Multi-scale representation; Keypoint; Fuzzy partition; Fuzzy transform

We are focused on a new fast and robust algorithm of image/signal feature extraction in the form of representative keypoints. We analyze various multi-scale representations of a one-dimensional signal in spaces with a closeness relation determined by a symmetric and positive semi-definite kernel. We show that kernels arising from generating functions of fuzzy partitions can be used in a scale space representation of a one-dimensional signal. We show that the reconstruction from the proposed multi-scale representations is of better quality than the reconstruction from MLP with almost double the number of neurons in 4 hidden layers. Finally, we propose a new algorithm of keypoints localization and description and test it on financial time series with high volatility.