Pavel Vlašánek

Image reconstruction by means of F-transform

We propose a new image reconstruction technique that uses approximation properties of the fuzzy (F-)transform and its ability to remove noise. The proposed technique is based on the inverse F-transform and combines it with an original image on a non-damaged area. We present two algorithms of the F-transform based reconstruction: one-step and multi-step. We demonstrate how these algorithms cope with various corruptions. We compare results with interpolation and advanced inpainting techniques.

Influence of various types of basic functions on image reconstruction using F-transform

Technique of image reconstruction using Ftransform uses basic functions for computation. Radius and partition of these functions affects quality of the reconstruction. In this article we are focusing on influence of the basic function shape on the quality of reconstruction and providing results of nondecreasing, nonincreasing and oscillating examples.

Image Reconstruction with Usage of the F-Transform

The article is focused on image reconstruction with usage of the F-transform. The results will be demonstrated on the picture of the Lena damaged by three kinds of the masks. We will compare reconstructed images based on the 2D F-transform with reconstructed images based on Gaussian radial basis function.

Patch based inpainting inspired by the F1-transform

We propose to solve the problem of image inpainting using the F-transform technique particularly of the zero and first degrees. We focus on the so-called patch inpainting. The proposed technique creates a feature vector of an image that characterizes the weighted average levels of the corresponding intensity function and its partial derivatives over certain areas. The results of the proposed algorithm are demonstrated on various patch sizes, and the issue of reconstruction quality is discussed.

Generating suitable basic functions used in image reconstruction by f-transform

Image reconstruction technique based on F-transform uses clearly defined basic functions. These functions have strong impact on the quality of reconstruction. We can use some predefined shape and radius, but also we can create a new one from the scratch. The aim of this paper is to analyze the creating process and based on that find best basic function for input set of damaged testing images.

Image Reconstruction by the Patch Based Inpainting

The paper is focused on demonstration of image inpainting technique using the F-transform theory. Side by side with many algorithms for the image reconstruction we developed a new method of patch-based filling of an unknown (damaged) image area. The unknown area is proposed to be recursively filled by those known patches that have non-empty overlaps with the unknown area and are the closest ones among others from a database. We propose to use the closeness measure on the basis of the F\(^1\)-transform.

Enhanced F-transform Exemplar Based Image Inpainting

This paper focuses on a completion of the partially damaged image. There are a variety of techniques to deal with this task. Our contribution belongs to the group of exemplar based image inpainting techniques which process the image what was separated to the many small regions. The regions are called patches and the task of inpainting becomes the task of searching for the most suitable patch from the undamaged part of the image to replace the partially damaged one. Our novelty is in processing based on fuzzy mathematics and new filling order prioritization function.

Patch based inpainting method based on the F1-transform

We propose to solve the problem of image inpainting with the technique of the F-transforms, especially of the zero and first degrees. We are focused on the so called patch inpainting. The proposed technique creates a feature vector of an image characterizing weighted average levels of the corresponding intensity function and its partial derivatives over certain areas. The results of the proposed algorithm are demonstrated on various patch sizes and the issue of a reconstruction quality is discussed.

From F-transform to image creation

We propose the technique of the semi-automatic image creation. By this we mean an automatic completion of an image that is partially defined on the given domain. The essential feature of this technique is that the complementary area is much larger than that where the image is defined. Moreover, the proposed technique can be used in image upsampling, image inpainting, etc. In this contribution, we propose the technique of F-transform as a universal tool for the image completion that is independent on the initial distribution of the image pixels.