectance characteristics. Specular reflections are viewpoint dependent and may thus cause large intensity differences at corresponding image points. In the presence of specular reflections, traditional stereo approaches are often unable to establish correspondences at all, or the inferred disparity values tend to be inaccurate, or the established correspondences do not belong to the same physical surface point. The stereo image analysis framework for non-Lambertian surfaces presented in this contribution combines geometric cues with photometric and polarimetric information into an iterative scheme that allows to establish stereo correspondences in accordance with the specular reflectance behaviour and at the same time to determine the surface gradient field based on the known photometric and polarimetric reflectance properties. The described approach yields a dense 3D reconstruction of the surface which is consistent with all observed geometric and photopolarimetric data. Initially, a sparse 3D point cloud of the surface is computed by traditional blockmatching stereo. Subsequently, a dense 3D profile of the surface is determined in the coordinate system of camera 1 based on the shape from photopolarimetric reflectance and depth technique. A synthetic image of the surface is rendered in the coordinate system of camera 2 using the illumination direction and reflectance properties of the surface material. Point correspondences between the rendered image and the observed image of camera 2 are established with the blockmatching technique. This procedure yields an increased number of 3D points of higher accuracy, compared to the initial 3D point cloud. The improved 3D point cloud is used to compute a refined dense 3D surface profile. These steps are iterated until convergence of the 3D reconstruction. An experimental evaluation of our method is provided for areas of several square centimetres of forged and cast iron objects with rough surfaces displaying both diffuse and significant specular reflectance components, where traditional stereo image analysis largely fails. A comparison to independently measured ground truth data reveals that the root-mean-square error of the 3D reconstruction results is typically of the order 30–100 μm at a lateral pixel resolution of 86 μm. For two example surfaces, the number of stereo correspondences established by the specular stereo algorithm is several orders of magnitude higher than the initial number of 3D points. For one example surface, the number of stereo correspondences decreases by a factor of about two, but the 3D point cloud obtained with the specular stereo method is less noisy, contains a negligible number of outliers, and shows significantly more surface detail than the initial 3D point cloud. For poorly known reflectance parameters we observe a graceful degradation of the accuracy of 3D reconstruction.     

Image segmentation and similarity of color-texture objects

We aim for content-based image retrieval of textured objects in natural scenes under varying illumination and viewing conditions. To achieve this, image retrieval is based on matching feature distributions derived from color invariant gradients. To cope with object cluttering, region-based texture segmentation is applied on the target images prior to the actual image retrieval process. The retrieval scheme is empirically verified on color images taken from textured objects under different lighting conditions.     

Determining Generative Models of Objects Under Varying Illumination: Shape and Albedo from Multiple Images Using SVD and Integrability

We describe a method of learning generative models of objects from a set of images of the object under different, and unknown, illumination. Such a model allows us to approximate the objects' appearance under a range of lighting conditions. This work is closely related to photometric stereo with unknown light sources and, in particular, to the use of Singular Value Decomposition (SVD) to estimate shape and albedo from multiple images up to a linear transformation (Hayakawa, 1994). Firstly we analyze and extend the SVD approach to this problem. We demonstrate that it applies to objects for which the dominant imaging effects are Lambertian reflectance with a distant light source and a background ambient term. To determine that this is a reasonable approximation we calculate the eigenvectors of the SVD on a set of real objects, under varying lighting conditions, and demonstrate that the first few eigenvectors account for most of the data in agreement with our predictions. We then analyze the linear ambiguities in the SVD approach and demonstrate that previous methods proposed to resolve them (Hayakawa, 1994) are only valid under certain conditions. We discuss alternative possibilities and, in particular, demonstrate that knowledge of the object class is sufficient to resolve this problem. Secondly, we describe the use of surface consistency for putting constraints on the possible solutions. We prove that this constraint reduces the ambiguities to a subspace called the generalized bas relief ambiguity (GBR) which is inherent in the Lambertian reflectance function (and which can be shown to exist even if attached and cast shadows are present (Belhumeur et al., 1997)). We demonstrate the use of surface consistency to solve for the shape and albedo up to a GBR and describe, and implement, a variety of additional assumptions to resolve the GBR. Thirdly, we demonstrate an iterative algorithm that can detect and remove some attached shadows from the objects thereby increasing the accuracy of the reconstructed shape and albedo.     

