@conference {12589,
	title = {Symmetric Objects are Hardly Ambiguous},
	booktitle = {Computer Vision and Pattern Recognition, 2007. CVPR {\textquoteright}07. IEEE Conference on},
	year = {2007},
	month = {2007/06//},
	pages = {1 - 7},
	abstract = {Given any two images taken under different illumination conditions, there always exist a physically realizable object which is consistent with both the images even if the lighting in each scene is constrained to be a known point light source at infinity. In this paper, we show that images are much less ambiguous for the class of bilaterally symmetric Lambertian objects. In fact, the set of such objects can be partitioned into equivalence classes such that it is always possible to distinguish between two objects belonging to different equivalence classes using just one image per object. The conditions required for two objects to belong to the same equivalence class are very restrictive, thereby leading to the conclusion that images of symmetric objects are hardly ambiguous. The observation leads to an illumination-invariant matching algorithm to compare images of bilaterally symmetric Lambertian objects. Experiments on real data are performed to show the implications of the theoretical result even when the symmetry and Lambertian assumptions are not strictly satisfied.},
	keywords = {algorithm;symmetric, bilaterally, images;image, Lambertian, MATCHING, matching;, objects, objects;illumination-invariant, objects;symmetric, symmetric},
	doi = {10.1109/CVPR.2007.383289},
	author = {Aggarwal,G. and Biswas,S. and Chellapa, Rama}
}
@conference {14861,
	title = {Non-negative lighting and specular object recognition},
	booktitle = {Computer Vision, 2005. ICCV 2005. Tenth IEEE International Conference on},
	volume = {2},
	year = {2005},
	month = {2005/10//},
	pages = {1323 -1330 Vol. 2 - 1323 -1330 Vol. 2},
	abstract = {Recognition of specular objects is particularly difficult because their appearance is much more sensitive to lighting changes than that of Lambertian objects. We consider an approach in which we use a 3D model to deduce the lighting that best matches the model to the image. In this case, an important constraint is that incident lighting should be non-negative everywhere. In this paper, we propose a new method to enforce this constraint and explore its usefulness in specular object recognition, using the spherical harmonic representation of lighting. The method follows from a novel extension of Szego{\textquoteright}s eigenvalue distribution theorem to spherical harmonics, and uses semidefinite programming to perform a constrained optimization. The new method is faster as well as more accurate than previous methods. Experiments on both synthetic and real data indicate that the constraint can improve recognition of specular objects by better separating the correct and incorrect models},
	keywords = {and, distribution, eigenfunctions;image, eigenvalue, harmonic, Lambertian, lighting;nonnegative, lighting;semidefinite, matching;object, object, objects;Szego, optimization;incident, programming;specular, recognition;optimisation;, recognition;spherical, representation;eigenvalues, theorem;constrained},
	doi = {10.1109/ICCV.2005.168},
	author = {Shirdhonkar,S. and Jacobs, David W.}
}
@article {14886,
	title = {Lambertian reflectance and linear subspaces},
	journal = {Pattern Analysis and Machine Intelligence, IEEE Transactions on},
	volume = {25},
	year = {2003},
	month = {2003/02//},
	pages = {218 - 233},
	abstract = {We prove that the set of all Lambertian reflectance functions (the mapping from surface normals to intensities) obtained with arbitrary distant light sources lies close to a 9D linear subspace. This implies that, in general, the set of images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately by a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce nonnegative lighting functions. We also show a simple way to enforce nonnegative lighting when the images of an object lie near a 4D linear space. We apply these algorithms to perform face recognition by finding the 3D model that best matches a 2D query image.},
	keywords = {2D, 4D, 9D, analog;, analytic, characterization;, convex, convolution, distant, functions;, harmonics;, image, image;, intensities;, Lambertian, light, lighting, linear, methods;, nonnegative, normals;, object, optimization;, programming;, query, recognition;, reflectance;, reflectivity;, set;, sources;, space;, spherical, subspace;, subspaces;, surface},
	isbn = {0162-8828},
	doi = {10.1109/TPAMI.2003.1177153},
	author = {Basri,R. and Jacobs, David W.}
}
@conference {12718,
	title = {Rank constrained recognition under unknown illuminations},
	booktitle = {Analysis and Modeling of Faces and Gestures, 2003. AMFG 2003. IEEE International Workshop on},
	year = {2003},
	month = {2003/10//},
	pages = {11 - 18},
	abstract = {Recognition under illumination variations is a challenging problem. The key is to successfully separate the illumination source from the observed appearance. Once separated, what remains is invariant to illuminant and appropriate for recognition. Most current efforts employ a Lambertian reflectance model with varying albedo field ignoring both attached and cast shadows, but restrict themselves by using object-specific samples, which undesirably deprives them of recognizing new objects not in the training samples. Using rank constraints on the albedo and the surface normal, we accomplish illumination separation in a more general setting, e.g., with class-specific samples via a factorization approach. In addition, we handle shadows (both attached and cast ones) by treating them as missing values, and resolve the ambiguities in the factorization method by enforcing integrability. As far as recognition is concerned, a bootstrap set which is just a collection of two-dimensional image observations can be utilized to avoid the explicit requirement that three-dimensional information be available. Our approaches produce good recognition results as shown in our experiments using the PIE database.},
