DBC-RGB

The fractal dimension (FD) is a quantitative parameter widely used to analyze digital images in many application fields such as image segmentation, feature extraction, object recognition, texture analysis, and image compression and denoising, among many others. A variety of algorithms have been previously proposed for estimating the FD, however most of them are limited to binary or gray-scale images only. In recent years, several authors have proposed algorithms for computing the FD of color images. Nevertheless, almost all these methods are computationally inefficient when analyzing large images. Nowadays, color images can be very large in size, and there is a growing trend toward even larger datasets. This implies that the time required to calculate the FD of such datasets can become extremely long. The software DBC-RGB is a very efficient GPU algorithm, implemented in CUDA, for computing the FD of RGB color images. The software DBC-RGB is an extension to RGB of the differential box-counting (DBC) algorithm for gray-scale images. The software DBC-RGB simplifies the box-counting computation to very simple operations which are easily combined across iterations. DBC-RGB performed very well and achieved speedups of up to 7.9× and 6,172.6× regarding the reference GPU and CPU algorithms for computing the FD of RGB images, respectively. In addition, DBC-RGB achieved average error rates similar to those obtained by these two reference algorithms when estimating the FD for synthetic images with known FD values, and even outperformed them when processing large images. Therefore, the software DBC-RGB offers a highly reliable and ultra-fast solution for estimating the FD of color images.