Fast Box-counting

The box-counting (BC) algorithm is one of the most popular methods for calculating the fractal dimension (FD) of binary data. FD analysis has many important applications in the biomedical field, such as cancer detection from 2D computed axial tomography images, Alzheimer’s disease diagnosis from magnetic resonance 3D volumetric data, and consciousness states characterization based on 4D data extracted from electroencephalography (EEG) signals, among many others. Currently, these kinds of applications use data whose size and amount can be very large, with high computation times needed to calculate the BC of the whole datasets. Fast Box-counting is a very efficient parallel implementation of the BC algorithm for its execution on Graphics Processing Units (GPU).盒计数（box-counting, BC）算法是计算二值数据分形维数（fractal dimension, FD）的主流方法之一。分形维数分析在生物医学领域拥有诸多重要应用场景，例如基于二维计算机轴向断层扫描图像开展癌症检测、依托磁共振三维体数据进行阿尔茨海默病诊断，以及基于脑电图（electroencephalography, EEG）信号提取的四维数据实现意识状态表征等。当前此类应用所处理的数据规模与体量往往极为庞大，计算全数据集的盒计数结果所需的计算时长极高。快速盒计数（Fast Box-counting）是一种专为图形处理器（Graphics Processing Units, GPU）并行执行设计的高效BC算法实现。