Abstract: Aiming at the problem that fractional Brownian motion model can only calculate the fractal dimension when the sea surface wind speed is slow and the image spectrum is isotropic, the fractal model of the sea surface with the isotropic and anisotropic characteristics of sea surface infrared image was proposed. In view of the improper selection of scale range in variation method, the fractal dimension of sea surface infrared image can not be accurately estimated. First the selection criterion of the minimum scale was proposed for maintaining the fractal property of infrared image and avoiding the aliasing effect of image. Then the optimal function relationship among scale interval and the fractal dimension of sea infrared image, fundamental spatial wavelength of image and pixel size was determined by choosing the established sea surface model as reference model of sea infrared image, building minimum costs as target function, using the optimization of the algorithm and least square fitting. Finally, the necessity of the optimal estimation for scale range is proved by simulation.

Key words: fractal model, variation method, fractal dimension, sea surface infrared image