Two image segmentation methods are presented and compared in terms of rate-distortion within an object-based coding scheme. The LOMO segmentation exploits the relationship between mathematical morphology and local monotonicity in producing a multiscale segmentation.The process is a morphological analogy to the Laplacian of Gaussian. The level set approach uses area morphology to generate segmented regions having a specified minimum area. Segments are optimally chosen from the connected components of the image level sets. A simple object-based coding scheme using the discrete cosine transform is used to avoid the artifacts produced by conventional block-based coding at segment boundaries. Results of each segmentation method are given and compared to one another and to conventional JPEG coding by rate-distortion and the presence of boundary artifacts.