An almost complete curvature scale space representation: Euclidean case

Here, we intend to propose local shape curve features which are invariant under planar Euclidean transformations and independent with respect to the original curve parameterization. The present work generalizes the family of Curvature Scale Space descriptors in order to increase the shape information quantity to tend to the completeness property. For this, a more pragmatic criterion is introduced in this paper which we call the almost completeness. We define it as a pre-completeness for a given resolution of features. Such descriptors are formed by the curvatures on the set of curve points obtained from the antecedents of different curvature levels. This level set is fixed with a given rule. The idea of the almost completeness is to make a compromise between the cardinal of the set of curvature's levels and the optimal number of scales. The rule is submitted to an unsupervised statistical study and the scales are obtained with a spectral analysis. Experiments are conducted on several known datasets. Promising results in the sense of shape retrieval and shape recognition rates are demonstrated.