Differentiation by the F-transform and application to edge detection

In this contribution, we consider integrable functions of many (in particular, two) variables and extend for them the technique of F-transform to F1-transform. We prove that linear coefficients in the representation of the F1-transform component approximate the first partial derivatives. We give estimates for this approximation. Finally, we discuss the application to the edge detection problem. We propose a new algorithm where the technique of F1-transform is combined with the Canny detector. A theoretical justification and advantages of the proposed approach are emphasized and illustrative examples are presented.