Petr Hurtik

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.

A color image reduction based on fuzzy transforms

We present a new method for color image reduction based on the concept of fuzzy transform. Any image in a single band can be considered as a fuzzy matrix which is subdivided into submatrices called blocks. Each block is compressed with various_compression rates by means of a fuzzy transform in two variables. We compare our method with recent three algorithms due to G. Beliakov, H. Bustince and D. Paternain based on the minimizing penalty functions defined over a discrete lattice. The quality of the reduced image is measured by the Mean Square Error (MSE) and Penalty function (PEN) obtained by comparing both magnified and original images. We also point out a threshold of the compression rate beyond which the MSE follows a linear trend and the corresponding loss of information is still acceptable.

F 1 -transform Edge Detector Inspired by Canny's Algorithm

In this paper the edge detection technique based on the F 1-transform is presented. The method F 1-transform is used for preprocessing in the well known Canny detector. A justification of using F 1-transform in edge detection is presented. Finally, a comparative analysis of the “classical” Canny algorithm and the F 1-transform edge detector together with various examples is given.

Recognition of damaged letters based on mathematical fuzzy logic analysis

This paper reports a real application whose task was to recognize characters printed on metal ingots. The problem is that surface of ingots is very uneven - ingots are hot or cold, cut by rough instrument, the printing machine can be worn down, etc. In this paper, we present two original recognition methods: the first one is based on application of mathematical fuzzy logic and the second one is based on representation of an image by a fuzzy-valued function. Results of these methods are compared with a simple neural network classifier and few other common methods.

Image reduction method based on the F-transform

We present a new method of (color) image reduction based on the F-transform technique with a generalized fuzzy partition. This technique successfully combines approximation (when reduction is performed) and interpolation (when reconstruction is produced). The efficiency of the proposed method is theoretically justified by its linear complexity and by comparison with interpolation, and aggregation-based reductions. We also analyze the measures (

Image compression methodology based on fuzzy transform using block similarity

\mathrm{MSE}

Bilinear Interpolation over fuzzified images: Enlargement

MSE,