Self-similarity is a profound concept that shapes many of the laws governing nature and underlying human thought. It is a property of widespread scientific importance and is at the centre of much of the recent work in chao fractals, and other areas of current research and popular interest. Self-similarity is related to symmetry analysis is an attribute of many physical laws: particle physics and those governing Newton's laws of gravitation. Symmetry, found throughout the biological universe, is also a basic property of the mathematical universe. In this book the author explores the idea's of scaling, self-similarity, chaos. and fractals as they appear throughout the universe of pure and applied mathematics. Because of his formidable research experience, stretching from the acoustical modelling of concert halls to pure number theory, Schroeder is able to take the reader on an intellectual excursion through this vast forest of topics. Requires a basic familiarity with undergraduate mathematics and elementary physics.

Fractals, chaos, power laws ; Minutes from an infinite paradise, by Manfred Schroeder. Pp 429. £24.49. 1991. ISBN 0-7167-2136-8 (Freeman)

This paper proposes a method for line matching based on invariance of feature points Firstly, feature points are roughly matched by Normalized Cross Correlation (NNC) and Average of Square Difference (ASD) Additionally, feature points obtained from the two views are grouped into matched point pairs Finally, curve segments between matched point pairs are matched by dynamic programming algorithm with edge potential functions (EPF) taken as the measure The proposed method makes full use of feature points, the relationship between feature points and the curve, and space information of the gray image

A Method of Line Matching Based on Feature Points

Medical images are visualized by computer and processed to obtain larger, more organized, and three-dimensional (3D) images. Thus, significant images are provided. The processed data facilitate diagnosis and treatment in the medical fields. The 3D surface models of related areas are formed by using volumetric data obtained by employing medical imaging methods such as Magnetic Resonance (MR) and Computer Tomography (CT). The purpose of this study is to obtain 3D images from the two-dimensional CT slices. These slices are obtained from the existing medical imaging devices and transferred to the z space and a mesh structure is provided between them. In addition, we investigated 3D imaging techniques, visualization, basic data types, conversion into main graphical components, and imaging algorithms. At the phase of obtaining 3D images; the image processing methods such as surface and volume imaging techniques, smoothing, denoising, and segmentation were used. The complexity and efficiency properties of the imaging algorithms were investigated and image enhancement algorithms were utilized.

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Three-Dimensional Modeling in Medical Image Processing by Using Fractal Geometry

Generally the fractal image compression is a technique based on the presentation of an image by a contractive transform, on the space of image, for which the fixed point is close to the original image. The fractal image compression is rapidly growing principle covers a wide variety of coding scheme in various domains. A large number of theoretical aspects of this concept are available. However, a few concentrations have been given to the image encoding model which justifies its proper implementation. Most fractal base schemes are not competitive with the current state of the art like JPEG, JPEG2000. To identify the performance of fractal image compression, specifically for the medical images, a comprehensive review of worldwide contributions from 1990 to 2013 has been carried out. As a result, the fractal image compression techniques are classified into four domains, i.e., spatial, frequency, soft computing, and hybrid. It is found that, fractal theory in spatial domain, fractal theory along with discrete cosine transform and wavelet transform in frequency domain, fractal theory along with fuzzy logic and neural network in soft computing domain, and combination of fractal theory along with discrete cosine transform, wavelet transform, fuzzy logic and neural network in hybrid domain are often used by the contributors. It is found that the fractal dimension and fuzzy logic approach on regular image processing are sufficiently suitable for image texture analysis. Consequently fuzzy logic is successfully applied in regular image and found outstanding results. On the basis of these facts it is anticipated that the fractal dimension and fuzzy logic could be a suitable approach in medical image compression using fractal theory as a future expansion is discussed in this review article.

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Performance of Fractal Image Compression for Medical Images: A Comprehensive Literature Review

A new active contour modeling method for processing-path extraction of flexible material

In this paper we present an auto-detection corner based on eigenvalues product of covariance matrices (ADEPCM) of boundary points over multi-region of support. The algorithm starts with extracting the contour of an object, and then computes the eigenvalues product of covariance matrices of this contour at various regions of support. Finally determine automatically peaks of the graph of eigenvalues product function. We consider that points corresponding to peaks of eigenvalues product graph are reported as corners, which avoids human judgment and curvature threshold settings. Experimental results show that the proposed method has more robustness for noise and various geometrical transform.

Auto-Corner Detection Based on the Eigenvalues Product of Covariance Matrices over Multi-Regions of Support

The paper has presented a fractal combining with wavelet idea for edges extraction, which firstly computes fractal dimension values of R, G, B components of every pixel in images, and then synthesizes color image by normalized fractal dimension values, finally decomposes histogram of synthetic image by wavelet transform to determine the threshold of extraction edges, at the same time, improved the thresholding segmentation based on wavelet transform –AEEM (Automatic Extraction Edges Method) which determines automatically the extraction threshold. Comparing with the histogram-based approach, the experimental results demonstrate that the approach yields better segmentation.

Edges Extraction Method based on Fractal and Wavelet

In this paper we present a corner detection which makes use of eigenvalues of covariance matrices of different support regions over edge points. Edges are first extracted through the use of Canny edge detection, and then determine corners according to eigenvalues product of covariance matrices of the edge at various regions of support. Experimental results show that the proposed method has more robustness for noise and various geometrical transform. Index Terms—Corner detection, Covariance matrix, Eigenvalues product, Region of support

Yanxia Wang

Papers

Auto-Corner Detection Based on the Eigenvalues Product of Covariance Matrices over Multi-Regions of Support

Edges Extraction Method based on Fractal and Wavelet

Corner Detection Based on Eigenvalues product of Covariance Matrices over Edges