CIP A 2003 XIX 11 ' International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
Figure 2: Left sides of the leaves, eaten by the mouse. 
In the final step, a Tree Search scheme that starts from the 18 th 
(fixed) leaf and ends at the 66 th (relaxed) leaf was established to 
generate the most probable sequence. Every node in the tree 
was defined as a leaf and branched to the most probable 
neighbor leaves. The similarity measures were expressed as 
costs of the arcs, which connect two nodes in the tree. The 
sequence which has minimum total path cost was proposed as 
the most probable original sequence. 
The paper is organized as follows. In the second section, the 
adopted methodology that is used to predict the most probable 
sequence is described. The methodology includes the 
rectification of the images, boundary tracing, shape description, 
and evaluation of the shape data using tree-search. The obtained 
results and the conclusions are given in the third section. 
2. METHODOLOGY 
2.1 Image Acquisition 
Figure 3: Imaging geometry and common points. 
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Figure 4: (left) raw image, (right) rectified image. 
Radial distortion of the CCD camera was neglected because it is 
not relevant to our problem. After the projective transformation, 
each leaf in the images was cropped and saved as an image file. 
In the cropping process, the holes in the center of the leaves 
were assumed as the origin of the predefined 2D leaf coordinate 
system. This approach puts all leaves to the same alignment. 
The digital images of the leaves were acquired with a Sony 
DSC-F505 Cybershot CCD camera in free-hand mode at the 
Museum Rietberg Zuerich. The image size was 1600x1200 
pixels, and the focal length was set at 7.1 mm, which is the 
widest-angle position for the camera. Three of the leaves, 
placed on an A4-sized white paper, were imaged in per image. 
The corners of the A4-sized page were used as reference points 
in the following rectification process, which will be described 
in the following section. 
2.2 Rectification of the Images 
Due to the varying orientation of the camera, perspective 
differences among the images occurred. Especially, the 
perspective effect due to the unstable Omega angle was 
observed in most images (Figure 3). In order to compensate this 
effect, projective transformation and b[-linear resampling 
processes were applied to each image. In this transformation, 
the corners of the A4-sized white page were used as reference 
points. Projective transformation parameters ( a, ) were 
calculated using four common points according to the well 
known formula (Equation 1). 
x Qp Xj + a i y t +a 2 Y fljXj+fl v yj+a 5 (1) 
' x i + a 7 y; + 1 ’ ' a 6 x { +a 7 y { +\ 
where i = {1,2,3,4}. Then, the bi-linear resampling process was 
applied to obtain the corrected images (Figure 4). 
2.3 Boundary Tracing 
Segmentation is one of the most important image analysis tasks. 
Its main goal is to delineate certain objects in the image and to 
distinguish them from irrelevant image parts. There are 
different segmentation methods according to their search 
strategies: thresholding techniques, edge based, region based, 
and hybrid methods. Edge based methods commonly use edge 
detection operators such as Laplacian, Sobel, Kirs dr Marr- 
Hildreth, and Canny operators. This is usually followed by 
other processing steps in order to combine edges into edge 
chains, for example Hough transformation. Some of the edge 
based segmentation methods need prior information about 
shape, such as Snakes (Kass et al., 1987) and graph searching or 
dynamic programming based edge following methods (Martelli, 
1972, Furst 1986). A successful application of LSB-Snakes and 
dynamic programming for road extraction was given by Gruen 
and Li (1997). boundary tracing is another well-known edge 
based segmentation method used to delineate closed shapes 
(Liow, 1991, Kovalevsky, 1992). 
To generate the boundary-based descriptors, boundaries of 
every leaf must be delineated. Because of simplicity and 
suitability to our case, an inner boundary tracing method was 
adopted to segment the leaves from image background (Sonka, 
Hlavac, Boyle, 1993). Basically it comes in 4-connectivity and 
8-connectivity modes. We opted for the 8-connectivity mode