An algorithm for improving the accuracy of discrete ROI integrals

Many problems in the analysis of medical digital images, e.g., digitized x-ray radiograph, computed tomography (CT), magnetic resonance imaging (MRI), or positron emission tomography (PET), require a detailed and precise analysis of user chosen regions of interest (ROIs). Examples of their use include calculating integrals of area, volume, mass, structural moments, and statistical measures for either organs, tumors, or the musculoskeletal system. Among various ROI scan conversion schemes, binary approximate scan conversion is usually preferred due to its efficiency. In this paper, geometric area error is tabulated for typical scan conversion techniques, including whole pixel (WP) approximation and subpixel (SP) approximation methods, and compared to exact pixel (EP) coverage methods for medical ROIs. A new efficient and general EP method for scan conversion of these ROIs is presented. The algorithm traverses the boundary of the polygon while simultaneously scan converting the ROI, and calculates the fractional area of each pixel covered at the perimeter. The resultant geometric area is substantially more accurate than the SP or WP methods, without a significant loss of speed. The numerical results for a ROI with a large ratio of boundary to polygon area demonstrated that the geometric error for a SP method was 40% of the total polygon area, and 150% of the total polygon area for a WP method. The new algorithm could "exactly" calculate the pixel coverage area, in addition to being four times faster than the widely used EP method of Catmull. Efficient and accurate calculation of ROI integrals is essential for comparative analysis.