Robustness of geodesics to affine transformation

This paper will determine the geometric invariance of geodesic on the surface that can handle the affine transform. The unique characteristics of the calculated from the differential geometry contained curvature surface that lies above the standard of Gaussian curve. When applied the affine transformed to the surface according to the condition, the surface characteristics will also be transformed. Therefore, the characteristics of the surface will still contain original form, in which we can use as the comparable properties for matching. In this work, the method is performed with 3 dimensional data and provided a satisfactory result.