Application: Symmetric Enclosure versus Template Matching

While the selective symmetry operation resembles template matching in the way it intersects the edge map with its semi-elliptical deformable model, it also utilizes the principles of symmetric enclosure. Concepts derived from Reisfeld [37], Sela [42] and Kelly [20] seem to enhance the template matching process. Symmetric enclosure is used to weight the response to the contours being detected by template intersection. The measurement of symmetric enclosure and the projection of edges along the template normals filter out a variety of inappropriate edge configurations which do not form adequate contours. These also amplify desired contours that would fail to trigger template matching. Figure  demonstrates the advantages of the selective symmetry operation.

  

Figure 2.18: Symmetric enclosure versus traditional template matching. (a) Although these edges trigger many of the template's angular bins by intersection, they are severely misaligned with the template's normals and would yield very weak magnitudes when attenuated via Equation  under the selective symmetry operation. Traditional matching would erroneously register a strong response. (b) This contour would erroneously trigger a strong template match but not the selective symmetry operation due to a low measure of perceptual enclosure. (c) The contour here would erroneously fail to trigger template matching but will properly register under the selective symmetry operation due to a strong sense of enclosure around the model's center.

Thus, the selective symmetry operation reliably detects the desired contours in a manner similar to template matching, with the added benefits of wide non-circular annular sampling regions, non-circular phase orientation weighting, and symmetric enclosure calculations. Furthermore, the selective symmetry operation is a higher resolution blob detector than Sela's symmetry transform since it keeps track of edge magnitude and gradually attenuates misaligned edges instead of discarding them. Furthermore the use of more bits to describe angular bins, edge orientation and edge magnitude provides a more reliable response.

However, the selective symmetry operation is not tuned for speed and does not use pre-calculated lookup tables. The symmetry calculations must be repeatedly evaluated. Thus, it is computationally slower than the symmetry transform.

The selective symmetry detector is not intended to replace the symmetry transform but to be used in conjunction with it. By applying the selective symmetry operation in a neighbourhood around peaks in the interest map, we can refine the output and localize interest peaks more precisely. Furthermore, by varying the templates used by the operation, we can detect the specific shape that triggered the interest map around the interest point. Thus, the selective symmetry operation is applied as a post-processing step after applying the symmetry transform to improve the location of the peaks of the interest map and to estimate the contours that generated them.