2D images; F-transform; Fast algorithms; Graph laplacians; Image regularization; Keypoints; Laplacian operator; Local extremum; Regularisation; Robust algorithm

We focus on a new fast and robust algorithm for selecting keypoints in 2D images using the following techniques: image regularization, selection of spaces with closeness, and design of the corresponding graph Laplacians. Then, the representative keypoints are local extrema in the image after the Laplacian operator is applied. The convolution kernels, used for regularization, are extracted from the uniform partition of the image domain, and the graph Laplacian is constructed using the theory of F0-transforms. Empirically, we show that sequences of F-transform kernels that correspond to different regularization levels share the property that they do not introduce new local extrema into the image under convolution. This justifies the computation of keypoints as points where local extrema are reached and allows them to be classified according to the values of the local extrema. We show that the extracted key points are representative in the sense that they allow a good approximate reconstruction of the original image from the calculated components of the F-transform taken from different convolutions. In addition, we show that the proposed algorithm is resistant to Gaussian noise.