The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008
1021
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[Original image (A), noise added image (B), edge penalty
function using gradient (C), and using edge flow (D)]
To summarize, we achieve the level set formulation of the edge
flow-driven active contour as equation (19)
This active contour scheme propagates initial rock boundaries
obtained from the first texture-based segmentation stage for
refinement with edge flows. Figure 5 demonstrates the edge
flow generation and edge penalty function computation, which
are obtained through applying the aforementioned procedures to
a rock image. The box marks the zoomed in area.
(A) (B) (C)
Figure 5. Edge flow and edge penalty function from rock image
[Edge flow vector field (A), edge flows corresponding to the
zoomed-in area (B), and computed edge penalty function (C)]
This refinement stage using active contours based on level set
method can offer not only finer rock boundaries as shown in
figure 6(A), but also correct topological errors caused by coarse
resolution of the texture-based image segmentation as shown in
figure 6(B).
(A) (B)
Figure 6. Rock boundary refinement by edge-flow driven active
contours. [Yellow line denotes initial rock boundaries before
refinement, red line is rock boundaries after refinement, and
green lines is boundary propagation during refinement].
4. IMPLEMENTATION AND RESULTS
The suggested framework for automated rock segmentation is
applied into Mars surface images for automatic rock detection
to examine its performance. Mars surface images for this
implementation are collected by rover Spirit using MER
PANCAM with various filters. Additionally, implementation is
extended to NAVCAM image (Eisenman, 2004). Each image
consists of 1024 by 1024 pixels with 256 gray levels.
After pre-processing such as histogram equalization, the texture
features are extracted by the proposed wavelet-based texture
feature extraction method. In this experiment, three resolution
levels are used for feature extraction and each resolution level
contain four Fisher information contents of each channel such
that the extracted texture feature vector V is composed of 12
Fisher information contents { AT, , AT 2 , AT 3 }. Also, the texture
feature vectors with three scale levels {V', V 2 , V 3 } are used for
inter-scale decision fusion. They are extracted using windows
of three sizes. Equation (20) shows the resultant texture feature
vectors in this implementation, where the window size for
calculating the Fisher information K"f is determined by
16x2mv/2- / .
1
V
1
1
*
1
Kf
II
1L
Kl
II
'k
k;!
1
1
1
>1
After multi-scale texture feature vectors are generated, the
inter-scale decision fusion is performed through clustering
explained in previous section. As a result, the initial rock
boundaries are achieved. Figure 7 shows rock detection result
superimposed atop the original image. From the initial rock
boundaries shown in Figure 7a, the final rock boundaries are
extracted by contour evolution based on level set method with
further refinement. In the contour evolution step, the edge flow
vector field is first generated and the edge penalty function is
computed considering the scale determined by the
variance a 2 of the Gaussian kernel G a (x, >•). We focus on rocks
larger than 1/2500 of the entire image, i.e., about 20x20 pixels
or more. Finally, after the boundary refinement, the rock
segmentation results are yielded as shown in Figure 7b.
Additionally, figure 8 shows segmentation results from the
other MER PANCAM images, which demonstrate satisfactory
performance. Figure 9 represent some failed cases. On the
upper left comer in Figure 9, the structured soil region is
misclassified into rocks. Also it shows difficulty to segment
rocks partly covered by soil which have ambiguous boundaries.
In figure 10 and 11, the implementation is extended to
NAVCAM which has wider field of view (FOV: 45 degree)
than PANCAM (FOV: 16 degree). Despite of more spatial
resolution variation due to the wider FOV, the proposed method
still shows satisfactory rock segmentation results, although
figure 11 suffers from similar problems of figure 9.
5. CONCLUSION AND FUTURE WORK
Automated rock detection is necessary for the Mars Exploration
Rover mission. This paper presents a framework to segment
rocks from the MER images. In the two stage solution, rocks
are firstly detected by texture-based image segmentation. For
that purpose, three methods, wavelet based multi-resolution
histograms, multi-channel approach, and inter-scale decision
fusion are integrated. It yields reliable rock detection results but
shows poor localization quality. To compensate this
shortcoming, the rock boundary is refined by active contour
algorithm based on the level set method in the second stage.
The edge flow vector field is used as the external force to
enforce the contour moving towards the edges and the stopping
function is derived from the edge flow instead of the traditional
gradient edge penalty function to warrant more robust results.
This framework is applied to MER PANCAM and NAVCAM
images to investigate its performance.
Experiments demonstrate satisfactory rock segmentation results
through this fully automated process and give several worthy
notes. First, the suggested framework can account for variations
of rock size with no parameter tuning through the multi-scale