Analysis of 3 d maxillofacial image data 5

135 Chapter Conclusion 5.1 • Overview of Achievements Gradient Orientation Analysis We have described the concept and implementation of the novel technique we call gradient orientation analysis (GOA). Through comparative studies with other closely related methods, we have shown that GOA can detect crease edges of various gradient magnitudes equally and also can detect 3-D lines in noisy data. GOA has been successfully used for detecting dental features such as the cutting edges of the incisors (sharp crease edges) and cusps of the molars (gentle crease edges) in the plan-view range image, which leads to automatic determination of the dental arch that plays an important role in our method for tooth segmentation. Extended to 3-D, GOA has also been applied to CT data for detecting the 3-D tubular hollow space that corresponds to the mandibular nerve canal. Despite the open structure of the surrounding bone, the nerve canal was well detected, which makes it possible to automatically trace a nerve segment of interest in 3-D space. Unlike gradient magnitude, gradient orientation has not received much attention from researchers in the area of image processing. Eigenvalue analysis is a technique based on gradient orientation that provides an attractive mathematical framework for the analysis of both image sequences and volumetric data sets. Successful applications of the technique have proved the usefulness of gradient orientation. However, eigenvalue 136 analysis is aimed at 3-D structure analysis and requires the target object to be well defined. In contrast, GOA focuses on the detection of the discontinuities in gradient orientation and is more tolerant to noise and the detection of vaguely defined objects. We have shown that GOA is well suited to the detection of low-level image features such as edges. An intriguing feature of GOA is that it can detect seemingly hidden features in an image because it is not affected by image intensity and gradient magnitude. It should be stressed that image intensity and gradient magnitude are largely influenced by external factors such as illumination, whereas gradient orientation is more dependent on the local structure of an object. • Tooth Segmentation We have presented an automated method for tooth segmentation of dental study models (plaster casts of the dentition) with a variety of malocclusions (incorrect bites). The study model is digitized into triangular mesh data by a laser scanner. Instead of processing the 3-D mesh model directly, we have devised algorithms that are applied to the range images generated from the mesh data. We first compute a plan-view range image of the model and determine the dental arch based on the arrangement of the teeth. Since this tooth-based dental arch passes through orthodontic features irrespective of the malalignment of the teeth, it greatly relaxes the restriction on the models that the method can deal with. This is an important contribution of the method. Using the dental arch as the reference, we next compute a panoramic range image of the model, which describes the distance between the reference and the buccal surface of the teeth. The pixel size and the gray levels of these two range images are determined by the spatial and depth resolutions of the laser scanner. In this way, the 137 details of the model necessary for tooth segmentation are efficiently transferred from an irregular mesh domain to a regular image domain. Several benefits accrue by conversion of the 3-D mesh data into the regular data structure represented by the range image. It allows the application of mathematical operations such as convolution, and the employment of robust techniques such as GOA and surface normal analysis (SNA) for extracting image features. As stated above, the advantage of GOA lies in its ability to detect crease edges irrespective of their gradient magnitude, which is particularly important since dental features include sharp incisal edges as well as cusps with gentle slopes. The 1-D version of SNA was used for detecting both vertical valleys (tooth interstices) and horizontal valleys (gum margin) in the panoramic range image. Hence, a complex 3-D tooth segmentation problem is greatly simplified by employing two range images. For effective detection of tooth interstices, both range images are employed, with the results from both views subsequently combined to obtain the locations and the orientations of the interstices. The plan-view range image plays an important role in the detection of the interstices between the posterior (back) teeth and also between malaligned teeth. The panoramic range image has an important complementary role, as it is suited to the detection of interstices between well-aligned teeth, particularly the anterior (front) teeth. Meanwhile, the teeth are separated from the gums in the panoramic range image. A validation test on 34 dental models with various malocclusions has shown that the method is robust and accurate. 