A new approach is proposed for edge detection in ultrasound. The technique examines the image intensity profile for unit roots based on the Dickey–Fuller statistical test of stationarity. The existence of the unit root is a sign of nonstationarity and a possible edge. A simple algorithm to build a segmentation method based on this edge detection approach is also proposed, which is capable of delineating the perimeter of hollow structures such as blood vessels and cysts. In this approach, the radial edge profiles originating from the center of the object of interest are scanned for the change from stationary to nonstationary status. The algorithm treats the radial intensity profiles as a time series and uses the Dickey–Fuller statistical test along the radii to find the location at which the profile becomes nonstationary. A priori criteria for edge continuity, shape, and size of the object of interest are applied to enhance the stability of the algorithm. The accuracy is demonstrated on simulated ultrasound. Further, the method is examined on two different image sets of blood vessels and validated based on contours marked by experts. The worst case distance from expert contours is . The average area difference between the expert and the extracted contours is and of the vessel area in the two datasets. The proposed segmentation method is also compared to segmentation using active contours on ultrasound images of breast and ovarian cysts and shown to be accurate and stable.