Property of robustness to size and its realization on fractal dimension

Images in one class often have varied sizes due to different imaging system. Thus it will provide convenience to image classification if the indicator used in the classification is robust to the size of images. We regard the robustness to size of image as a property of image indicator. The property means that images from one class have small variance with the sizes, and is different from such traditional properties as the robustness to scale, rotation and illumination. Fractal dimension is an indicator which has the three traditional properties. We realize the property on fractal dimension in the statistical sense by modifying differential-box counting method. Tests on two classes of images demonstrate the effectiveness of the modifications. Tests on scaling process give a standard of FD' robustness as 0.0611, and experiments on both the two class and four sets of images show the statistical validity of the standard and verify the realization. An indicator with this property can be a tool for the classification. (C) 2013 Elsevier GmbH. All rights reserved.