Comparative Evaluation of Symmetric SVD Algorithms for Real-time Face and Eye Tracking

摘要

Computation of singular value decomposition (SVD) has been a topic of concernby many numerical linear algebra researchers. Fast SVD has been a veryeffective tool in computer vision in a number of aspects, such as: facerecognition, eye tracking etc. At the present state of the art fast andfixed-point power efficient SVD algorithm needs to be developed for real-timeembedded computing. The work in this paper is the genesis of an attempt tobuild an on-board real-time face and eye tracking system for human drivers todetect loss of attention due to drowsiness or fatigue. A major function of thison-board system is quick customization. This is carried out when a new drivercomes in. The face and eye images are recorded while instructing the driver formaking specific poses. The eigen faces and eigen eyes are generated at severalresolution levels and stored in the on-board computer. The discriminating eigenspace of face and eyes are determined and stored in the on-board flash memoryfor detection and tracking of face and eyes and classification of eyes (open orclosed) as well. Therefore, fast SVD of image covariance matrix at variouslevels of resolution needs to be carried out to generate the eigen database. Asa preliminary step, we review the existing symmetric SVD algorithms andevaluate their feasibility for such an application. In this article, we comparethe performance of (1) Jacobi's, (2) Hestenes', (3) Golub-Kahan, (4)Tridiagonalization and Symmetric QR iteration and (5) Tridiagonalization andDivide and Conquer algorithms. A case study has been demonstrated as anexample.