Derivation of optimal filters for the detection of coronary arteries

In this paper optimal filters for the detection of coronary arteries with 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 requirements for optimal detection. First, the filter should maximize the number of detected true edges and minimize the number of detected false 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 the grey value profile in a digital X-ray image associated with an arterial vessel is asymmetric, the theory on edge detection derived by Canny has been expanded with two additional boundary constraints to make it suitable for the derivation of filters for asymmetric edges. It is demonstrated that it is possible to derive optimal filters for coronary segments. The localization error, defined by the square root of the sum of the squared systematic and random errors in the assessment of the arterial diameter, depends on the size of the coronary artery and the amount of noise in the image. In this paper, an evaluation study is described to assess the relationship between localization error and the amount of noise upon the vessel profile. For that purpose, an analytical description of the vessel profile in an angiographic image was derived. For the larger arteries the relation between noise and localization error was found to be linear and no systematic over- or underestimations were observed, even if the noise level was very high. However, it can be shown that the smallest diameter that can be measured depends on the amount of noise present in the data. Even for images that contain only a low amount of noise, arterial diameters below 0.7 mm cannot be measured accurately. If the noise in the image increases, the lowest measurable arterial diameter value also increases. Also the random 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].