Fractal Dimension Of Profile Research Articles

Determination of the fractal dimension of a shore platform profile

Morphological studies of shore platforms have focused on elements like width, gradient and elevation, while mostly ignoring the surface roughness as a morphometric attribute. This paper uses the Roughness-length method to show how the Fractal Dimension of a shore platform profile can be obtained. The higher the value of the fractal dimension, the higher is the roughness of the platform. The studied profile is situated in Houghton Bay on the south coast of Wellington, New Zealand. The fractal dimension of the profile under consideration was found to be 1.314. However, one profile is not sufficient to provide information about the surface roughness of a shore platform. Therefore, a number of profiles should be taken to have an idea about surface roughness.

Fruits fractal dimension of fruits based on digital image

Quantitative description about difference in contours of paraspherical fruits was conducted with fractal dimension using perimeter-area method. Test sample sets are 20 Wenzhou mandarin oranges, 17 Mayang bingtang oranges and 18 red fuji apples. Threshold values of red or blue component of fruit calyx and profile image are used to convert the image to binary image. Red, green and blue components within/out of fruit region are set to 0/1. After boundary thinning, pixel numbers of boundary and fruit region are treated as perimeter and area of fruit region. Fractal dimensions of calyx and profile of three kinds of fruits are calculated with perimeter-area method. Test results show fractal dimension of calyx images is smallest among three kinds of fruits in two directions, and deviation of calyx is not significant between different fruits; fractal dimension varies significantly in profile images. In conclusion, the shape feature of paraspherical fruit can be described by fractal dimension especially fractal dimension of profile.

Fractal dimension of profiles and surfaces using fuzzy morphological coverings

In this paper, we propose a new method, based on fuzzy morphology coverings, to estimate the fractal dimension of profiles and surfaces. This method is geometrically intuitive and simple to implement. Algorithmically, the method fits a covering to the frames or blocks of the profile or surface using fuzzy morphology. Varying the dimension of the frame or block, estimates of the length or area covered are then used to find the fractal dimension. Validation of the proposed method is performed by comparing its results with known fractal dimensions of mathematical profiles. The method is used to obtain the fractal dimension of rock profiles and surfaces.