Principal Angles Separate Subject Illumination Spaces in YDB and CMU-PIE

• Published in: IEEE transactions on pattern analysis and machine intelligence Vol. 31; no. 2; pp. 351 - 363
• Main Authors: Beveridge, J.R., Draper, B.A., Jen-Mei Chang, Kirby, M., Kley, H., Peterson, C.
• Format: Journal Article
• Language: English
• Published: Los Alamitos, CA IEEE 01.02.2009; IEEE Computer Society; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Computer science; control theory; systems; Computer vision; Exact sciences and technology; Face - anatomy & histology; Face recognition; Humans; Illumination; illumination subspaces; Image databases; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Imaging, Three-Dimensional - methods; Intelligence; Lighting; Lighting - methods; Matching; Pattern analysis; Pattern Recognition, Automated - methods; Pattern recognition. Digital image processing. Computational geometry; principal angle; Reproducibility of Results; Sensitivity and Specificity; set > to > set classification; Solids; Subspaces; Subtraction Technique; Testing; Similarity measures; Feature evaluation and selection; Face and gesture recognition; Useful information; Face recognition; Image processing; Image databank; illumination subspaces; Pattern recognition; principal angle; Luminance; Image matching; Vector space; Classification; Facies; Illumination; Pattern analysis; Artificial intelligence; set-to-set classification
• ISSN: 0162-8828; 1939-3539
• DOI: 10.1109/TPAMI.2008.200

The theory of illumination subspaces is well developed and has been tested extensively on the Yale Face Database B (YDB) and CMU-PIE (PIE) data sets. This paper shows that if face recognition under varying illumination is cast as a problem of matching sets of images to sets of images, then the minimal principal angle between subspaces is sufficient to perfectly separate matching pairs of image sets from nonmatching pairs of image sets sampled from YDB and PIE. This is true even for subspaces estimated from as few as six images and when one of the subspaces is estimated from as few as three images if the second subspace is estimated from a larger set (10 or more). This suggests that variation under illumination may be thought of as useful discriminating information rather than unwanted noise.