Improved B-Spline Contour Fitting Using Genetic Algo- rithm for the Segmentation of Dental Computerized To- mography Image Sequences

In the dental field, 3D tooth modeling, in which each tooth can be manipulated individually, is an essential component of the simulation of orthodontic surgery and treatment. However, in dental computerized tomography slices teeth are located closely together or inside alveolar bone having an intensity similar to that of teeth. This makes it difficult to individually segment a tooth before building its 3D model. Conventional methods such as the global threshold and snake algorithms fail to accurately extract the boundary of each tooth. In this paper, we present an improved contour extraction algorithm based on B-spline contour fitting using genetic algorithm. We propose a new fitting function incorporating the gradient direction information on the fitting contour to prevent it from invading the areas of other teeth or alveolar bone. Furthermore, to speed up the convergence to the best solution we use a novel adaptive probability for crossover and mutation in the evolutionary program of the genetic algorithm. Segmentation results for real dental images demonstrate that our method can accurately determine the boundary for individual teeth as well as its 3D model while other methods fail. Independent manipulation of each tooth model demonstrates the practical usage of our method. © 2007 Society for Imaging Science and Technology. DOI: XXXX INTRODUCTION The accurate 3D modeling of the mandible and the simulation of tooth movement play an important role in preoperative planning for dental and maxillofacial surgery. The 3D reconstruction of the teeth can be used in virtual reality based training for orthodontics students and for preoperatory assessment by dental surgeons. For 3D modeling tooth segmentation to extract the individual contour of a tooth is of critical importance. Automated tooth segmentation methods from 3D digitized images have been researched for the measurement and simulation of orthodontic procedures. These methods provide interstices along with their locations and orientations between the teeth for segmentation result. However, it does not give individual tooth contour information which manifests more details that are helpful in dental study. A thresholding method, used in the existing segmentation and reconstruction systems, is known to be efficient for automatic hard tissue segmentation. Some morphological filtering methods are used for creating intermediary slices by interpolation for modeling teeth in 3D. The morphological operations are also combined with the thresholding method for dental segmentation in x-ray films. However, neither the thresholding method nor the morphological filtering method is suitable for separating individual tooth regions using tooth computerized tomography (CT) slices, because some teeth touch each other and some are located inside of alveolar bone with a CT slice intensity profile similar to teeth. A modified watershed algorithm was suggested to create closed-loop contours of teeth while alleviating the over-segmentation problem of the watershed algorithm. Although this reduces the number of regions significantly, it still produces many irrelevant basins that make it difficult to define an accurate tooth contour. A seed-growing segmentation algorithm was suggested based on B-spline fitting for arbitrary shape segmentation in sequential images. The best contour of an object is determined by fitting the initial contour passed by previous frame to the edges detected in the current frame. For the fitting operation, the objective function defined by the sum of distances between the initial contour and the object edges is used. For this algorithm to work properly, the complete object boundary should be extracted by global thresholding and the object should be located apart from other objects. If other objects are located nearby as in the case of the tooth CT image, the shape of the initial contour should be very close to the actual object contour to prevent being fitted to the boundaries of the nearby objects. Many snake algorithms have been proposed for medical image analysis applications. However, in the CT image sequence where objects are closely located, the classical snake algorithms have not yet been successful due to difficulties in initialization and the existence of multiple extrema. It is only successful when it is initialized close to the structure of interest and there is no object which has similar intensity values to those of interest. The snake models for object boundary detection search for an optimal contour that minimizes (or maximizes) an objective function. The objective function generally consists of the internal energy representing the properties of a contour shape and the external potential energy depending on the image force. The final shape of the contour is influenced by how these two energy terms are represented. However, many snakes tend to shrink when its external energy is relatively small due to the lack of image Journal of Imaging Science and Technology® 51(4): 1–XXXX, 2007. © Society for Imaging Science and Technology 2007