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## Acquiring linear subspaces for face recognition under variable lighting (2005)

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Venue: | IEEE Transactions on Pattern Analysis and Machine Intelligence |

Citations: | 317 - 2 self |

### Citations

3879 | Eigenfaces for recognition - Turk, Pentland - 1991 |

2800 | Matrix Computations - Golub, Loan - 1989 |

526 | Lambertian Reflectance and Linear Subspaces,” in
- Basri, Jacobs
- 2001
(Show Context)
Citation Context ...tem designers. In the past few years, many appearance-based methods have been proposed to handle this problem, and new theoretical insights as well as good recognition results have been reported [1], =-=[2]-=-, [3], [5], [7], [9]. The main insight gained from these results is that there are both empirical and analytical justifications for using low dimensional linear subspaces to model image variations of ... |

470 | Precomputed radiance transfer for realtime rendering in dynamic, low-frequency lighting environments.
- SLOAN, KAUTZ, et al.
- 2002
(Show Context)
Citation Context ...1) is accompanied by ray tracing to account for the cast shadows. 2.2 Lambertian Reflection and Spherical Harmonics In this section, we briefly summarize the recent work presented in [2], [14], [15], =-=[19]-=-. Consider a convex Lambertian object with uniform albedo illuminated by distant isotropic light sources, and p is a point on the surface of the object. Pick a local ðx; y; zÞ coordinates system Fp ce... |

389 | What is the set of images of an object under all possible lighting condition?”. CVPR
- Belhumeur, Kriegman
- 1997
(Show Context)
Citation Context ...e next section. The good recognition results reported in [2] have indicated very clearly that the linear subspace H generated by the harmonic images is a good approximation to the illumination cone C =-=[3]-=-. Fig. 2a gives a reasonable depiction of the relation between H and C. In particular, we can imagine geometrically that the illumination cone is “thick” in the directions parallel to H, while it is “... |

353 | Face recognition: the problem of compensating for changes in illumination direction.
- Adini, Moses, et al.
- 1997
(Show Context)
Citation Context ...system designers. In the past few years, many appearance-based methods have been proposed to handle this problem, and new theoretical insights, as well as good recognition results, have been reported =-=[1]-=-, [2], [3], [5], [7], [9]. The main insight gained from these results is that there are both empirical and analytical justifications for using low-dimensional linear subspaces to model image variation... |

248 | A ssignal-processing framework for inverse rendering,” in
- Ramamoorthi, Hanrahan
- 2001
(Show Context)
Citation Context ...i and Jacobs have shown that for a convex Lambertian surface, its illumination cone can be accurately approximated by a nine-dimensional linear subspace that they called the harmonic plane [2], [14], =-=[15]-=-. The major contribution of their work is to treat Lambertian reflection as a convolution process between two spherical harmonics representing the lighting condition and the Lambertian kernel. By obse... |

234 | The CMU pose, illumination, and expression (PIE) database
- Sim, Baker, et al.
- 2002
(Show Context)
Citation Context ...e Face Database [7]. This database was designed primarily for studying illumination effects on face recognition. A more recent database designed for similar purposes is the PIE database from CMU (See =-=[18]-=-). We have tested our recognition algorithm on the PIE database, and the results are shown in Figure 10. For the illumination component of the PIE database, there are 1, 587 images of 69 individuals a... |

146 |
A low-dimensional representation of human faces for arbitrary lighting conditions,” in
- Hallinan
- 1994
(Show Context)
Citation Context ...past few years, many appearance-based methods have been proposed to handle this problem, and new theoretical insights, as well as good recognition results, have been reported [1], [2], [3], [5], [7], =-=[9]-=-. The main insight gained from these results is that there are both empirical and analytical justifications for using low-dimensional linear subspaces to model image variations of human faces under di... |

124 | On photometric issues in 3D visual recognition from a single 2D image
- Shashua
- 1993
(Show Context)
Citation Context ...ly work showed that the variability of images of a Lambertian surface in fixed pose, but under variable lighting, where no surface point is shadowed, is a three-dimensional linear subspace [9], [12], =-=[17]-=-, [22]. What has been perhaps more surprising is that, even with cast and attached shadows, the set of images is still well approximated by a relatively low-dimensional subspace, albeit with a bit hig... |

115 | Illumination cones for recognition under variable lighting: Faces,” in - Georghiades, Kriegman, et al. - 1998 |

115 | Analytic PCA Construction for Theoretical Analysis of Lighting Variability in Images of Lambertian Object,
- Ramamoorthi
- 2002
(Show Context)
Citation Context ...ercent of the reflected energy. Using this nine-dimensional harmonic plane, a straightforward face recognition scheme can be developed, and results obtained in [2] are excellent. Recently Ramamoorthi =-=[13]-=- developed a novel method based on spherical harmonics to analytically compute low-dimensional (less than nine-dimensional) linear approximations to illumination cones. His results give a theoretical ... |

111 | From few to many: Generative models for recognition under variable pose and illumination,”
- Georghiades, Kriegman, et al.
- 2001
(Show Context)
Citation Context ... the past few years, many appearance-based methods have been proposed to handle this problem, and new theoretical insights, as well as good recognition results, have been reported [1], [2], [3], [5], =-=[7]-=-, [9]. The main insight gained from these results is that there are both empirical and analytical justifications for using low-dimensional linear subspaces to model image variations of human faces und... |