138 • CT Segmentation We first presented a method for selecting the appropriate threshold value for extracting the skull in CT data. This step is necessary for any medical applications where an object of interest is bone. The appropriate threshold value for excluding background is selected by Otus’s method, while the threshold value for removing soft tissue is determined by the intensities of those voxels in the transition area between the skull and the background. This method does not require intensive computation and is fully automatic. One advantage of this method is that it is robust to outlying data or noise because the threshold value is determined by the mean value of a group of edge voxels. Next, we described a method for automatically segmenting the mandible from the skull. We localize the contact surfaces between the mandible and the maxilla by extracting the tooth enamel. We define the boundary of the mandible by separating the tooth enamel of the mandible from that of the maxilla. This separation step employs a double-thresholding technique that is found to be effective to separate false connections because of the partial volume effect. The entire mandible is then extracted by region growing via connected component labelling. The method does not require lengthy processing time and works well when the inter-slice distance is not too wide ( ≤ mm ). One limitation of the method, however, is that it is not applicable to data sets of children because they have tooth buds of the permanent teeth embedded within the mandible and the maxilla. In this case, the tooth enamel extracted does not directly define the occlusal plane. We may need to devise a step to separate the tooth enamel of erupted teeth from that of embedded teeth. 139 Lastly, we have presented a method for extracting the inferior alveolar nerve canal (IAC). In preparation for this task, we compute a series of panoramic CT images that exhibit cross-sections along curved planes through the mandible. Tubular hollow canals are enhanced by 3-D GOA. In the literature, eigenvalue analysis has been intensively studied for extracting 3-D line structures. We have shown that eigenvalue analysis is not effective for our task because of the open structure of the surrounding bone of the IAC. In contrast, 3-D GOA has robustly detected tubular canals in the panoramic CT images. GOA detects both tubular hollow spaces and thin bony structures because they similarly exhibit high discontinuities in gradient orientation. However, the false responses from thin bony structures are suppressed by means of the voxel values. This is effective since the voxel values of hollow canals and thin bone are very different. Furthermore, we have devised a novel 3-D line tracing technique that is capable of tracing out a 3-D line in a noisy space. The technique is characterized by two features, (a) mask operation, and (b) bi-directional tracing. The masking operation directs the trace toward a target point with some tolerance to a curved path. Coupled with the mask operation, bi-directional tracing makes the technique robust and reliable by pruning spurious branches of a line to be traced. 5.2 Future Work • Tooth Segmentation From our experiments, it is obvious that the teeth are not always separated by a straight line. To improve the success rate of detecting the tooth interstices, it will be effective to use a curved inspection spoke when the present method fails to detect a tooth interstice. In addition, we may introduce a post-processing step to refine the separation surfaces between adjoining teeth on the polyhedral model when perfect segmentation 140 is required. It is not easy to process polyhedral data directly, but in this case, since the area of interest is localized, it will be possible to clean the separation surfaces efficiently. Meanwhile, to make the second indicator more sensitive to malaligned teeth, it will be worth testing the use of a line-fitting technique in place of the vertical projection. Furthermore, it will be interesting to investigate an optimal combination of the two tooth-interstice indicators that can vary adaptively according to the arrangement of the teeth. • Alignment of CT Data An important issue that affects our schemes in volume segmentation is the orientation of the head in CT data. The mandible is separated from the maxilla on a column-bycolumn basis under the assumption that the occlusal (biting) plane is approximately parallel to the CT image plane. The accuracy of the separation will be degraded according to the degree of the deviation between the two planes. Similarly, the IAC is not efficiently captured in panoramic CT images when the assumption is violated. Our anatomic feature detection method will be also significantly affected by any tilt, slant, and rotation of the head. Therefore, it is desired that the head be aligned to a standard orientation in the first place. To facilitate this alignment step, we will need to define two planes, the mid-sagittal plane (MSP) and the occlusal plane. Quite a few research projects are being conducted on the automatic determination of the MSP of the head [79]−[83]. In fact, the detection of the MSP is an important step in spatial normalization (or anatomical standardization) and registration with other modalities of data. We may be able to use these techniques with some modifications. We have successfully determined the occlusal plane based on tooth enamel. However, as previously mentioned, the method is only applicable to CT data sets from adults. To 141 extend the method to CT data from children, we will need to separate the tooth enamel already erupted from the tooth enamel still embedded within the jawbones. This may be possible by examining the CT values of the voxels surrounding the tooth enamel. With the inclusion of the step, described above, computer-aided analysis of 3-D maxillofacial image data could lead to the realization of more advanced computerbased systems for orthodontic treatment and maxillofacial surgery. . above, computer-aided analysis of 3- D maxillofacial image data could lead to the realization of more advanced computer- based systems for orthodontic treatment and maxillofacial surgery. . The study model is digitized into triangular mesh data by a laser scanner. Instead of processing the 3- D mesh model directly, we have devised algorithms that are applied to the range images. applicable to data sets of children because they have tooth buds of the permanent teeth embedded within the mandible and the maxilla. In this case, the tooth enamel extracted does not directly define