Recognition of Digital Images of the Human Face at Ultra Low Resolution Via Illumination Spaces

Abstract

Recent work has established that digital images of a human face, collected under various illumination conditions, contain discriminatory information that can be used in classification. In this paper we demonstrate that sufficient discriminatory information persists at ultralow resolution to enable a computer to recognize specific human faces in settings beyond human capabilities. For instance, we utilized the Haar wavelet to modify a collection of images to emulate pictures from a 25pixel camera. From these modified images, a low-resolution illumination space was constructed for each individual in the CMU-PIE database. Each illumination space was then interpreted as a point on a Grassmann manifold. Classification that exploited the geometry on this manifold yielded error-free classification rates for this data set. This suggests the general utility of a low-resolution illumination camera for set-based image recognition problems.

Advances in matrix manifolds for computer vision

“…The image-set classification was performed using the truncated [15] and smallest [28] canonical angles. This study was further extended to low resolution imagery in illumination spaces [16] and unconstrained image-sets [25].…”

“…Liu et al [12] 2004 Still imagery Grassmann CMU-PIE, ORL Yan and Tang [13] 2006 Still imagery Grassmann CMU-PIE, XM2VTS, AR Lin et al [14] 2006 Still imagery Grassmann FERET, XM2VTS, PURDUE Cheng et al [15,16] 2006 Image set Grassmann CMU-PIE Hamm and Lee [17,18] 2008 Image set, video Grassmann YaleB, Extended YaleB Pham and Venkatesh [19] 2008 Still imagery Stiefel CMU-PIE, YaleB, FERET Wang et al [20] 2008 Video Grassmann Honda/UCSD, CMU-MoBo Turaga et al [21] 2008 Video Grassmann Honda/UCSD Tron and Vidal [22] 2008 Still imagery SE(3) Weizmann Pang et al [23] 2008 Still imagery Sym n + AR, FERET Zhao et al [24] 2008 Still imagery Riemannian FRGC Exp 4 Lui et al [25] 2008 Image set Grassmann FRGC Exp 4 Lui and Beveridge [26] 2008 Still imagery Grassmann FERET Lui et al [27] 2009 Still imagery Stiefel CMU-PIE, YaleB, Extended YaleB Beveridge et al [28] 2009 Image set Grassmann CMU-PIE, YaleB Wang and Shi [29] 2009 Image set Grassmann CMU-PIE Yu et al [30] 2009 3D range imagery Riemannian UND Biometrics Database Sirvalingam et al [31] 2010 Still imagery Sym n + FERET Park and Savvides [32] 2011 Still imagery Grassmann CMU-PIE, Extended YaleB Harandi et al [33] 2011 Image set, video Grassmann CMU-PIE, BANCA, CMU-MoBo Turaga et al [34] Appear Image set, video Grassmann CMU-PIE, MBGC the derivative of the trace quotient problem was equivalent to the projection on the horizontal space on the Grassmann manifold where the projection vectors were the eigenvectors of a weighted difference matrix. Whereas discriminant analysis learns a projection that maximizes the trace quotient, multivariate regression learns a projection by fitting the class labels in a regression space.…”

Cone Fields and Topological Sampling in Manifolds with Bounded Curvature

“…Examples of manifolds with nowhere negative curvature are Stiefel and Grassmannian manifolds. These examples are important because there are many applications where data naturally lies on these manifolds such as in dynamic textures [10], face recognition [5], gait recognition [3] and affine shape analysis and image analysis [20].…”

Set-to-Set Face Recognition Under Variations in Pose and Illumination

“…Algorithms that rely on the framework of set-to-set comparison tion under award DMS-0434351 and the DOD-USAF-Office of Scientific have shown significant promise in their ability to classify both Research under contract FA9550-04-1-0094. Any opinions, findings, and still-images and video sequences [11,12,13,5].conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views ofthe National Science FounWhen a collection of images are available for a subject, dation or the DOD-USAF-Office of Scientific Research. we view the data as sampling (with noise) an underlying man-1-4244-1 549-7/07/$25.OO…”

“…Algorithms that rely on the framework of set-to-set comparison tion under award DMS-0434351 and the DOD-USAF-Office of Scientific have shown significant promise in their ability to classify both Research under contract FA9550-04-1-0094. Any opinions, findings, and still-images and video sequences [11,12,13,5].…”