Fast blending of planar shapes based on invariant invertible and stable descriptors

In this paper, a novel method for blending planar shapes is introduced. This approach is based on the Fined-Fourier-based Invariant Descriptor (Fined-FID) that is invertible, invariant under Euclidean transformations and stable. Our approach extracts the Fined-FID from the two shapes of interest (the source and the target ones). Then, the extracted descriptors are averaged enabling the calculation of intermediate descriptors. Finally, thanks to the inversion criterion, the intermediate shapes are easily recovered by applying the inverse analytical expression to these intermediate descriptors. Compared to previous works, the Fined-FID-based morphing avoid the usual registration step, generates naturally closed intermediate contours and ensure invariance under Euclidean transformations and invariance to the starting point, while being computationally efficient (almost-linear complexity). The performed experiments show the performance of the proposed blending approach with respect to curvature-based methods.