A resistant method for landmark-based analysis of individual asymmetry in two dimensions  

作　　者：Sebastian Torcida Paula Gonzalez Federico Lotto 

机构地区：[1]Dpto. Matematica-Exactas, UNCPBA. Tandil 7000, Argentina. [2]Fac. de Ciencias Naturales y Museo, UNLP-CONICET. La Plata 1900, Argentina [3]Instituto de Veterinaria Ing. Fernando N. Dulout (IGEVET), Facultad de Cs. Veterinarias, UNLP-CONICET. La Plata 1900,Argentina

出　　处：《Frontiers of Electrical and Electronic Engineering in China》2016年第4期270-282,共13页中国电气与电子工程前沿（英文版）

摘　　要：Symmetry of biological structures can be thought as the repetition of their parts in different positions and orientations. Asymmetry analyses, therefore, focuses on identifying and measuring the location and extent of symmetry departures in such structures. In the context of geometric morphometrics, a key step when studying morphological variation is the estimation of the symmetric shape. The standard procedure uses the least-squares Procrustes superimposition, which by averaging shape differences often underestimates the symmetry departures thus leading to an inaccurate description of the asymmetry pattern. Moreover, the corresponding asymmetry values are neither geometrically intuitive nor visually perceivable. Methods： In this work, a resistant method for landmark-based asymmetry analysis of individual bilateral symmetric structures in 2D is introduced. A geometrical derivation of this new approach is offered, while its advantages in comparison with the standard method are examined and discussed through a few illustrative examples. Results： Experimental tests on both artificial and real data show that asymmetry is more effectively measured by using the resistant method because the underlying symmetric shape is better estimated. Therefore, the most asymmetric （respectively symmetric） landmarks are better determined through their large （respectively small） residuals. The percentage of asymmetry that is accounted for by each landmark is an additional revealing measure the new method offers which agrees with the displayed results while helping in their biological interpretation. Conclusions： The resistant method is a useful exploratory tool for analyzing shape asymmetry in 2D, and it might be the preferable method whenever a non homogeneous deformation of bilateral symmetric structures is possible. By offering a more detailed and rather exhaustive explanation of the asymmetry pattern, this new approach will hopefully contribute to improve the quality of biological or developmental inferences.Symmetry of biological structures can be thought as the repetition of their parts in different positions and orientations. Asymmetry analyses, therefore, focuses on identifying and measuring the location and extent of symmetry departures in such structures. In the context of geometric morphometrics, a key step when studying morphological variation is the estimation of the symmetric shape. The standard procedure uses the least-squares Procrustes superimposition, which by averaging shape differences often underestimates the symmetry departures thus leading to an inaccurate description of the asymmetry pattern. Moreover, the corresponding asymmetry values are neither geometrically intuitive nor visually perceivable. Methods： In this work, a resistant method for landmark-based asymmetry analysis of individual bilateral symmetric structures in 2D is introduced. A geometrical derivation of this new approach is offered, while its advantages in comparison with the standard method are examined and discussed through a few illustrative examples. Results： Experimental tests on both artificial and real data show that asymmetry is more effectively measured by using the resistant method because the underlying symmetric shape is better estimated. Therefore, the most asymmetric （respectively symmetric） landmarks are better determined through their large （respectively small） residuals. The percentage of asymmetry that is accounted for by each landmark is an additional revealing measure the new method offers which agrees with the displayed results while helping in their biological interpretation. Conclusions： The resistant method is a useful exploratory tool for analyzing shape asymmetry in 2D, and it might be the preferable method whenever a non homogeneous deformation of bilateral symmetric structures is possible. By offering a more detailed and rather exhaustive explanation of the asymmetry pattern, this new approach will hopefully contribute to improve the quality of biological or developmental inferences.

关 键 词：resistant procrustes method shape asymmetry matching and object symmetry landmarks 

分 类 号：TG386.32[金属学及工艺—金属压力加工] TP18[自动化与计算机技术—控制理论与控制工程]