In this work, a geometric invariant curve and surface normalization method is presented. Translation, scale and shear are normalized by Principal 14 Component Analysis (PCA) whitening. Independent Component Analysis (ICA) and the third order moments are then employed for rotation and reflection normalization. By applying this normalization, curves and surfaces that are related by geometric transformations (affine or rigid) can be transformed into a canonical representation. Proposed technique is verified with several 2D and 3D object matching and recognition experiments.