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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