Accurate Measurement of Normal Vectors and Principal Curvatures of the Left Ventricle from MRI Data Using Variational Calculus

Normal vectors are of primary importance in reconstructing the surface of the left ventricle from MR images of the heart. They are fundamental for accurate measurement of wall thickness, which is a very important parameter in assessing ventricular function. In this work, we present a novel technique for computing accurate normal vectors. This technique is based on variational calculus. It explicitly enforces and controls the smoothness of normal vectors along and across outlines. The computed normal vectors are used to describe the surface of the LV through the t of local osculating paraboloids, from which principal curvatures and principal directions are also computed. Besides being fast and simple, this approach applies equally well to the right ventricle, and more generally to any surface sampled in terms of digitised outlines. Extensive experiments are performed using simulated surfaces, for varying sampling resolution to determine the robustness and accuracy of the our method. Finally, this method is applied to segmented MR images of the human left ventricle, and the results are presented.