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A method is proposed for the automatic, rapid, and stable identification and measurement of objects in three-dimensional (3-D) images. It is based on local shape properties derived statistically from populations of medial primitives sought throughout the image space. These shape properties are measured at medial locations within the object and include scale, orientation, endness, and medial dimensionality. Medial dimensionality is a local shape property differentiating sphere-like, cylinder-like, and slab like structures, with intermediate dimensionality also possible. Endness is a property found at the cap of a cylinder or the edge of a slab. In terms of an application, the cardiac left ventricle (LV) during systole is modeled as a large dark cylinder with an epical cap, terminated at the other end by a thin bright slab-like mitral valve (MV). Such a model, containing medial shape properties at just a few locations, along with the relative distances and orientations between these locations, is intuitive and robust and permits automated detection of the LV axis in vivo, using real-time 3-D (RT3D) echocardiography. The statistical nature of these shape properties allows their extraction, even in the presence of noise, and permits statistical geometric measurements without exact delineation of boundaries, as demonstrated in determining the volume of balloons in RT3D scans. The inherent high speed of the method is appropriate for real-time clinical use.