81 |
5 2 Eigenimages suffice: an empirical investigation of low-dimensional lighting models. In:
- Epstein, Hallinan, et al.
- 1995
(Show Context)
Citation Context ...s. In the past few years, many appearance-based methods have been proposed to handle this problem, and new theoretical insights, as well as good recognition results, have been reported [1], [2], [3], =-=[5]-=-, [7], [9]. The main insight gained from these results is that there are both empirical and analytical justifications for using low-dimensional linear subspaces to model image variations of human face... |

80 | In search of illumination invariants.
- Chen, Belhumeur, et al.
- 2000
(Show Context)
Citation Context ...ation. The recognition results of using our configuration of nine lighting directions together with recent illumination-insensitive recognition algorithms, such as Harmonic Images [2], Gradient Angle =-=[4]-=-, and other methods reported previously in [7] are shown in Table I, ordered by decreasing overall error rate. The correlation method, the Eigenface methods, the linear subspace method, and the cones ... |

65 |
A theory of multiplexed illumination.”
- Schechner, Nayar, et al.
- 2003
(Show Context)
Citation Context ...s under different illumination condidim1 dim2 dim3 dim4 dim5−9 32stions. The usual complicated intermediate steps, such as the 3D reconstruction, can be completely avoided. Recently, Schechner et al. =-=[16]-=- pointed out that taking a set of images under multiplexed illumination rather than by a collection of single point light sources, the signal-to-noise ratio (SNR) will be reduced. Without noise, the r... |

62 | Nine points of light: Acquiring subspaces for face recognition under variable lighting,” in
- Lee, Ho, et al.
- 2001
(Show Context)
Citation Context ... detailed in Section 3, and Section 4 presents experimental results. The final section contains a brief summary and conclusion of this paper. Preliminary results on this topic were presented in [10], =-=[11]-=-. Some notation used in this paper is listed in Table 1.sLEE ET AL.: ACQUIRING LINEAR SUBSPACES FOR FACE RECOGNITION UNDER VARIABLE LIGHTING 3 2 PRELIMINARIES 2.1 Illumination Cone Let x 2 IR n denote... |

31 | Symmetric shape-from-shading using self-ratio image - Zhao, Chellappa |

28 |
Theoretical analysis of illumination in pcabased vision systems.
- Zhao, Yang
- 1999
(Show Context)
Citation Context ...k showed that the variability of images of a Lambertian surface in fixed pose, but under variable lighting, where no surface point is shadowed, is a three-dimensional linear subspace [9], [12], [17], =-=[22]-=-. What has been perhaps more surprising is that, even with cast and attached shadows, the set of images is still well approximated by a relatively low-dimensional subspace, albeit with a bit higher di... |

25 |
Partial differential equations,
- Strauss
- 1992
(Show Context)
Citation Context ...itch the roles of and . l ð5Þs4 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 5, MAY 2005 Legendre functions (its precise definition is not important here, however, see =-=[20]-=-). In particular, there are nine spherical harmonics with l<3. One significant property of the spherical harmonics is that the polynomials with fixed l-degree form an irreducible representation of the... |

21 |
An efficient representation for irradiance environment
- Ramamoorthi, Hanrahan
(Show Context)
Citation Context ..., Basri and Jacobs have shown that for a convex Lambertian surface, its illumination cone can be accurately approximated by a nine-dimensional linear subspace that they called the harmonic plane [2], =-=[14]-=-, [15]. The major contribution of their work is to treat Lambertian reflection as a convolution process between two spherical harmonics representing the lighting condition and the Lambertian kernel. B... |

20 | Dimensionality of Illumination in Appearance Matching
- Nayar, Murase
- 1996
(Show Context)
Citation Context ...ons. Early work showed that the variability of images of a Lambertian surface in fixed pose, but under variable lighting where no surface point is shadowed, is a threedimensional linear subspace [9], =-=[12]-=-, [17]. What has been perhaps more surprising is that even with cast and attached shadows, the set of images is still well approximated by a relatively low dimensional subspace, albeit with a bit high... |

5 |
Lambertian Reflectance and Linear
- Basri, Jacobs
(Show Context)
Citation Context ...m designers. In the past few years, many appearance-based methods have been proposed to handle this problem, and new theoretical insights, as well as good recognition results, have been reported [1], =-=[2]-=-, [3], [5], [7], [9]. The main insight gained from these results is that there are both empirical and analytical justifications for using low-dimensional linear subspaces to model image variations of ... |

4 |
Dimensionality of Illumination
- Nayar, Murase
- 1996
(Show Context)
Citation Context ...s. Early work showed that the variability of images of a Lambertian surface in fixed pose, but under variable lighting, where no surface point is shadowed, is a three-dimensional linear subspace [9], =-=[12]-=-, [17], [22]. What has been perhaps more surprising is that, even with cast and attached shadows, the set of images is still well approximated by a relatively low-dimensional subspace, albeit with a b... |

2 | On Reducing the Complexity of Illumination Cones for Face Recognition
- Ho, Lee, et al.
- 2001
(Show Context)
Citation Context ...on are detailed in Section 3, and Section 4 presents experimental results. The final section contains a brief summary and conclusion of this paper. Preliminary results on this topic were presented in =-=[10]-=-, [11]. Some notation used in this paper is listed in Table 1.sLEE ET AL.: ACQUIRING LINEAR SUBSPACES FOR FACE RECOGNITION UNDER VARIABLE LIGHTING 3 2 PRELIMINARIES 2.1 Illumination Cone Let x 2 IR n ... |