A new bubble wave algorithm provides automatic segmentation of three-dimensional magnetic resonance images of both the peripheral vasculature and the brain. Simple connectivity algorithms are not reliable in these medical applications because there are unwanted connections through background noise. The bubble wave algorithm restricts connectivity using curvature by testing spherical regions on a propagating active contour to eliminate noise bridges. After the user places seeds in both the selected regions and in the regions that are not desired, the method provides the critical threshold for segmentation using binary search. Today, peripheral vascular disease is diagnosed using magnetic resonance imaging with a timed contrast bolus. A new blood pool contrast agent MS-325 (Epix Medical) binds to albumen in the blood and provides high-resolution three-dimensional images of both arteries and veins. The bubble wave algorithm provides a means to automatically suppress the veins that obscure the arteries in magnetic resonance angiography. Monitoring brain atrophy is needed for trials of drugs that retard the progression of dementia. The brain volume is measured by placing seeds in both the brain and scalp to find the critical threshold that prevents connections between the brain volume and the scalp. Examples from both three-dimensional magnetic resonance brain and contrast enhanced vascular images were segmented with minimal user intervention.