牙科臨床中，齒列模型對於齒顎矯正治療是相當重要的工具，齒顎矯正醫師可在模型上計算牙齒的大小，分析空間的需求，和模擬上下顎的咬合關係，然後訂定最佳的治療計畫。隨著病歷資料數位化的發展趨勢，三維數位化齒列模型具有以下優點：1、防止石膏模型損毀，2、節省模型儲存空間，3、強化醫生患者互動溝通，和4、增進遠距病例討論。本研究的目在於建構一套數位化齒模咬合關係，並探討分析應用"陰影造形"演算法所重建三維數位化齒模於咬合模式之精準度。本研究之實驗方法首先選取25組齒列整齊病患之上下顎石膏齒模，和25組齒列擁擠病患之上下顎石膏齒模，然後從不同角度拍攝4張影像，再應用"陰影造形"演算法重建三維數位齒列模型。其次測量石膏齒模與數位齒模之上下顎右側第一大臼齒至左側第一大臼齒共24顆牙齒每一顆牙齒的寬度，藉由統計分析評估數位化模型的精準度。接著利用病患口內的咬合記錄判斷上下顎共同之咬合接觸點，將此接觸點從影像對應至三維數位齒模，使用最小平方誤差方法將上下顎數位齒模做立體咬合對位，以模擬病患真實的咬合關係。從實驗結果顯示，齒列整齊組上顎12顆牙齒總和之誤差為1.65mm，下顎12顆牙齒總和之誤差為0.88mm。齒列擁擠組上顎12顆牙齒總和之誤差為4.03mm，下顎12顆牙齒總和之誤差為3.75mm；上下顎咬合關係之誤差右側為1.41mm，左側為1.23mm。本研究發現應用"陰影造形"演算法所重建的三維數位齒模在咬合關係的精準度方面，齒列整齊組的誤差是可以被接受的；而齒列擁擠組的誤差及上下顎咬合關係則需進一步的改進，以符合臨床需求。

In dental clinical practice, the dental plaster model is an important tool for orthodontic treatment. Orthodontists always use it to calculate the tooth width, to evaluate the space requirement, to simulate the maxilla and mandible occlusal relationship, and to plan a good treatment. With the trends of digital and electronic medical records, the 3D digital dental models may have the following advantages: 1. To avoid dental plaster models broken or damage, 2. To save dental plaster storage space, 3. To strengthen the communication between orthodontist and patient, and 4. To promote the case teleconference. The purposes of this study are to establish the occlusal relationship for bite registration of digital dental model reconstructed using shape-from-shading method, and then to investigate the associated accuracy. In this study, the dental plaster models for 25 orthodontic patients with well-aligned maxillary and mandibular dentition are collected as group I, and the dental plaster models for 25 orthodontic patients with upper and lower crowding dentition are collected as group II. Then, the 3D digital dental models may be reconstructed from 4 images taken from different views using shape-from-shading method. The sizes of twelve teeth from right first molar to left first molar (the space requirement) of plaster and digital models are measured in both arches. In order to determine the contact points of upper and lower digital models of occlusal record, the contact points are located from 2D record and mapped to 3D digital models. The difference of space requirement between plaster and digital models in group I are 1.65 mm for upper arch and 0.88 mm for lower arch, respectively. Those in group II are 4.03 mm and 3.75 mm for upper and lower arch, respectively. The difference of two jaw occlusal relationship for right side is 1.4mm, and left side is 1.2 mm. In the study, it is shown that the differences between plaster and digital models for well-aligned dentition group are small enough for clinical use. While, these differences for crowding dentition group are very significant and need further improvement.

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