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     

Evaluating the effect of diffuse light on photometric stereo reconstruction

Photometric stereo surface reconstruction requires each input image to be associated with a particular 3D illumination vector. This signifies that the subject should be illuminated in turn by various directional illumination sources. In real life, this directionality may be reduced by ambient illumination, which is typically present as a diffuse component of the incident light. This work assesses the photometric stereo reconstruction quality for various ratios of ambient to directional illuminance and provides a reference for the robustness of photometric stereo with respect to that illuminance ratio. In our analysis, we focus on the face reconstruction application of photometric stereo, as faces are convex objects with rich surface variation, thus providing a suitable platform for photometric stereo reconstruction quality evaluation. Results demonstrate that photometric stereo renders realistic reconstructions of the given surface for ambient illuminance as high as nine times the illuminance of the directional light component.     

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.     

Auto-calibrating photometric stereo using ring light constraints

We propose an auto-calibration method for photometric stereo. Our method exploits constraints placed on light sources to recover their positions and the surface normals of an object up to a scaling and planar rotation ambiguity. The ambiguity is resolved with multi-view consistency constraints leading to a Euclidean reconstruction of the geometric shape of the object. Auto-calibration methods are helpful to overcome the limitations imposed by calibrating objects. We evaluate our algorithm with experiments on real world scenes.     

Robust 3D face capture using example-based photometric stereo

We show that using example-based photometric stereo, it is possible to achieve realistic reconstructions of the human face. The method can handle non-Lambertian reflectance and attached shadows after a simple calibration step. We use spherical harmonics to model and de-noise the illumination functions from images of a reference object with known shape, and a fast grid technique to invert those functions and recover the surface normal for each point of the target object. The depth coordinate is obtained by weighted multi-scale integration of these normals, using an integration weight mask obtained automatically from the images themselves. We have applied these techniques to improve the PhotoFace system of Hansen et al. (2010).     

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.     

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.     

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.     

Shape Reconstruction of 3D Bilaterally Symmetric Surfaces

The paper presents a new approach for shape recovery based on integrating geometric and photometric information. We consider 3D bilaterally symmetric objects, that is, objects which are symmetric with respect to a plane (e.g., faces), and their reconstruction from a single image. Both the viewpoint and the illumination are not necessarily frontal. Furthermore, no correspondence between symmetric points is required.The basic idea is that an image taken from a general, non frontal viewpoint, under non-frontal illumination can be regarded as a pair of images. Each image of the pair is one half of the object, taken from different viewing positions and with different lighting directions. Thus, one-image-variants of geometric stereo and of photometric stereo can be used. Unlike the separate invocation of these approaches, which require point correspondence between the two images, we show that integrating the photometric and geometric information suffice to yield a dense correspondence between pairs of symmetric points, and as a result, a dense shape recovery of the object. Furthermore, the unknown lighting and viewing parameters, are also recovered in this process.Unknown distant point light source, Lambertian surfaces, unknown constant albedo, and weak perspective projection are assumed. The method has been implemented and tested experimentally on simulated and real data.     

3D modeling of multiple-object scenes from sets of images

This paper proposes a new approach for multi-object 3D scene modeling. Scenes with multiple objects are characterized by object occlusions under several views, complex illumination conditions due to multiple reflections and shadows, as well as a variety of object shapes and surface properties. These factors raise huge challenges when attempting to model real 3D multi-object scene by using existing approaches which are designed mainly for single object modeling. The proposed method relies on the initialization provided by a rough 3D model of the scene estimated from the given set of multi-view images. The contributions described in this paper consists of two new methods for identifying and correcting errors in the reconstructed 3D scene. The first approach corrects the location of 3D patches from the scene after detecting the disparity between pairs of their projections into images. The second approach is called shape-from-contours and identifies discrepancies between projections of 3D objects and their corresponding contours, segmented from images. Both unsupervised and supervised segmentations are used to define the contours of objects.     

