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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B4. Beijing 2008 
than specific rock extraction technique. Gor et al. (2000) 
integrate intensity data and range data by using unsupervised 
classification. They detect the height-map discontinuities that 
indicate the top of rocks and then perform a region growing 
segmentation. However, this algorithm needs image scale as a 
significant control parameter and the range data produced from 
stereo imagery. 
More recently, Castano et al. (2004) detect rocks using edges 
extracted from multi-resolution images. Small rocks are 
detected by finding small closed contours from the edge image 
generated by Sobel and Canny operators, while large rocks are 
detected in the same way using a resolution-reduced image. 
When rocks are detected at both high and low resolutions, the 
ones detected at the highest resolution are retained. On the other 
hand, if rocks are detected only at the low resolution, they refit 
the boundary using snakes (Kass et al., 1988). This rock 
detection algorithm is efficient when intensity differences 
between rocks and background (soil) are significant to show 
clearly linked boundaries. Thompson et al. (2005) propose rock 
detection from colour image based on machine learning 
approach. Their rock detection algorithm consists of two steps; 
segmentation and detection. Image segmentation is performed 
by split-and-merge method using three bands: hue, saturation 
and intensity. They then detect rocks using belief network, of 
which the input vector contains colour, texture, and shape. 
However, the difficulty remains that a rock may have non- 
homogeneous intensity and colour, which varies in terms of the 
illumination and geometry of the rock surface. Dunlop et al. 
(2007) propose an approach to rock detection and segmentation 
using super-pixel segmentation followed by a region-merging to 
search for the most probable groups of super-pixels. A model of 
rock appearances learned from the training data set identifies all 
rocks by scoring candidate super-pixel groups with 
incorporating features from multiple scales such as texture, 
shading, and two-dimensional shape. Although this rock 
segmentation algorithm based on supervised multi-scale 
segmentation provides promising results for rock detection, 
some problems such as training set determination and boundary 
localization still remain. A comparison on the performance of 
rock extraction algorithms is provided by Thompson and 
Castano (2007). 
3. METHODOLOGY 
The proposed framework for rock segmentation in this study 
consists of two stages: rock detection using texture-based image 
segmentation and boundary refinement using the edge-flow 
driven active contours. The first stage is to provide initial rock 
detection through the following steps. First, multi-channels 
containing different texture properties are generated by 
applying a wavelet transform to the input image. Specifically, 
four coefficient channels of Haar wavelet transform, including 
approximation, horizontal, vertical, and diagonal detail 
coefficients are used as the resultant channels. After the multi 
resolution histograms are obtained, their changes across the 
resolutions are measured by the generalized Fisher information 
content to extract texture feature, which represents the spatial 
variation on the image. Finally, the inter-scale decision fusion 
designed by adopting the hierarchical and interactive k-means 
algorithm is performed to achieve the initial segmentation. As 
the second stage, the initial rock boundaries are refined using 
edge-driven active contours based on the level set method to 
compensate inaccurate localization of the initial segmentation. 
The refinement starts with the computation of the edge flow 
direction and the edge energy to generate the edge flows. These 
edge flows form a vector field as an external force to enforce 
the initial boundaries move towards the pixels with high 
probability being rock boundaries. After that, an edge penalty 
function is yielded by solving a Poisson equation to satisfy the 
condition that the Laplacian of the edge penalty function is 
equivalent to the divergence of the edge flow vector field. 
Finally, the initial rock boundaries propagate under the 
constraints of the prepared edge flow vector field and edge 
penalty function to yield the refined rock segmentation. 
3.1 Rock detection using texture-based segmentation 
Texture feature extraction. This study extracts the texture 
features by employing a multi-channel, multi-resolution 
approach. This is accomplished through image decomposition 
and diffusion by Haar wavelet transform. Haar wavelet 
decomposition works through averaging two adjacent values in 
a one-dimensional function at a given resolution to form a 
smoothed signal, namely approximation coefficients. The 
differences between the values and their averages become the 
detail coefficients. In discrete data set such as digital image, the 
construction of Haar wavelet coefficients can be interpreted as 
two dimensional filtering with four local transform filters: 
smoothing filter and horizontal, vertical, and diagonal edge 
detection filters. To achieve the Haar wavelet transformed 
image of size m by n, the image is convolved with each filter 
and then down-sampled by 2. As an outcome of this procedure, 
an approximation coefficient and three detail coefficients of 
size ml 2 by n/2 are produced. This filtering and down- 
sampling process can be iterated, leading the image from fine to 
coarse resolution. This decomposition ability of Haar wavelet 
transform allows the multi-channel approach to transform an 
image into a set of feature maps by using local transforms to 
achieve additional and condensed information for texture 
analysis. 
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Figure 1. Histograms of multi-resolution images generated by 
Haar wavelet transform 
Let the four channels formed by the wavelet transform 
coefficients be ( L u , L lh , L hl , L hh ). From each channel, the 
texture features are extracted by measuring the change of 
histograms across different resolutions, namely the multi 
resolution histogram method (Hadjidemetrous et al., 2004). 
Figure 1 shows that although the histograms of two input 
images with different shades are identical at the high resolution, 
they differ considerably in coarser resolutions due to the 
different spatial structures in the two original images Such