Petra Hodáková

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.

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.

Advanced F-transform-based image fusion

We propose to use the modern technique of the F-transform in order to show that it can be successfully applied to the image fusion. We remind two working algorithms (SA--the simple algorithm, and CA--the complete algorithm) which are based on the F-transform and discuss, how they can be improved. We propose a new algorithm (ESA--the enhanced simple algorithm) which is effective in time and free of frequently encountered shortcomings.

Edge detection using F-transform

This contribution shows how the technique of F-transform can be used for handling the problem of edge detection. A justification of the proposed approach is given and the based on it algorithm is presented. Various examples demonstrate effectiveness of the proposed algorithm and compare it with some established techniques.

The use of F-transform for image fusion algorithms

We show that on the basis of F-transform, the problem of reconstruction of corrupted images can be solved. The proposed technique is called image fusion. A simple linear algorithm of image fusion, based on F-transform, is proposed and justified. A measure of degradation of an image is proposed as well.

F^1-transform of Functions of Two Variables

In this contribution, the F 1-transform of functions of two variables is introduced. It combines properties of the F-transform of functions of two variables and the F 1-transform of functions of one variable. The aim of this study is to prove approximation properties of the F 1-transform components and of the inverse F 1-transform in this particular case.

Fuzzy and Fourier Transforms

The fuzzy transform (F-transform for short) is a universal tool for a fuzzy modeling with convincing applications to image processing. The aim of this contribution is to explain the eect of the Ftransform in image processing. With this purpose, we investigate properties of the Fourier transform over the F-transform components. We prove that the direct F-transform is a low-pass filter. This explains specific tools and methodologies that are developed in the F-transform applications to the image processing.

Approximate Pattern Matching Algorithm

We propose a fast algorithm of image pattern (instance) matching which is based on an efficient encoding of the pattern and database images. For each image, the encoding produces a matrix of the F-transform components. The matching is then realized by comparing the F-transform components of the pattern and the database images. The optimal setting of the algorithm parameters is discussed, the success rate and the run time are exhibited.

FTIP: A tool for an image plagiarism detection

The goal of this paper is to introduce a task of image plagiarism detection. More specifically, we propose a method of searching for a plagiarized image in a database. The main requirements for searching in the database are computational speed and success rate. The proposed method is based on the technique of F-transform, particularly Fs-transform, s ≥ 0. This technique significantly reduces the domain dimension and therefore, is speeds-up the whole process. we present several experiments and measurements which prove the speed and accuracy of our method. We also propose examples to demonstrate an ability of using this method in many applications.

Fuzzy Transform Theory in the View of Image Registration Application

In this paper, the application of the fuzzy transforms of the zero degree (F 0-transform) and of the first degree (F 1-transform) to the image registration is demonstrated. The main idea is to use only one technique (F-transform generally) to solve various tasks of the image registration. The F 1-transform is used for an extraction of feature points in edge detection step. The correspondence between the feature points in two images is obtained by the image similarity algorithm based on the F 0-transform. Then, the shift vector for corresponding corners is computed, and by the image fusion algorithm, the final image is created.