Knowledge-based interpolation of curves: Application to femoropopliteal arterial centerline restoration

We present a novel algorithm, Partial Vector Space Projection (PVSP), for estimation of missing data given a database of similar datasets, and demonstrate its use in restoring the centerlines through simulated occlusions of femoropopliteal arteries, derived from CT angiography data. The algorithm performs Principal Component Analysis (PCA) on a database of centerlines to obtain a set of orthonormal basis functions defined in a scaled and oriented frame of reference, and assumes that any curve not in the database can be represented as a linear combination of these basis functions. Using a database of centerlines derived from 30 normal femoropopliteal arteries, we evaluated the algorithm, and compared it to a correlation-based linear Minimum Mean Squared Error (MMSE) method, by deleting portions of a centerline for several occlusion lengths (OL: 10 mm, 25 mm, 50 mm, 75 mm, 100 mm, 125 mm, 150 mm, 175 mm and 200 mm). For each simulated occlusion, we projected the partially known dataset on the set of basis functions derived from the remaining 29 curves to restore the missing segment. We calculated the maximum point-wise distance (Maximum Departure or MD) between the actual and estimated centerline as the error metric. Mean (standard deviation) of MD increased from 0.18 (0.14) to 4.35 (2.23) as OL increased. The results were fairly accurate even for large occlusion lengths and are clinically useful. The results were consistently better than those using the MMSE method. Multivariate regression analysis found that OL and the root-mean-square error in the 2 cm proximal and distal to the occlusion accounted for most of the error.