Appearance characterization of linear Lambertian objects, generalized photometric stereo, and illumination-invariant face recognition

Traditional photometric stereo algorithms employ a Lambertian reflectance model with a varying albedo field and involve the appearance of only one object. In this paper, we generalize photometric stereo algorithms to handle all appearances of all objects in a class, in particular the human face class, by making use of the linear Lambertian property. A linear Lambertian object is one which is linearly spanned by a set of basis objects and has a Lambertian surface. The linear property leads to a rank constraint and, consequently, a factorization of an observation matrix that consists of exemplar images of different objects (e.g., faces of different subjects) under different, unknown illuminations. Integrability and symmetry constraints are used to fully recover the subspace bases using a novel linearized algorithm that takes the varying albedo field into account. The effectiveness of the linear Lambertian property is further investigated by using it for the problem of illumination-invariant face recognition using just one image. Attached shadows are incorporated in the model by a careful treatment of the inherent nonlinearity in Lambert's law. This enables us to extend our algorithm to perform face recognition in the presence of multiple illumination sources. Experimental results using standard data sets are presented     

The Amsterdam Library of Object Images

We present the ALOI collection of 1,000 objects recorded under various imaging circumstances. In order to capture the sensory variation in object recordings, we systematically varied viewing angle, illumination angle, and illumination color for each object, and additionally captured wide-baseline stereo images. We recorded over a hundred images of each object, yielding a total of 110,250 images for the collection. These images are made publicly available for scientific research purposes.     

Determining surface orientations of specular surfaces by using the photometric stereo method

The orientation of patches on the surface of an object can be determined from multiple images taken with different illumination, but from the same viewing position. The method, referred to as photometric stereo, can be implemented using table lookup based on numerical inversion of reflectance maps. Here we concentrate on objects with specularly reflecting surfaces, since these are of importance in industrial applications. Previous methods, intended for diffusely reflecting surfaces, employed point source illumination, which is quite unsuitable in this case. Instead, we use a distributed light source obtained by uneven illumination of a diffusely reflecting planar surface. Experimental results are shown to verify analytic expressions obtained for a method employing three light source distributions.     

3D reconstruction for a scanning electron microscope

An algorithm for the reconstruction of the 3D shape of the surface of a micro-object from a stereo pair of images obtained on a raster electron microscope (REM) has been considered. A model of building an image in REM has been presented. The SIFT algorithm was used for determination of the correspondence points. The correspondence points are used to determine the mutual position of the object in a stereo pair by the RANSAC method. A set of points is created in the 3D space, which is later interpolated to reconstruct the 3D surface.     

Nonstructured light-based sensing for 3D reconstruction

Structured light-based sensing (SLS) requires the illumination to be coded either spatially or temporally in the illuminated pattern. However, while the former demands the use of uniquely coded spatial windows whose size grows with the reconstruction resolution and thereby demanding increasing smoothness on the imaged scene, the latter demands the use of multiple image captures. This article presents how the illumination of a very simple pattern plus a single image capture can also achieve 3D reconstruction. The illumination and imaging setting has the configuration of a typical SLS system, comprising a projector and a camera. The difference is, the illumination is not much more than a checkerboard-like pattern - a non-structured pattern in the language of SLS - that does not provide direct correspondence between the camera’s image plane and the projector’s display panel. The system works from the image progressively, first constructing the orientation map of the target object from the observed grid-lines, then inferring the depth map by the use of a few tricks related to interpolation. The system trades off little accuracy of the traditional SLSs with simplicity of its operation. Compared to temporally coded SLSs, the system has the essence that it requires only one image capture to operate; compared with spatially coded SLSs, it requires no use of spatial windows, and in turn a less degree of smoothness on the object surface; compared with methods like shape from shading and photometric stereo, owing to the use of artificial illumination it is less affected by the surface reflectance property of the target surface and the ambient lighting condition.     

A Geometric Approach for the Theory and Applications of 3D Projective Invariants

A central task of computer vision is to automatically recognize objects in real-world scenes. The parameters defining image and object spaces can vary due to lighting conditions, camera calibration and viewing position. It is therefore desirable to look for geometric properties of the object which remain invariant under such changes in the observation parameters. The study of such geometric invariance is a field of active research. This paper presents the theory and computation of projective invariants formed from points and lines using the geometric algebra framework. This work shows that geometric algebra is a very elegant language for expressing projective invariants using n views. The paper compares projective invariants involving two and three cameras using simulated and real images. Illustrations of the application of such projective invariants in visual guided grasping, camera self-localization and reconstruction of shape and motion complement the experimental part.     

