ABSTRACT
CONTENTS 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 2.2 Theory and Algorithm of Ellipsoidal Filtering . . . . . . . . . . . . . . . . . . . . . . . . 75 2.3 Three-Dimensional Median and Three-Dimensional Directional
Filtering: Comparison with Scale-Space Ellipsoidal Filtering . . . . . . . . 82 2.4 MR Angiography Filtering: Implementation Issues . . . . . . . . . . . . . . . . . . 92 2.5 Conclusions, Challenges, and the Future: Angiographic Filtering . . . 93 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Vascular diseases are one of the major sources of deaths in the U.S. A report [1] states that “Aneurysm rupture is not a rare occurrence as evidenced by the fact that this event currently ranks thirteenth on the list for leading causes of death in the U.S.A.” Also, this report [1] says that “Chronic venous insufficiency is a common problem in the U.S., affecting approximately 5% of the general population. It is estimated that half a million patients suffer from ulceration of the lower extremity as a result of longstanding venous disease.” This report raises the importance of research needed in the area of angiography, the branch of medicine which deals with veins and arteries. In the field of cerebrovascular diseases [1], “Ischemic and hemorrhagic stroke account for one of the principal causes of death and disability in older aged population. In fact, stroke currently ranks third on the list of leading causes of death in the United States (see also trial reports from North America (NASCET) [2] and Europe (ECST) [3], and Wiebers et al. [4]). Each year approximately 500,000 people suffer a new or recurrent stroke in the U.S., and approximately 150,000 die as a result of this process. In addition, more than one third of stroke survivors are left with permanent physical disability which currently accounts for the leading cause of nursing home admissions in the U.S.”
