The gliding box method for multifractal modeling

The so-called ‘gliding box’ algorithm proposed originally for lacunarity analysis has been extended to multifractal modeling and provides an alternative to the ‘box-counting’ method for implementing multifractal modeling. This method can be used to implement several multifractal techniques including but not limited to the moment and multiplier methods. The results obtained by the ‘gliding box’ and ‘box-counting’ methods for multifractal modeling show the gliding box method may provide better results with less uncertainty when the number of samples and data resolution are limited. Both methods have been applied with the aid of geographic information systems (GIS) to remote sensing data. It is relatively straightforward to implement the gliding box method with the aid of GIS for comparison with the box-counting method. The pixel values of the Landsat TM imagery band 5 from the Mitchell-Sulphurets Area, northwestern BC, Canada, were analyzed as multifractal measure using both box-counting and gliding box algorithm yielding the characteristic values τ(0)≈−2, τ(1)≈0, and τ(2)≈1.92.