Discrete Images and Hilbert Spaces - Vision with Direction - page 53

0 0.2 0.4 0.6 0.8 1

Fig. 3.7. On the top , a digital photograph of a text (Aramaic), in which individual characters
are to be automatically identified, is displayed. In the middle , the directional cosines between
the template of a character (alaph) and the local images is shown in color. At bottom , the
identification result is shown for 3 letters where the same color represents the same letter

U , V

cos( ϕ )= (3.58)

U · V

Because the values in the matrices are greater than or equal to zero, the interval
for cos( ϕ ) will be [0 , 1]. In the case when the scalar product

equals zero,
the angle ϕ will be 90 degrees (orthogonal), i.e., least similar. By contrast, if they
share direction, then we will have V = α U , where α is a positive scalar. Because

U , V

U , U = U 2 ,