	keywords = {albedo, approach;, constrained, database;, databases;, decomposition;, factorization, field;, illumination, image;, information;, Lambertian, lighting;, model;, object, object-specific, PIE, rank, recognition;, reflectance, samples;, singular, three-dimensional, two-dimensional, value, variations;, visual},
	doi = {10.1109/AMFG.2003.1240818},
	author = {Zhou, S. and Chellapa, Rama}
}
@conference {14857,
	title = {Lambertian reflectance and linear subspaces},
	booktitle = {Computer Vision, 2001. ICCV 2001. Proceedings. Eighth IEEE International Conference on},
	volume = {2},
	year = {2001},
	month = {2001///},
	pages = {383 -390 vol.2 - 383 -390 vol.2},
	abstract = {We prove that the set of all reflectance functions (the mapping from surface normals to intensities) produced by Lambertian objects under distant, isotropic lighting lies close to a 9D linear subspace. This implies that the images of a convex Lambertian object obtained under a wide variety of lighting conditions can be approximated accurately with a low-dimensional linear subspace, explaining prior empirical results. We also provide a simple analytic characterization of this linear space. We obtain these results by representing lighting using spherical harmonics and describing the effects of Lambertian materials as the analog of a convolution. These results allow us to construct algorithms for object recognition based on linear methods as well as algorithms that use convex optimization to enforce non-negative lighting functions},
	keywords = {functions;spherical, harmonics;convex, Lambertian, lighting;object, object;convex, objects;convex, optimization;isotropic, programming;object, recognition;, recognition;reflectance},
	doi = {10.1109/ICCV.2001.937651},
	author = {Basri,R. and Jacobs, David W.}
}
@conference {14844,
	title = {In search of illumination invariants},
	booktitle = {Computer Vision and Pattern Recognition, 2000. Proceedings. IEEE Conference on},
	volume = {1},
	year = {2000},
	month = {2000///},
	pages = {254 -261 vol.1 - 254 -261 vol.1},
	abstract = {We consider the problem of determining functions of an image of an object that are insensitive to illumination changes. We first show that for an object with Lambertian reflectance there are no discriminative functions that are invariant to illumination. This result leads as to adopt a probabilistic approach in which we analytically determine a probability distribution for the image gradient as a function of the surface{\textquoteright}s geometry and reflectance. Our distribution reveals that the direction of the image gradient is insensitive to changes in illumination direction. We verify this empirically by constructing a distribution for the image gradient from more than 20 million samples of gradients in a database of 1,280 images of 20 inanimate objects taken under varying lighting condition. Using this distribution we develop an illumination insensitive measure of image comparison and test it on the problem of face recognition},
	keywords = {comparison;image, gradient;face, invariants;image, Lambertian, recognition;, recognition;illumination, recognition;object, reflectance;face},
	doi = {10.1109/CVPR.2000.855827},
	author = {Chen,H. F and Belhumeur,P. N. and Jacobs, David W.}
}
@conference {14843,
	title = {Comparing images under variable illumination},
	booktitle = {Computer Vision and Pattern Recognition, 1998. Proceedings. 1998 IEEE Computer Society Conference on},
	year = {1998},
	month = {1998/06//},
	pages = {610 - 617},
	abstract = {We consider the problem of determining whether two images come from different objects or the same object in the same pose, but under different illumination conditions. We show that this problem cannot be solved using hard constraints: even using a Lambertian reflectance model, there is always an object and a pair of lighting conditions consistent with any two images. Nevertheless, we show that for point sources and objects with Lambertian reflectance, the ratio of two images from the same object is simpler than the ratio of images from different objects. We also show that the ratio of the two images provides two of the three distinct values in the Hessian matrix of the object{\textquoteright}s surface. Using these observations, we develop a simple measure for matching images under variable illumination, comparing its performance to other existing methods on a database of 450 images of 10 individuals},
	keywords = {conditions;matching, illumination;visual, images;point, Lambertian, matching;object, model;database;lighting, object, recognition;, recognition;image, reflectance, sources;pose;variable},
	doi = {10.1109/CVPR.1998.698668},
	author = {Jacobs, David W. and Belhumeur,P. N. and Basri,R.}
}
@conference {14840,
	title = {Linear fitting with missing data: applications to structure-from-motion and to characterizing intensity images},
	booktitle = {Computer Vision and Pattern Recognition, 1997. Proceedings., 1997 IEEE Computer Society Conference on},
	year = {1997},
	month = {1997/06//},
	pages = {206 - 212},
	abstract = {Several vision problems can be reduced to the problem of fitting a linear surface of low dimension to data, including the problems of structure-from-affine-motion, and of characterizing the intensity images of a Lambertian scene by constructing the intensity manifold. For these problems, one must deal with a data matrix with some missing elements. In structure-from-motion, missing elements will occur if some point features are not visible in some frames. To construct the intensity manifold missing matrix elements will arise when the surface normals of some scene points do not face the light source in some images. We propose a novel method for fitting a low rank matrix to a matrix with missing elements. We show experimentally that our method produces good results in the presence of noise. These results can be either used directly, or can serve as an excellent starting point for an iterative method},
	keywords = {data;structure-from-affine-motion;structure-from-motion;vision, estimation;, fitting;linear, images;iterative, Lambertian, matrix;intensity, matrix;missing, method;linear, methods;motion, problems;computer, rank, scene;data, surface;low, vision;iterative},
	doi = {10.1109/CVPR.1997.609321},
	author = {Jacobs, David W.}
}
