Study On Segmentation Of Cephalogram Lateral Based On Fractal Theory

Cephalometric analysis is a basic method to diagnose and treat patients with facial skeleton and dental abnormalities in the fields of orthodontics and orthognathia surgery. It is also a significant step for the therapeutic effect and peirod. But the Cephalometric is still at the stag of manual or computer assisted which has tedious work and uncontrolled errors. The image segmentation is the basic and important step to recognize landmarks and auto-Cephalometric because most of Landmarks are on the edge of tissues. The recognization of landmarks and auto-Cephalometric depend on the segmentation for different tissues.The computer auto-Cephalometric includes two steps: one is the computer auto-recognition to segment the soft and bone tissues and the other is auto point- Landmarks. Presently existing and effective approaches to segment the cephalogram generally can be classifed into three categories: edge-based approaches, such as Canny and Sobel operator, region-based approaches such as threshold segmentation and region aggregation, and some theory-based approaches. The X-ray image has high overlapping, high noise, low contrast, much amount of data, high resolution needed. It is very difficult to process X-ray image and the classical methods are faced a difficult challenge, especially for X-ray cephalogram. Cephalometric analysis is still at the beginning of the study.Based on fractal geometry, this paper investigates the use of fractal model and multifractal model to characterize and classify the cephalogram lateral, and performs the segmentation of the cephalogram lateral. As a kind of new mathematic theory, fractal geometry research object is the irregular and random set or system that presents characteristics of self-similarity and self-affinity in the nature. Among the fractal theories, the fractional Brownian motion (FBM), which is the generalized form of ordinary Brownian motion, is one of the most useful mathematical models for characterization of natural image. The FBM model regards naturally occurring rough surfaces as the end result of random walks. Such random walks are basic physical processes in our universe. Multifractal spectrum can all-out describe the characters of distribution for the different geometric structure or different physical property. In fact, the edge of an image can be defined with probability distribution in the given scale as well as its geometric characters. The approach based on grey gradient operation only considers the geometric character of the edge. The multifractal method considers the statistical characters by multifractal spectrum as well as the geometric characters by the odd exponent. So that the main edge information can be remained and stressed as well as the minor edge information can be neglected.Research achievements and innovations are as follows:1. Discrete Fractional Brownian Incremental Random is presented to describe the cephalogram lateral. The scale-invariant region of smaller regions of the cephalogram lateral is confirmed by experiments. The First Region is segmented for the cephalogram lateral including the outside soft tissure outlinethe and landmarks of Nasion and Sella.2. The multifractal spectrum approach based on Multi-Correlation Variance is presented in this paper. 5-neighbour multi-correlation function is structured and the normalization multi-correlation variance probability is defined. Multi-correlation variance approach used to estimate the multifractal spectrum can overcome the drawback of sensing to the noise for the multifractal spectrum and slowly convergence for the weight factor. Multifractal model is presented to describe the cephalogram lateral. The multifractal linear region of the cephalogram and multifractal spectrum are analyzed by researching the relationship between the multifractal spectrum and its weighted factor. The Second Region is segmented for the cephalogram lateral.3. Another novel approach is presented to estimate the multifractal spectrum. The approach is based on Euclid Distance Correlation function. Although Multi-Correlation Variance approach has good property of repressing the noise, a Euclid Distance Correlation Function for the cephalogram is structured and the normalization Euclid Distance Correlation Fuction probability is defined to describe the different statistical characters of the cephalogram. Multifractal model is presented to describe the cephalogram lateral. The multifractal linear region of the cephalogram and multifractal spectrum are analyzed by researching the relationship between the multifractal spectrum and its weighted factor. Third Region is segmented for the cephalogram lateral.The results of simulation experiments have demonstrated that the proposed technique can accurately and effectively than the edge-based segmentations of Canny and Sobel operator.