Ferrario V F, Sforza C, Poggio C E, D'Addona A, Taroni A
Istituto di Anatomia Umana Normale, Facoltà di Medicina e Chirurgia, Università degli Studi di Milano, Italy.
Cleft Palate Craniofac J. 1996 May;33(3):206-12. doi: 10.1597/1545-1569_1996_033_0206_faocs_2.3.co_2.
Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the Fourier series. A method for the reconstruction of outlines starting from selected landmarks and for their Fourier analysis has been developed and applied to analyze the age differences in shape in the tracings of the Bolton standards (lateral view) from 1 to 18 years of age. The size-independent shape of the Bolton standard at 18 years was larger at the chin, at the gonion, and in the anterior cranial base than the shape at 1 year of age. Conversely, the younger shape was larger in the middle part of face, corresponding roughly to the maxillary bone, than the older shape. When standardized for size, growth thus seemed to modify craniofacial shape with progressive lengthening and narrowing. This shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods.
颅面生长发育涉及大小和形状的变化。形状变化可以使用傅里叶级数等数学方法独立于大小进行评估。已经开发出一种从选定地标重建轮廓并对其进行傅里叶分析的方法，并将其应用于分析博尔顿标准（侧视图）1至18岁年龄段追踪图中的形状年龄差异。18岁时博尔顿标准的与大小无关的形状在下巴、下颌角和前颅底比1岁时的形状更大。相反，较年轻的形状在面部中部（大致对应上颌骨）比年长的形状更大。当按大小标准化时，生长似乎通过逐渐延长和变窄来改变颅面形状。这种形状效应在很大程度上被非常明显的大小增加所掩盖，并且只能使用适当的数学方法来测量。