Face recognition under arbitrary illumination using illuminated exemplars

Recently, the importance of face recognition has been increasingly emphasized since popular CCD cameras are distributed to various applications. However, facial images are dramatically changed by lighting variations, so that facial appearance changes caused serious performance degradation in face recognition. Many researchers have tried to overcome these illumination problems using diverse approaches, which have required a multiple registered images per person or the prior knowledge of lighting conditions. In this paper, we propose a new method for face recognition under arbitrary lighting conditions, given only a single registered image and training data under unknown illuminations. Our proposed method is based on the illuminated exemplars which are synthesized from photometric stereo images of training data. The linear combination of illuminated exemplars can represent the new face and the weighted coefficients of those illuminated exemplars are used as identity signature. We make experiments for verifying our approach and compare it with two traditional approaches. As a result, higher recognition rates are reported in these experiments using the illumination subset of Max-Planck Institute face database and Korean face database.     

Moment invariants for recognition under changing viewpoint and illumination

Generalised color moments combine shape and color information and put them on an equal footing. Rational expressions of such moments can be designed, that are invariant under both geometric deformations and photometric changes. These generalised color moment invariants are effective features for recognition under changing viewpoint and illumination. The paper gives a systematic overview of such moment invariants for several combinations of deformations and photometric changes. Their validity and potential is corroborated through a series of experiments. Both the cases of indoor and outdoor images are considered, as illumination changes tend to differ between these circumstances. Although the generalised color moment invariants are extracted from planar surface patches, it is argued that invariant neighbourhoods offer a concept through which they can also be used to deal with 3D objects and scenes.     

What Is the Set of Images of an Object Under All Possible Illumination Conditions?

The appearance of an object depends on both the viewpoint from which it is observed and the light sources by which it is illuminated. If the appearance of two objects is never identical for any pose or lighting conditions, then–in theory–the objects can always be distinguished or recognized. The question arises: What is the set of images of an object under all lighting conditions and pose? In this paper, we consider only the set of images of an object under variable illumination, including multiple, extended light sources and shadows. We prove that the set of n-pixel images of a convex object with a Lambertian reflectance function, illuminated by an arbitrary number of point light sources at infinity, forms a convex polyhedral cone in IRⁿ and that the dimension of this illumination cone equals the number of distinct surface normals. Furthermore, the illumination cone can be constructed from as few as three images. In addition, the set of n-pixel images of an object of any shape and with a more general reflectance function, seen under all possible illumination conditions, still forms a convex cone in IRⁿ. Extensions of these results to color images are presented. These results immediately suggest certain approaches to object recognition. Throughout, we present results demonstrating the illumination cone representation.

     

From few to many: illumination cone models for face recognitionunder variable lighting and pose

We present a generative appearance-based method for recognizing human faces under variation in lighting and viewpoint. Our method exploits the fact that the set of images of an object in fixed pose, but under all possible illumination conditions, is a convex cone in the space of images. Using a small number of training images of each face taken with different lighting directions, the shape and albedo of the face can be reconstructed. In turn, this reconstruction serves as a generative model that can be used to render (or synthesize) images of the face under novel poses and illumination conditions. The pose space is then sampled and, for each pose, the corresponding illumination cone is approximated by a low-dimensional linear subspace whose basis vectors are estimated using the generative model. Our recognition algorithm assigns to a test image the identity of the closest approximated illumination cone. Test results show that the method performs almost without error, except on the most extreme lighting directions     

Stereoscopic Segmentation

We cast the problem of multiframe stereo reconstruction of a smooth shape as the global region segmentation of a collection of images of the scene. Dually, the problem of segmenting multiple calibrated images of an object becomes that of estimating the solid shape that gives rise to such images. We assume that the radiance of the scene results in piecewise homogeneous image statistics. This simplifying assumption covers Lambertian scenes with constant albedo as well as fine homogeneous textures, which are known challenges to stereo algorithms based on local correspondence. We pose the segmentation problem within a variational framework, and use fast level set methods to find the optimal solution numerically. Our algorithm does not work in the presence of strong photometric features, where traditional reconstruction algorithms do. It enjoys significant robustness to noise under the assumptions it is designed for.