The prevalent model for second order variation in 3-D volumes is an ellipsoid spanned by the magnitudes of the Hessian eigenvalues. Here, we describe this variation as a vector in an orthogonal shape space spanned by spherical harmonic basis functions. From this newsh ape-space, a truly rotation- and shape-invariant signal energy is defined, consistent orientation information is extracted and shape sensitive quantities are employed. The advantage of these quantities is demonstrated in detection of stenosis in Magnetic Resonance Angiography( MRA) volume. The news hape space is expected to improve both the theoretical understanding and the implementation of Hessian based analysis in other applications as well.