By American Academy of Ophthalmology, Debra J. Shetlar, MD
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Extra resources for 2007-2008 Basic and Clinical Science Course Section 4: Ophthalmic Pathology and Intraocular Tumors
In fact, the large cubes may intersect with small parts of silhouette and it needs checking of more points to identify the intersection. In small cubes, this situation can not be occurred and there is no need to check more points. By choosing NL=8 (checking only corners of cube in last level) and increasing checked points with the factor of 'k' in lower levels, we can minimize Ntot (max) as below: 8k k ⎛ 8k 8k ⎞ ⎛ k k ⎞ N tot ( max ) ≥ S ⋅ C L ⎜ 8+ 1 + 2 + 3 + ··· ⎟ ≥ 8 ⋅ S ⋅ C L ⎜ 1+ 1 + 2 + 3 + ··· ⎟ (46) 8 64 512 8 64 512 ⎝ ⎠ ⎝ ⎠ The final approach to increase the speed is to check the edge points hierarchically.
The amount of kij depends on the shape of cone(j) and silhouette i. For hierarchical checking method, consider that each ray is divided into n part at first. To find the exact position of each start and end points, log 2 ( N ray / n ) points should be checked. In convex parts, bounding edges are formed in one segment. Therefore, the number of checking points in each ray is: ( NH ray = n + 2 ⋅ log 2 N ray / n ) (49) Figure 14. (a) Projection of ray to the silhouette images to extract the bounding edges (b) hierarchical method to find the start and the end of segments.
Hence, the uniqueness-checking process will fail to find the best match. On the contrary, the long curves are more descriptive in shape and result in high confidence matching, as the number of detected similar curves will be decreased. Occlusion and branching are the other factors that restrict lengthening of the curves, so that the number of appropriate curves reduces by increasing the length of curves. Our experiments show that the curve length between 20 to 40 points (for 480×640 image size) provides good result.
2007-2008 Basic and Clinical Science Course Section 4: Ophthalmic Pathology and Intraocular Tumors by American Academy of Ophthalmology, Debra J. Shetlar, MD