The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B4. Beijing 2008 
1021 
r 
[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