Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fracta...Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.展开更多
The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonome...The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization.展开更多
In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain Holder&&exponent of the image pixels is first computed.then,its multi-fractal spectrum is est...In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain Holder&&exponent of the image pixels is first computed.then,its multi-fractal spectrum is estimated by the kernel estimation method.Finally,the image edge detection is done by means of different multi-fractal spectrum values.Simulation results show that this method is efficient and has better locality compared with the traditional edge detection methods such as the Sobel method.展开更多
基金The National Natural Science Foundation of China (No.10171080)
文摘Bush type fractal functions were defined by means of the expression of Cantor series of real numbers. The upper and lower bound estimates for the K-dimension of such functions were given. In a typical case, the fractal dimensional relations in which the K-dimension equals the box dimension and packing dimension were presented; moreover, the exact Holder exponent were obtained for such Bush type functions.
基金Board of Research in Nuclear Science (BRNS), Department of Atomic Energy Government of India
文摘The classical example of no-where differentiable but everywhere continuous function is Weierstrass function. In this paper we have defined fractional order Weierstrass function in terms of Jumarie fractional trigonometric functions. The H?lder exponent and Box dimension of this new function have been evaluated here. It has been established that the values of H?lder exponent and Box dimension of this fractional order Weierstrass function are the same as in the original Weierstrass function. This new development in generalizing the classical Weierstrass function by use of fractional trigonometric function analysis and fractional derivative of fractional Weierstrass function by Jumarie fractional derivative, establishes that roughness indices are invariant to this generalization.
基金Supported by National Natural Science Foundation of China(Grant No.60375001)。
文摘In this paper,an image edge detection method based on multi-fractal spectrum analysis is presented.The coarse grain Holder&&exponent of the image pixels is first computed.then,its multi-fractal spectrum is estimated by the kernel estimation method.Finally,the image edge detection is done by means of different multi-fractal spectrum values.Simulation results show that this method is efficient and has better locality compared with the traditional edge detection methods such as the Sobel method.
