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Mechanization of Cognition 89

Figure 3.10 Gabor logon local image features. Logons are defined as images with real-valued pixel brightnesses
(i.e., both positive and negative values are allowed) defined by geometrical plane rotations and translations (in the
2
2
image plane) of the canonical two-dimensional functions sin(Gx)/exp(Ex þ Fy ) (called a sine logon) and cos(Gx)/
2
2
exp(Ex þ Fy ) (termed a cosine logon); where E, F, and G are positive constants and x and y are image plane
coordinates in the translated and rotated coordinates of the logon frame. Note that E and F define the principal axis
lengths of a two-dimensional Gaussian-type ellipsoid and G defines the spatial frequency of a plane grating (with
oscillations along the x-axis). The ratio E/F is fixed for all logons used. Each individual logon is considered as a (real
valued) digital image, that is as image vectors of the same dimension as the wide-angle video camera frames.
Malsburg, 1990). In the vision work done in my lab we have typically set the ratio E/F to 5/8 and the
G/E ratio to 3p/2 for every logon in every jet (these are the values that seem to be used by domestic
cats; Hecht-Nielsen, 1990).
Each jet consists, for example, of pairs of a sine logon and a cosine logon at each of seven scales
(E ¼ 2, 3, 5, 9, 15, 20, and 35 pixel units) and 16 regularly spaced angular orientations, including
having the major ellipse axis of one logon pair vertical. Thus, each jet at each gridpoint has 224
logons. Again, each individual logon is viewed as a 67,108,864-dimensional floating point real
vector, with each component value given by the evaluation of its formula (Figure 3.10, properly
translated and rotated) evaluated at the pixel location corresponding to that component (obviously,
with most of its values at pixels distant from the gridpoint very close to zero). Thus, there are a total
of 224 263,169 ¼ 58,949,856 logons in all of the gridpoint jets; almost as many as there are
pixels in the high-resolution camera image.
The image feature vector V of a single camera (assumed to employ a progressive scan) frame
is defined to be the 29,474,928-dimensional vector obtained by first calculating the inner product
of each logon of each jet with the image vector, and then, to get each component of V, adding