Performance analysis of maximum intensity projection algorithm for display of MRA images. 
The maximum intensity projection (MIP) is a popularly used algorithm for display of MRA images, but its performance has not been rigorously analyzed before.  In this paper, four measures are proposed for the performance of the MIP algorithm and the quality of images projected from three-dimensional (3-D) data, which are vessel voxel projection probability, vessel detection probability, false vessel probability, and vessel-tissue contrast-to-noise ratio (CNR).  As side products, vessel-missing probability, vessel receiver operating characteristics (ROC's), and mean number of false vessels are also studied.  Based on the assumptions that the intensities of vessel, tissue, and noise along a projection path are independent Gaussian, these measures are derived and obtained all in closed forms.  All the measures are functions of explicit parameters: vessel-to-tissue noise ratio (VTNR) and CNR of 3-D data prior to the MIP, vessel diameter, and projection length.  It is shown that the MIP algorithm increases the CNR of large vessels whose CNR prior to the MIP is high and whose diameters are large.  The increase in CNR increases with projection path length.  On the other hand, all the proposed measures indicate that the small vessels that have low CNR prior to the MIP and small diameters suffer from the MIP.  The performance gets worse as projection path length increases.  All measures demonstrate a better performance when the vessel diameter is larger.  Other properties and possible applications of the derived measures are also discussed.