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After noting the edges intersecting the template and attenuating them
appropriately, the edges are sorted into 32 angular bins depending on the
region of the template they fall under. Figure displays the
division of the model by a ray emanating from its center at 32 angular
intervals to form these bins. Within each bin i, the strongest projected
edge magnitude is stored as
. In this way, we form an angular
profile of the edge data as shown in Figure . Symmetric
enclosure is then computed by summing the contribution to symmetry of each
pair of bins as in Equation which is derived from
Equation [20]:

(2.9) 

 Angular position of i^{th} bin

 Peak projected edge magnitude in i^{th} bin
Figure 2.16:
Splitting templates into angular bins

Figure 2.17:
Computing the angular profile of a contour

Due to the pixelization of the edge data, smaller templates will not overlap
enough pixels in the edge map to trigger each of their 32 angular bins. Thus,
small templates will yield consistently lower values of SE. Therefore
each template's output is normalized and presented as a percentage of the
possible peak output of the template. For each template, we compute the maximum
possible value of SE. The final output is a value from 0 to 100%
allowing the implementation of a templateindependent threshold on SE. Thus,
resolution variations in the image due to scaling and discretization will not
affect the response of our templatebased symmetry detection.
Next: Application: Symmetric Enclosure versus
Up: Selective Symmetry Detection for
Previous: Projecting Edges onto the
Tony Jebara
20000623