Typically, computer vision applications which require feature localisation employ some form of correlation as a preprocessing step. It is well-known, however, that grayscale correlation techniques tend to exhibit a large degree of illumination sensitivity. For applications where the desired feature is largely defined by its geometrical structure, it seems reasonable to employ a correlation technique which for the most part ignores individual gray values and instead focuses on the local structure that is determined by small groups of gray values. This is the motivation behind orientation template correlation.
Orientation template correlation (OTC) is a technique which operates on the orientation map of an image rather than on the image itself. The orientation map for an image is an array of two-dimensional vectors which indicate the strengths and angles of the dominant orientations that are present locally throughout the image. An example of an orientation map is shown in Figure 1. The depicted orientation map was computed using the algorithm described in Section 3.1.3.
Figure 1: Example of an orientation map.
The idea of performing processing on the orientation map representation was introduced by G.H. Granlund in his important work from 1978 entitled ``In Search of a General Picture Processing Operator'', [Gra78]. Using what Granlund refers to as ``transformations of higher-level complex fields,'' one can proceed to search for curvature [BGK90], boundaries between differently oriented regions (e.g., between cloth and woodgrain textures) [KG83],[MP90],[GBGP94], circular symmetries [GK95] and a number of other highly descriptive image features. Moreover, estimates of local orientation can be used in the task of image enhancement [Knu82], and in higher dimensions, image sequence enhancement [KHG90].
For the purposes at hand, we are interested in reliably locating
specific objects (namely, facial features) based on their appearance
in the orientation map representation. We will refer to the
orientation map for a specific object as the orientation
template for that object. One straightforward method of locating
regions in the orientation map of an image which resemble a given
orientation template is to slide the template over the orientation map
of the image, computing at each shift the sum of the dot products of
each vector in the template with each of the underlying vectors in the
orientation map. We refer to this process as orientation
template correlation (OTC).
If we represent the orientation vectors as complex numbers, OTC can be
equivalently be regarded as the real part of the 2D correlation between
, the orientation map of the image, with 
,
the complex conjugate (computed component-wise) of the orientation template:
where 
represents the usual 2D correlation operation.
A review of the literature will reveal that OTC as described above is not a new idea, however. Freeman and Roth [FR94] and Freeman and Weissman[FW94] make use of essentially the same technique for the task of locating a human hand in front of a white background, and Bichsel [Bic91] employs dot products between orientation maps for purposes of face recognition. Bichsel in particular provides a large platform of support -- both computational and biological -- for the use of orientation maps for feature detection. He cites evidence that measures of local orientation are robust to ``the most important object transformations'' (aside from global rotation) which include both local and global illumination/brightness changes and minor variations in object size and shape [Bic91]. Freeman, moreover, reported ``somewhat better performance than pixel intensities'' with regard to correlation on the orientation map representation. We will now discuss methods for the estimation of local orientation.