DERIVATION OF OPTIMAL FILTERS FOR THE DETECTION OF CORONARY-ARTERIES

In this paper optimal filters for the detection of coronary arteries w ith a diameter range of 0.5-6.0 mm in digital X-ray images are derived using a computational approach. This approach is based on the two req uirements for optimal detection. First, the filler should maximize the number of detected true edges and minimize the number of detected fal se edges. Second, if an edge has been detected, its position should be as close as possible to the true edge position in the image. Since th e grey value profile in a digital X-ray image associated with an arter ial vessel is asymmetric, the theory on edge detection derived by Cann y has been expanded with two additional boundary constraints to make i t suitable for the derivation of filters for asymmetric edges. It is d emonstrated that it is possible to derive optimal filters for coronary segments. The localization error, defined by the square root of the s um of the squared systematic and random errors in the assessment of th e arterial diameter, depends on the size of the coronary artery and th e amount of noise in the image. In this paper, an evaluation study is described to assess the relationship between localization error and th e amount of noise upon the vessel profile. For that purpose, an analyt ical description of the vessel profile in an angiographic image was de rived. For the larger arteries the relation between noise and localiza tion error was found to be linear and no systematic over- or underesti mations were observed, even if the noise level was very high. However, it can be shown that the smallest diameter that can be measured depen ds on the amount of noise present in the data. Even for images that co ntain only a low amount of noise, arterial diameters below 0.7 mm cann ot be measured accurately. If the noise in the image increases, the lo west measurable arterial diameter value also increases. Also the rando m error increases rapidly for vessel diameters below 1.2 mm, but with a limited amount of noise and a diameter value above 0.7 mm the random error is still acceptable [0.15 mm (21%) for 0.7-mm vessels, 0.06 mm (6%) for 1-mm vessels].