CONTOUR TRACKING BY REGIONAL MINIMAL COST PATH APPROACH. APPLICATION TO CEPHALOMETRY. B. Romaniuk

M. Desvignes

GREYC Image 6, Bvd Mar´echal Juin 14050 Caen Cedex, France [email protected]

LIS-ENSERG 961 rue de la Houille Blanche, BP 46 38402 Saint Martin d’H`eres Cedex, France [email protected]

ABSTRACT In this paper, a regional minimal cost approach without parameters is used for contour tracking with a good robustness. Dynamic programming is exploited for its efficiency. This general method is applied to the extraction of the cranial contour on higth resolution X-Ray image. Ellipse is then fitted on the extracted contour to represent it as a first step for automatic localisation of cephalometric points. This method is tested on 424 X-Ray images, with different acquisition parameters.

Fig. 1. X-ray radiography used in cephalometry.

1. INTRODUCTION In orthodontics, cephalometry is used as an aid for therapeutic decision making and as a tool for early detection of dental dysharmonies in young children. Both applications having a positive effect on the efficiency of the treatments. Cephalometric image landmarks are bony landmarks and are first located on the hight resolution digital radiograph. Cephalometry analysis is based on the comparison of angles and lengths between cephalometric points in an individual to corresponding normative values. These points are usually identified on lateral radigraphs of the head with hight resolution (1576 1976 pixels). As our former work [1] on the automatic localization of cephalometric landmarks is based on the detection and modeling of the cranial contour, we present here a method for detecting this contour that is based on the concept of minimal cost path and its subsequent modeling by an ellipse. Our method is then tested on 424 images acquired on different systems (Figure 1). 2. METHOD The detection of the external cranial contour (dome of the skull limited by the nose and the lowest point of the cranium) by traditional methods used for image processing (gradients [2], active contours [3]) fails for some local configurations where gradients are low or inverted. Moreever, these

Fig. 2. Tracking with classical methods and universal parameters.

methods need the fine tuning of numerous threshold for a good detection of the contour (Figure 2). These parameters depend on the acquisition system. In particular, the very different osseous density along this contour leads the local methods to move away from the cranial contour in presence of notches towards the interior of cranium or noise. Global methods like the Level Sets [4] or graph search methods have the disadvantage of a high algorithmic cost. We propose to use a regional approach of type shortest path, on the gradient image, by using the regularity of the gravure screen of an image in order to combine robustness and low algorithmic cost. The method breaks up into 3 great stages, followed by the modeling of the contour.

2.1. Detection of two points on the cranial contour The first step of our method consists on detecting automatically two points on the cranial contour. This detection have to be independent of the source and the quality of X-rays. These two points are respectively localized in the front and in the back of the skull, in regions in which the cephalostat1 does not introduce supplementary information on the image. Two binary masks having the shape of arcs of circle are learned on a sample of images. They represent the former and the frontal parts of the cranial. Let I
and I  be the two points that we want to detect. These points have three properties : - they are the points of stronger gradient - they are locate on the orthogonal axis to the tangent to the model - they are locate less than 5 pixels from the point of maximum answer for the normalized correlation between the image and the binary masks.

2.2. Tracking contour by the regional minimal cost path method The following stage is the detection of the higher part of the cranial contour between the two points I
and I  (step 1 in the Figure 4). Tracking this contour procures the stronger gradient path between I
and I and uses an iterative approach. In this approach the best successor is computed for each iteration. I1 1 3

Roughness criterion

I2 2

Fig. 4. Three part of the contour to find In our regional  approach, we seek  the shortest path beand the point  defined by: tween the point





(a) Treated image

     

where  is the general direction of the tangent to the path.   We limit the search to the rectangle whose corners are  and  (Figure 5).

Di Ti Ci (b) Correlation with the masks

(c) Selected points

Fig. 3. Detection of two points on the cranial contour. Figure 3 presents this detection: image (a) is the image on which we will apply the masks; image (b) is the normalized correlation between the image and the binary masks, image (c) presents the detected points I
and I  . 1 The part of the machine that allows a good positioning of the patient during the acquisition of the image

Fig. 5. Research of the best successor By supposing that  the   cranial contour is a monotonic curve in the rectangle  , the shortest path can be iteratively and quickly computed by solving:

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