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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B5. Istanbul 2004 
  
Extraoral Radiograms 
  
  
Skull Cephalometric Panoramic 
       
         
  
  
  
  
  
  
Figure 2. Extraoral radiograms types 
2. REGISTRATION OF DENTAL RADIOGRAMS 
Since information gained from different dental radiograms 
acquired in the clinical track of events is usually of a 
complementary nature, proper integration of useful data 
obtained from the separate radiograms is often desired. The 
first step in this integration process is to bring the modalities 
involved into spatial alignment, a procedure referred to as 
registration. The goal of image registration is to find a 
transformation that aligns one image to another. Dental 
radiograin registration has emerged from this broad area of 
research as a particularly active field. This activity is due in 
part to the many clinical applications including diagnosis, 
longitudinal studies, and surgical planning (Kim and Muller, 
2002). 
Medical image registration, however, still presents many 
challenges. Several notable difficulties are a.) the 
transformation between images can vary widely and be 
highly nonlinear (elastic) in nature; b.) images acquired from 
different modalities may differ significantly in overall 
appearance and resolution; c.) there may not be a one-to-one 
correspondence between the images (missing/partial data); 
and d.) each imaging modality introduces its own unique 
challenges, making it difficult to develop a single generic 
registration algorithm (Josien er al, 2003). 
3. PROPOSED METHODOLOGY 
In this paper we propose a feature based hierarchical method, 
which employs a fuzzy reasoning strategy for digital image 
matching process and hence the matching operation is 
designed to be closer to the human operator’s decision 
making approach for the conjugate point identification. The 
fuzzy decision process for conjugate point determination 
simultaneously takes advantage of all the influential 
parameters that contribute during the conjugate point 
identification stage, namely: geometric constraints, 
radiometric similarities evaluated by correlation coefficient 
as well as texture differences. The overall strategy for our 
proposed registration method may be expressed by the 
following interrelated procedures: 
3.1 Multiresolution representation of information 
One of the main requirements needed for all registration 
algorithms is approximate values of two corresponding points 
which is related to the interrelation mathematical model of 
two images (or images and map). The best known solution to 
derive these approximations is to construct image pyramids 
and start the matching process at a low resolution level (i.e. 
from the top of the image pyramids). This can provide rough 
approximate values for the successive levels of image 
pyramids. 
« Multiresolution representation of Dental 
Radiograms: Construction of image pyramids in this 
paper is carried out according to wavelet transform. 
The wavelet transform features are used because 
wavelet transforms convey both space and time 
characteristics and their multi-resolution 
representations enable = efficient — hierarchical 
searching. 
=  Multiresolution representation of Point Features: 
Based on the generated image pyramids, the 
implemented system also extracts and constructs 
feature pyramids by applying a Forstner operator to 
each layer of the image pyramids (Foerstner and 
Guelch, 1987). The general structure of the normal 
equation matrix for the intersection points (xo,yo) by 
the Foerstner operator is given by: 
Sr * nt Xo i y ix +3 71,3 (1) 
Suus eX. 
where /, and /, are the local gradients in x and y 
directions respectively. The summation is performed 
over a predefined neighbourhood area. 
«  Multiresolution | representation of Mathematical 
Models: Mathematical modelling approaches for 
orientation and registration of different dental 
radiogram have been done based on a multiresolusion 
representation of Generic Sensor Models (GSMs), 
e.g. Rational functions. The Rational function uses a 
ratio of two polynomial functions to compute the x 
coordinate in the image, and a similar ratio to 
compute the y coordinate in the image. 
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Where x, y are normalized pixel coordinates on the 
image; X, Y, Z are normalized 3D coordinates on the 
object, and aj bj, cj, dj, are polynomial 
coefficients. The polynomial coefficients are called 
rational function coefficients (RFCs). 
3.2 Geometric and Semantic Conditions 
Certain factors can be employed to assist the conjugate point 
determination process. These factors may be categorized into 
geometric and semantic conditions. Geometric Conditions: 
The geometric parameters are considered to include the 
object and imaging geometry represented by x and y 
differences which are related to different mathematical 
models in each layer of information. Semantic Conditions: 
The semantic conditions are defined based on the radiometric 
similarities between the conjugate points. This can be 
determined via different similarity assessment algorithms. 
Our method takes advantage of two different algorithms, 
namely: the well known normalized correlation coefficient 
(NCC) and the rank differences. The so called rank values 
arc computed using window arrays constructed around