Narrow Results

We consider a generalization of aggregation and fusion functions when some of their inputs or outputs are undefined. For simplicity, we represent undefined values by a single NaN (not-a-number) value. We define four main methods of treating undefined values, observe some of their properties, and compare them with several mainstream implementations and norms for handling NaN values. Finally, as a case study demonstrating the apparatus's usefulness, the formalism is applied to the discrete fuzzy transform technique. The formalism allows us to prove a generalized approximation theorem for fuzzy transforms, which removes previously required restrictions on fuzzy partitions for sparse input data.

Extensive development has taken place in the field of image fusion and various algorithms of image fusion have attracted the attention of many researchers in the recent past. Various algorithms of image fusion are used to combine information from multiple source images into a single fused image. In this paper, fusion of multiple images using fuzzy transform is proposed. Images to be fused are initially decomposed into same size blocks. These blocks are then fuzzy transformed and fused using maxima coefficient value-based fusion rule. Finally, the fused image is obtained by performing inverse fuzzy transform. The performance of the proposed algorithm is evaluated by performing experiments on multifocus, medical and visible/infrared images. Further, the performance of the proposed algorithm is compared with the state-of-the-art image fusion algorithms, both subjectively and objectively. Experimental results and comparative study show that the proposed fusion algorithm fuses the multiple images effectively and produces better fusion results for medical and visible/infrared images.

Multiple images of a scene, captured using different imaging devices and containing complementary information, are required to be combined into a single fused image. The fused image, so obtained, should ideally contain all important features of individual input images. Further, color image processing is also gaining importance in most of the real-life applications. Color images provide better visual information and are highly suitable for human visual perception. Motivated by the gaining importance of color image processing, fusion of color images is proposed. The fusion algorithm is proposed in HSV color space where the luminance components of multiple input images, based on fuzzy transform and spatial frequency, are fused. The chrominance information of input images provides color to the fused image. The fused image contains all important information and possesses natural color appearance. Experiments performed on various pairs of visible–infrared and multifocus images demonstrate the superiority of the proposed algorithm over recent state-of-the-art image fusion algorithms.

Regularization is a principle, concerning a wide range of science domains. Several methods, using this technique, have been proposed. However, there are some limitations to the functionals used in regularization. To remove these, the idea is to employ nonlocal operators on weighted graphs in regularization process. In images, pixels have a specific organization expressed by their spatial connectivity. Therefore, a typical structure used to represent images is a graph. The problem is to choose the correct one, because the topology of graphs can be arbitrary and each type of graph is proper to different type of problem. In this work, we focus on method based on nonlocal Laplace operator, which has become increasingly popular in image processing. Moreover, we introduce the representation of F-transform based Laplace operator.

In this chapter, we provide the application of selected methods of fuzzy modeling to the identification of structural breaks in time series, forecasting, and automatic summarization of knowledge about time series expressed in natural language.

A new methodology for analysis of periodical time series is proposed. It is based on application of special soft computing techniques: fuzzy transform and perception-based logical deduction.

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

In this article, we propose a new method for prediction of cyclic components of a time series using fuzzy transform (F-transform) of higher degree.

In this paper we suggest to use special fuzzy modeling techniques for detection of structural breaks and perceptionally important points in time series, namely the fuzzy (F-)transform and one method of Fuzzy Natural Logic (FNL). The idea is based on application of the F¹-transform which makes it possible to estimate effectively slope of time series over an imprecisely specified area (ignoring its possible volatility) and its evaluation by a suitable evaluative linguistic expression. The method is computationally very effective.

Based on our recent research, where we the designed hybrid image compression algorithm combining F-transform and JPEG called FzT+JPEG, we now analyze the influence of noise on image compression. Our analysis is focused on the impact of a noise to a size of a compressed image and on the ability to decompress an image without noise by both FzT+JPEG and JPEG algorithms. On some benchmarks, we show that FzT+JPEG algorithm rapidly outperforms the pure JPEG in both aspects.