“…2, a circle in Cartesian coordinates of a gray-level ultrasonic volume can be parameterized with six variables, p = [x 0 , y 0 , z 0 , θ, ϕ, R], where X 0 = (x 0 , y 0 , z 0 ) defines the center of the circle, (θ, ϕ) are the angular parameters describing the unit normal to the circular plane, and R is the radius of the circle. A model for a circle c that employs parameters p can be written as the set of points X = (x, y, z) that lie on the intersection of a sphere and a plane as given by, (1) where…”