Abstract: Image compression based on fractal coding is a lossy
compression method and normally used for gray level images range
and domain blocks in rectangular shape. Fractal based digital image
compression technique provide a large compression ratio and in this
paper, it is proposed using YUV colour space and the fractal theory
which is based on iterated transformation. Fractal geometry is mainly
applied in the current study towards colour image compression
coding. These colour images possesses correlations among the colour
components and hence high compression ratio can be achieved by
exploiting all these redundancies. The proposed method utilises the
self-similarity in the colour image as well as the cross-correlations
between them. Experimental results show that the greater
compression ratio can be achieved with large domain blocks but more
trade off in image quality is good to acceptable at less than 1 bit per
pixel.
Abstract: In this paper, we introduce R Iterated Function System
and employ the Hutchinson Barnsley theory (HB) to construct a
fractal set as its unique fixed point by using Reich contractions in a
complete b metric space. We discuss about well posedness of fixed
point problem for b metric space.
Abstract: The main purpose of this paper is to prove the intuitionistic fuzzy contraction properties of the Hutchinson-Barnsley operator on the intuitionistic fuzzy hyperspace with respect to the Hausdorff intuitionistic fuzzy metrics. Also we discuss about the relationships between the Hausdorff intuitionistic fuzzy metrics on the intuitionistic fuzzy hyperspaces. Our theorems generalize and extend some recent results related with Hutchinson-Barnsley operator in the metric spaces to the intuitionistic fuzzy metric spaces.
Abstract: In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between l-systems and IFS.
Abstract: A new technique of topological multi-scale analysis is
introduced. By performing a clustering recursively to build a
hierarchy, and analyzing the co-scale and intra-scale similarities, an
Iterated Function System can be extracted from any data set. The study
of fractals shows that this method is efficient to extract
self-similarities, and can find elegant solutions the inverse problem of
building fractals. The theoretical aspects and practical
implementations are discussed, together with examples of analyses of
simple fractals.
Abstract: Image compression is one of the most important
applications Digital Image Processing. Advanced medical imaging
requires storage of large quantities of digitized clinical data. Due to
the constrained bandwidth and storage capacity, however, a medical
image must be compressed before transmission and storage. There
are two types of compression methods, lossless and lossy. In Lossless
compression method the original image is retrieved without any
distortion. In lossy compression method, the reconstructed images
contain some distortion. Direct Cosine Transform (DCT) and Fractal
Image Compression (FIC) are types of lossy compression methods.
This work shows that lossy compression methods can be chosen for
medical image compression without significant degradation of the
image quality. In this work DCT and Fractal Compression using
Partitioned Iterated Function Systems (PIFS) are applied on different
modalities of images like CT Scan, Ultrasound, Angiogram, X-ray
and mammogram. Approximately 20 images are considered in each
modality and the average values of compression ratio and Peak
Signal to Noise Ratio (PSNR) are computed and studied. The quality
of the reconstructed image is arrived by the PSNR values. Based on
the results it can be concluded that the DCT has higher PSNR values
and FIC has higher compression ratio. Hence in medical image
compression, DCT can be used wherever picture quality is preferred
and FIC is used wherever compression of images for storage and
transmission is the priority, without loosing picture quality
diagnostically.
Abstract: This paper proposes fractal patterns for power quality
(PQ) detection using color relational analysis (CRA) based classifier.
Iterated function system (IFS) uses the non-linear interpolation in the
map and uses similarity maps to construct various fractal patterns of
power quality disturbances, including harmonics, voltage sag, voltage
swell, voltage sag involving harmonics, voltage swell involving
harmonics, and voltage interruption. The non-linear interpolation
functions (NIFs) with fractal dimension (FD) make fractal patterns
more distinguishing between normal and abnormal voltage signals.
The classifier based on CRA discriminates the disturbance events in a
power system. Compared with the wavelet neural networks, the test
results will show accurate discrimination, good robustness, and faster
processing time for detecting disturbing events.
Abstract: This paper investigates the fractals generated by the dynamical system of intuitionistic fuzzy contractions in the intuitionistic
fuzzy metric spaces by generalizing the Hutchinson-Barnsley theory. We prove some existence and uniqueness theorems of fractals in the
standard intuitionistic fuzzy metric spaces by using the intuitionistic fuzzy Banach contraction theorem. In addition to that, we analyze
some results on intuitionistic fuzzy fractals in the standard intuitionistic fuzzy metric spaces with respect to the Hausdorff intuitionistic
fuzzy metrics.
Abstract: The IFS is a scheme for describing and manipulating complex fractal attractors using simple mathematical models. More precisely, the most popular “fractal –based" algorithms for both representation and compression of computer images have involved some implementation of the method of Iterated Function Systems (IFS) on complete metric spaces. In this paper a new generalized space called Multi-Fuzzy Fractal Space was constructed. On these spases a distance function is defined, and its completeness is proved. The completeness property of this space ensures the existence of a fixed-point theorem for the family of continuous mappings. This theorem is the fundamental result on which the IFS methods are based and the fractals are built. The defined mappings are proved to satisfy some generalizations of the contraction condition.
Abstract: The purpose of this paper is to present the fuzzy contraction
properties of the Hutchinson-Barnsley operator on the fuzzy
hyperspace with respect to the Hausdorff fuzzy metrics. Also we
discuss about the relationships between the Hausdorff fuzzy metrics
on the fuzzy hyperspaces. Our theorems generalize and extend some
recent results related with Hutchinson-Barnsley operator in the metric
spaces.
Abstract: Since 1984 many schemes have been proposed for
digital signature protocol, among them those that based on discrete
log and factorizations. However a new identification scheme based
on iterated function (IFS) systems are proposed and proved to be
more efficient. In this study the proposed identification scheme is
transformed into a digital signature scheme by using a one way hash
function. It is a generalization of the GQ signature schemes. The
attractor of the IFS is used to obtain public key from a private one,
and in the encryption and decryption of a hash function. Our aim is
to provide techniques and tools which may be useful towards
developing cryptographic protocols. Comparisons between the
proposed scheme and fractal digital signature scheme based on RSA
setting, as well as, with the conventional Guillou-Quisquater
signature, and RSA signature schemes is performed to prove that, the
proposed scheme is efficient and with high performance.