A system for detecting the dimensions and geometry of a native valve annulus for trans-catheter valve implantation includes a compliant balloon and a shaft within the balloon. One or more drive electrodes may be affixed to a surface of the balloon, and one or more sense electrodes may be affixed to the shaft. After insertion of the balloon into the native valve annulus, the drive electrodes may be energized with a predetermined voltage. Using a trained statistical model and the voltages measured at the sense electrodes, initial estimates of the cross-section of the valve annulus may be obtained. The initial estimates may then be provided to an optimization model of the valve annulus to obtain a highly accurate prediction of the cross-section of the valve annulus.