This paper describes a method for segmentation of convex shaped image regions. The wedge filter technique first employs the converging squares algorithm  to locate a region of interest. Then a region oriented boundary estimation technique, called the wedge filter, is applied. This wedge filter entails angular filtering and subsampling, and boundary interpolation. The technique is more capable of segmenting noncircular shapes than some earlier methods based on the Hough transform. In addition, unlike many edge-based segmentation schemes, this method is relatively tolerant to edge gaps and to blurred or thick edges. This technique is tested on a number of synthesized images over a range of convex shapes, for different algorithm parameters, and under various conditions of region size and image noise. In addition, the technique has been applied to segmentation of liver cell nuclei in light microscope images of human liver tissue.