Fracture Surface Fractal Dimension Determined Through An Extensive 3-D Reconstruction

Abstract

AbstractAn efficient image processing method is developed to determine the fractal dimension from a high resolution 3-D reconstruction of fracture surface. The third dimension of the fracture surface is obtained from a stereo pair. The elevation is locally determined through a recursive window matching algorithm centered on the cross-correlation operation. The method allows to reach high vertical and horizontal resolutions of the elevation map.The fractal dimension is obtained by an implementation of the slit-island method. A series of contour lines is extracted from the reconstructed surface. The images of the contour lines are progressively reduced in size and at every step the curve length is estimated. The result is then normalized according to the scale factor to build a Kolmogorov plot.The performance of this method is demonstrated on a synthetic image generated by a fracture surface mathematical model.