To the Graduate Council: I am submitting herewith a dissertation ...

Next a brief review of watershed-based segmentation algorithms for 2D images isgiven. A detailed review can be found in [12, 72]. Watersheds for image segmentationare described in the classic work of Serra [76] on mathematical morphology. 2D grayscaleimage can be segmented according to the watersheds of the image, where thewatersheds are the domains of attraction of rain falling over the region.A typicalwatershed-based segmentation has three steps. First, regional minima are detected anduniquely labeled. Then other pixels get the labels of regional minima that the swiftestdescending paths (SDP) lead to. The final segmentation is obtained by region merging.The plateau problem means that the SDP is undefined for pixels on a plateau. Theusual solution is transforming the image to a lower complete image [12] so that noplateau exists and the SDP is defined everywhere except at the regional minima. Lowercompletion is accomplished by raising the plateau according to the geodesic distanceto the lower boundary of the plateau. Vincent and Soille [98] used a first-in-first-out(FIFO) queue-based breadth-first algorithm [79] to propagate the label from the plateauboundary to the inside. However, the breadth-first algorithm can only find the shortestpath on the unweighted graphs such as a 2D regular grid for an image. For the weightedgraphs such as a 3D triangle mesh, a priority queue-based algorithm is necessary. Thegeodesic distance computed by Dijkstra’s algorithm [79], which is priority queue-based,is not accurate because the shortest path is restricted on triangle edges. The proposedfast marching watershed algorithm computes a more accurate geodesic distance usingSethian’s fast marching method [77] and precisely partitions the plateaus.32