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A framework for extracting salient local features from 3D models is presented in this study. In the proposed method, the amount of curvature at a surface point is specified by a positive quantitative measure known as the curvedness. This value is invariant to rigid body transformation such translation and rotation. The curvedness at a surface position is calculated at multiple scales by fitting a manifold to the local neighbourhoods of different sizes. Points corresponding to local maxima and minima of curvedness are selected as suitable features and a confidence measure of each keypoint is also calculated based on the deviation of its curvedness from the neighbouring values. The advantage of this framework is its applicability to both 3D meshes and unstructured point clouds. Experimental results on a different number of models are shown to demonstrate the effectiveness and robustness of our approach.