This paper presents a novel medical image registration algorithm that explicitly models the physical constraints imposed by objects or sub-structures of objects that have differing material composition and border each other, which is the case in most medical registration applications. Typical medical image registration algorithms ignore these constraints and therefore are not physically viable, and to incorporate these constraints would require prior segmentation of the image into regions of differing material composition, which is a difficult problem in itself. We present a mathematical model and algorithm for incorporating these physical constraints into registration / motion and deformation estimation that does not require a segmentation of different material regions. Our algorithm is a joint estimation of different material regions and the motion/deformation within these regions. Therefore, the segmentation of different material regions is automatically provided in addition to the image registration satisfying the physical constraints. The algorithm identifies differing material regions (sub-structures or objects) as regions where the deformation has different characteristics. We demonstrate the effectiveness of our method on the analysis of cardiac MRI which includes the detection of the left ventricle boundary and its deformation. The experimental results indicate the potential of the algorithm as an assistant tool for the quantitative analysis of cardiac functions in the diagnosis of heart disease.