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Using mean curvature (H) and Gaussian curvature (K) values or shape index (S) and curvedness (C) values, HK and SC curvature spaces are constructed in order to classify surface patches into types such as pits, peaks, saddles etc. Since both HK and SC curvature spaces classify surface patches in to similar types, their classification capabilities are comparable. Previously, HK and SC curvature spaces were compared in terms of their classification ability only at the given data resolution. When calculating H, K, C and S values, the scale/resolution ratio is highly effective. However, due to its scale invariant nature, shape index (S) values are independent of the resolution or the scale. Thus it is no wonder that SC method gives better results than HK method when the comparison is carried out at an uncontrolled scale/resolution level. In this study, the scale/resolution ratio is set to a constant value for the whole database and scale spaces based on both HK and SC methods are built. Scale and orientation invariant features are extracted using scale spaces and these features are used in object recognition tasks. The methods are compared both mathematically and experimentally in terms of their surface classification and object recognition performances.