Correlated Area

For a fair comparison between the cartesian and log-polar versions of the algorithm, the size of the object must be related with the area it occupies in the field of view of both geometries. Since the log-polar images represent a smaller field of view (the "corners" of the corresponding cartesian image are not represented) one object occuppies a bigger fraction of the log-polar visual field than the cartesian.

Also due to the different geometries of the defined templates, the effective area that is matched between the template and the current image is different in the cartesian and log-polar domains. The following table makes the correspondence between the size scale (used in the plot labels), the area scale (relation between the size of the object's area in the image and the full cartesian image area) and the effective matched area.

Size Scale Area Scale Effective Area (Cartesian) Effective Area (Log-Polar)
60% 36% 76.17% 96.98%
55% 30.25% 64.00% 81.49%
50% 25% 52.89% 67.34%
45% 20.25% 42.84% 54.55%
40% 16% 33.85% 43.10%
35% 12.25% 25.92% 33.00%
30% 9% 19.04% 24.24%
25% 6.25% 13.22% 16.84%
20% 4% 8.46% 10.78%
15% 2.25% 4.76% 6.06%