以體素法量化物體對稱度及找出最佳對稱面[1, 2]為顏面骨骼不對稱量化方法開啟了承先啟後階段性里程碑，該方法適用於幾近對稱且形狀不規則物體。本研究則進一步探討使用該方法的極限，在何種情況下，一個近似對稱物體會喪失對稱性，使得該物體最佳對稱面離開預期位置。藉由引入形變模擬，得以檢測最佳對稱值及最佳對稱面對於逐步擴大之不對稱結構的反應。當不對稱結構大於特定閥值時，最佳對稱面將偏離預期落點且最佳對稱值急遽下降，反應出不對稱量化方法之極限。
本研究更針對顱顏骨骼，以輪廓分析方法來分析下顏面輪廓的對稱性，利用上顎骨最佳對稱面及眼耳平面定義頭顱局部座標，據此擷取前視及下視之下顎骨輪廓線建立投影視覺上的對稱量化分析，藉此補助三維體素法對稱分析資訊上的限制。利用不對稱輪廓量化法結合體素法的最佳對稱面可獲得下顎輪廓不對稱的量化數據，下顎左右側輪廓型態變化得以數據具體顯現。三維體素法結合二維輪廓分析方法，兩者相輔相成，使顏顎骨不對稱性量化分析技術更趨完善。

The voxel-based symmetry quantification is applicable in symmetry-like objects with irregular morphology. Succeeded from this voxel-based methodology[1, 2], this study further investigates its limitations, that is, the condition that induces the optimal symmetry plane of a symmetry-like object, deflecting from the expected location. By introducing deformation simulation, the response of the optimal symmetry ratio and optimal symmetry plane to the gradually enlarging asymmetrical structure can be investigated. When the size of the deformation exceeds a specific threshold, the optimal symmetry plane deviates from the expected position, the optimal symmetry ratio drops dramatically, and in turn the limitations of the symmetry evaluation methodology are reflected.
Moreover, this research concentrating on the craniofacial complex purposes contour-based analysis to inspect the symmetry of the mandibular contour. Taking advantages of the mid-face optimal symmetry plane and Frankfort-Horizontal plane to define the canonical orientation, the frontal and submental mandibular contours are extracted to be analyzed in their symmetry on the projection planes of perception, and so as to complement the deficiency in the voxel-based approach. Mandibular asymmetry quantification is thus available by applying the optimal symmetry planes to contour-based methodology and the variations in morphology of the mandibular bilateral contours are visualized. Cooperation of the voxel-based and contour-based symmetry approaches masks the jaw asymmetry quantification more comprehensive.

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