## Pixel Processing Based Algorithms

The pixel processing-based approaches [49, 53, 86] work by adaptive filtering, morphological preprocessing segmentation, followed by thinning and branch point analysis. These methods require the processing of every image pixel and multiple operations per pixel. When these operations are highly regular, they can be implemented on fast workstations [86] and pipelined accelerators [25]. Other pixel processing approaches involve the use of neural networks [58, 99] and frequency analysis [111] to determine if individual pixels are vessels. Generally, the computational needs of pixel processing methods scale sharply with image size, and are usually unsuitable for fast, real-time processing without special hardware.

The method of Chaudhuri et al. [25] is based on two-dimensional matched filters. These filters are designed to maximize response over vessels and minimize the response in background regions. Prior to matched filtering, the images are smoothed using a 5 x 5 median filter to reduce the effect of spurious noise. This algorithm uses a Gaussian vessel model similar to that described earlier in Section 6.4. In this case, a vessel profile is described by the Gaussian function f (x, y) = A(1 - ke-d2/2a)

where d is the distance between the point and the center of the vessel, a is representative of the width of the profile, A is the intensity of the local background, and k is a measure of the contrast between the vessel and the local background. From this profile, a kernel K is developed that is defined by:

where L is the length of the kernel, which is the parameter associated with the length of a vessel. This algorithm bounds x at ±3a. The kernel given in the above equation matches (i.e., yields a maximum response for) a vertical vessel that is locally straight. For different orientations, a kernel with 15° of angular resolution is constructed by simply rotating it accordingly. The value of L is set to 9, which is experimentally determined to work well with both "normal" and highly tortuous (curvy) vessels. The value of a is fixed and set to 2.