Article citationsMore>>

W. Kendall, “Probability, Convexity and Harmonic Maps with Small Image I: Uniqueness and Fine Existence,” Proceedings of the London Mathematical Society, Vol. 61, 1990, pp. 371-406. doi:10.1112/plms/s3-61.2.371

has been cited by the following article:

• TITLE: Feature Patch Illumination Spaces and Karcher Compression for Face Recognition via Grassmannians

  AUTHORS: Jen-Mei Chang, Chris Peterson, Michael Kirby

  KEYWORDS: Grassmannians; Karcher Mean; Face Recognition; Illumination Spaces; Compressions; Feature Patches; Principal Angles

  JOURNAL NAME: Advances in Pure Mathematics, Vol.2 No.4, July 27, 2012

  ABSTRACT: Recent work has established that digital images of a human face, when collected with a fixed pose but under a variety of illumination conditions, possess discriminatory information that can be used in classification. In this paper we perform classification on Grassmannians to demonstrate that sufficient discriminatory information persists in feature patch (e.g., nose or eye patch) illumination spaces. We further employ the use of Karcher mean on the Grassmannians to demonstrate that this compressed representation can accelerate computations with relatively minor sacrifice on performance. The combination of these two ideas introduces a novel perspective in performing face recognition.