Automatic generation of a cardiac atlas from echocardiogram images requires that a good segmentation of all anatomical structures be available. In this paper, we present an algorithm for automatic segmentation of all relevant anatomical regions visible in four-chamber view echocardiogram images. Specifically, we propose a two-pass segmentation algorithm in which we first process the image to identify the heart muscle (bright) and chamber regions (dark) by adapting an edge-weighted centroidal Voronoi tessellation (AEWCVT) algorithm. We then partition the resulting bright and dark regions into approximately convex regions using a new convexity pursuit segmentation algorithm. Experimental comparison with several region segmentation algorithms for general imaging shows that our method outperforms these algorithms as it is able to better adapt to known cardiac anatomical structures.