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This paper describes a procedure for segmenting muscle cell pictures. The segmentation procedure is broken into two logical parts. The first part segments the picture into regions composed of cells or clumps of cells using a number of low-level operations. The second part of the procedure involves the segmentation of the cell clumps into individual cells. This is done by using a hierarchical clustering algorithm to group together those boundary points of a cell clump that belong to the same globally convex sections of the boundary. The dissimilarity measure used by the clustering algorithm is based only on information about the shape of the boundary, where this information is derived from line segments interior to the boundary. This procedure has given us satisfactory results on a number of test pictures.