Human Face Recognition and the Face Image Set

If we consider an n x n image as an n2 dimensional vector, then images of faces can be considered as points in this n2-dimensional image space. Our previous studies of physical transformations of the face, including translation, small rotations and illumination changes, showed that the set of face images consists of relatively simple connected sub-regions in image space [1]. Consequently linear matching techniques can be used to obtain reliable face recognition. However for more general transformations, such as large rotations or scale changes, the face subregions become highly non-convex. We have therefore developed a scale-space matching technique that allows us to take advantage of knowledge about important geometrical transformations and about the topology of the face subregion in image space. While recognition of faces is the focus of this paper, the algorithm is su ciently general to be applicable to a large variety of object recognition tasks. 2 List of Symbols : Greek italic small delta 180 : 180 degrees i: bold i n;m;N; i; j; k; f; x; y; dx; dy; F; I; d: Italic n,m,N,i,j,k,f,x,y,dx,dy,F,I,d S: calligraphic (script) S : Greek italic small theta : Approximately : Greek italic small lambda : Greek italic capital delta R : Integral 1: In nity : Greek italic small nu : Greek italic small pi r: Nabla operator : Greek italic small epsilon : Greek italic small alpha : Greek italic capital pi 3