Abstract— Standardized digital images of maxillary dental casts of 47 subjects were analyzed using MATLAB software whereby the two hamular notches and the incisive papilla defines the Cartesian vertical and horizontal axes, as well as the origin. The angle and length of the midpoints of the anterior teeth, mesiobuccal and distobuccal cusp of the posterior teeth were measured from the origin and denoted as 1 18 , , θ θ … and 1 18 , , l l … respectively. These values were collectively used to represent the shape of each dental cast. Clustering and principal component analyses were employed to find possible groups of dental arches using the above measure of shape. The main result of this study is that the 3 groups of dental arch shape may be represented by the novel feature vector 3 , 2 , 1 ), , , , , , , , ( 13 13 5 5 3 3 1 1 = = k l l l l v k k k k k k k k k θ θ θ θ . Knowledge of k v implies three impression trays should be sufficient in a particular prosthetic dentistry application for Malaysian patients. Further, given that k v are accurately measured, they may be potential candidates as evidence in specific application of forensic dentistry. I. INTRODUCTION HE shape and size of the dental arch has been the subjects of discussion and research in dentistry since early 1880. One of the areas of interest in determining the arch shape Manuscript received March 25, 2011. O. M. Rijal is with the Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, Malaysia (e-mail: omarrija@um.edu.my). N. A. Abdullah is with the Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, Malaysia (corresponding author to provide phone: +6013-394-2514 (mobile); fax: +603-7967-4143; e- mail: norlienih@yahoo.com). Z. M. Isa is with Department of Prosthetic Dentistry, Faculty of Dentistry, University of Malaya, Kuala Lumpur, Malaysia (e-mail: zakiah@um.edu.my). F. A. Davaei Abdullah is with the Institute of Mathematical Sciences, Faculty of Science, University of Malaya, Kuala Lumpur, Malaysia (e-mail: feisal_a_d@yahoo.com). N. M. Noor is with the Department of Electrical Engineering, UTM Razak School of Engineering and Advanced Technology, Universiti Teknologi Malaysia, Malaysia (e-mail: norliza@ic.utm.my). O. T. Farouq is with Department of Prosthetic Dentistry, Faculty of Dentistry, University of Malaya, Kuala Lumpur, Malaysia (e-mail: dromar_s@yahoo.com). arose from clinical experience in finding suitable impression trays that fits a dentate patient for impression making [1],[2]. Impression trays are generally U-shaped and multiple sizes are made to accommodate a range of mouth sizes. Though various choices of stock trays are available commercially, the problem of finding an impression tray that perfectly fits a patient still remains [1],[3]. Some trays are often too long or too short in relation to the extent of the oral soft and hard tissues that need to be recorded and modifications to the trays need to be carried out before the trays can be selected for making acceptable impressions. As for the inexperienced dental practitioners, selecting the right impression tray may be challenging and providing a few trays that generally accommodate a specific population would make the selection process easier. From a review of the literature, there appears to be no comprehensive study of stock tray designs in relation to the size and shape of the human dental arch. Therefore, describing shape and size of dental arches would be the first step in achieving a scientific design of stock trays. In earlier studies, the shape of the human dental arches had been qualitatively described as semi-ellipse, parabolic curve, and catenary curve [4]-[6]. Then, a more sophisticated representation of shape had been proposed by fitting polynomial equations, conic section, and beta function [7]-[9]. This study is aimed at exploring a novel method of representing the dental arch shape in relation to stock tray design. Knowledge of ) , , , , , , , ( 13 13 5 5 3 3 1 1 l l l l v θ θ θ θ = and groups of arch shape also has an important application in prosthetic dentistry (treatment of edentulous patient) and forensic dentistry [7], [10]-[15]. II. MATERIALS AND METHODS A. Data Selection and Stone Cast Making Forty seven dentate Malaysian adults aged between 19 and 32 years with well aligned maxillary anterior teeth and minimal attrition participated in this study. Subjects were excluded if they had a history of orthodontic treatment, anterior restoration or a fixed dental prosthesis in the maxilla or mandible. Impressions of dental and oral structures of the maxillary arches of the subjects were made with irreversible hydrocolloid (Duplast fast set alginate impression material; Dentsply Dental Co Ltd, Tianjin, China). Impressions were A Novel Shape Representation of the Dental Arch and its Applications in Some Dentistry Problems Omar M. Rijal, Norli A. Abdullah, Zakiah M. Isa, Feisal A. Davaei, Norliza M. Noor, Omar F. Tawfiq T 978-1-4244-4122-8/11/$26.00 ©2011 IEEE 5092 33rd Annual International Conference of the IEEE EMBS Boston, Massachusetts USA, August 30 - September 3, 2011