Uncalibrated flatfielding and illumination vector estimationfor photometric stereo face reconstruction

Within the context of photometric stereo reconstruction, flatfielding may be used to compensate for the effect of the inverse-square law of light propagation on the pixel brightness. This would require capturing a set of reference images at an off-line imaging session, which employs a calibrating device that should be captured under the exact conditions as the main session. Similarly, the illumination vectors, on which photometric stereo relies, are typically precomputed based on another dedicated calibration session. In practice, implementing such off-line sessions is inconvenient and often infeasible. This work aims at enabling accurate photometric stereo reconstruction for the case of non-interactive on-line capturing of human faces. We propose unsupervised methodologies, which extract all information that is required for accurate face reconstruction from the images of interest themselves. Specifically, we propose an uncalibrated flatfielding and an uncalibrated illumination vector estimation methodology, and we assess their effect on photometric stereo face reconstruction. Results demonstrate that incorporating our methodologies into the photometric stereo framework halves the reconstruction error, while eliminating the need of off-line calibration.     

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.     

Learning conditional photometric stereo with high-resolution features

Computational Visual Media - Photometric stereo aims to reconstruct 3D geometry by recovering the dense surface orientation of a 3D object from multiple images under differing illumination....     

Two-dimensional BRDF estimation from polarisation

This paper presents a novel technique for reflectance function (BRDF) estimation, which uses polarisation information and photometric stereo. The first stage of the technique is standard and involves the acquisition of polarisation information (angle and degree of polarisation) using a linear polariser and a digital camera. This yields a field of ambiguous surface normal estimates for an arbitrarily shaped object. A photometric stereo algorithm is then used with three different light source directions to disambiguate the surface normals. Next, the proposed algorithm constructs a 3D histogram of the surface normals and pixel brightnesses. A surface, representing the BRDF, is then fitted to the histogram data using simulated annealing optimisation. The result is a set of Cartesian triples that relate the surface normals to the observed pixel brightnesses. Unlike most previous techniques for BRDF estimation, the technique is image-based and does not require sophisticated equipment or intrusive light sources. Although the technique is restricted to smooth and slightly rough dielectric objects, no prior knowledge about the surface geometry is assumed.     

Photometric stereo with an arbitrary number of illuminants

We present an optimal generalisation of the 4-light photometric stereo technique for an arbitrary number of Q illuminants. We assume that the surface reflectance can be approximated by the Lambertian model plus a specular reflection. The algorithm works in a recursive manner eliminating the pixel intensities affected by shadows or highlights, based on a least squares error technique, retaining only the information coming from illumination directions that can be used for photometric stereo reconstruction of the normal of the corresponding surface patch. We report results for both simulated and real surfaces and compare them with the results of other state of the art photometric stereo algorithms.     

Fusing multiview and photometric stereo for 3D reconstruction under uncalibrated illumination

We propose a method to obtain a complete and accurate 3D model from multiview images captured under a variety of unknown illuminations. Based on recent results showing that for Lambertian objects, general illumination can be approximated well using low-order spherical harmonics, we develop a robust alternating approach to recover surface normals. Surface normals are initialized using a multi-illumination multiview stereo algorithm, then refined using a robust alternating optimization method based on the l(1) metric. Erroneous normal estimates are detected using a shape prior. Finally, the computed normals are used to improve the preliminary 3D model. The reconstruction system achieves watertight and robust 3D reconstruction while neither requiring manual interactions nor imposing any constraints on the illumination. Experimental results on both real world and synthetic data show that the technique can acquire accurate 3D models for Lambertian surfaces, and even tolerates small violations of the Lambertian assumption.     

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.

     

Online learning of dynamic multi-view gallery for person Re-identification

Person re-identification receives increasing attentions in computer vision due to its potential applications in video surveillance. In order to alleviate wrong matches caused by misalignment or missing features among cameras, we propose to learn a multi-view gallery of frequently appearing objects in a relatively closed environment. The gallery contains appearance models of these objects from different cameras and viewpoints. The strength of the learned appearance models lies in that they are invariant to viewpoint and illumination changes. To automatically estimate the number of frequently appearing objects in the environment and update their appearance models online, we propose a dynamic gallery learning algorithm. We specifically build up two datasets to validate the effectiveness of our approach in realistic scenarios. Comparisons with benchmark methods demonstrate promising performance in accuracy and efficiency of re-identification.     

一种新颖的多视点图像规正算法

在多视点图像系统中,由于场景光照或相机标定的原因,通常会导致同一对象在不同视点位置颜色外表的不一致。传统的亮度补偿算法难以有效地解决这个问题。基于Retinex颜色恒常性理论,提出了一种新颖的多视点图像规正算法,通过直方图均衡化、Retinex处理和颜色恢复手段,提取出反映物体本质特征的反射光系数来消除不一致光照的影响,在增强单视点图像对比度的同时,将视点间图像的颜色规正到一致的水平。