The Ordered Region Growing (ORG) algorithm has been proposed as a method for delineation of vessel paths from magnetic resonance angiography (MRA). In this paper we demonstrate that the ORG algorithm is a fundamental method for ridge detection that is analogous to watershed segmentation. First, we characterize the segmentation boundaries produced by the watershed as optimal paths. Watershed lines between two points satisfy the criteria that the minimum intensity of the line is maximal out of all possible connected paths between the two points. This is referred to as the greatest-minima criteria. This criteria is guaranteed to provide a unique solution when points in the image are unique-valued. We observe that detection of watershed boundaries from the 2D gradient magnitude image is a similar problem to detection of line-like objects in 3D images, including small vessels in 3D angiography. The ORG algorithm generates an acyclic graph that represents unique paths between any two given points in an image. We prove that paths within the acyclic graph generated by the ORG algorithm conform to the greatest-minima criteria and are thus fundamentally analogous to watershed segmentation boundaries.