TY - GEN

T1 - Asymmetry quantization and application to human mandibles

AU - Glerup, Nanna

AU - Nielsen, Mads

AU - Sporring, Jon

AU - Kreiborg, Sven

PY - 2004

Y1 - 2004

N2 - All biological objects exhibit some degree of asymmetry, but for some parts of the human body, excessive asymmetry is a sign of pathology. Hence, the problem is to draw the line between categorization of objects being too asymmetric and objects exhibiting normal asymmetry. With a measure of asymmetry, the statistics on asymmetry for normal and pathological anatomical structures can be compared. Symmetry is a well-known mathematical group theoretical concept. In this paper, we will mathematically define the concept of weak symmetry, including topological symmetry, which serves as a basis for quantizing asymmetry. The methodology is based on non-rigid registration in the sense that the "size" of a diffeomorphism describes the amount of asymmetry. We will define this size in terms of the minimum biological work needed. That is, we evaluate how much work the biological system must carry out in order to make the object symmetrical; or identically, how much work has been carried out in order to make the ideal symmetrical object into the current (slightly) asymmetrical object. The quantization of asymmetry is validated on a set of normal (assumed near symmetrical) mandibles, and a set of pathological assumed non-symmetric mandibles exhibiting a statistically significant increase of asymmetry.

AB - All biological objects exhibit some degree of asymmetry, but for some parts of the human body, excessive asymmetry is a sign of pathology. Hence, the problem is to draw the line between categorization of objects being too asymmetric and objects exhibiting normal asymmetry. With a measure of asymmetry, the statistics on asymmetry for normal and pathological anatomical structures can be compared. Symmetry is a well-known mathematical group theoretical concept. In this paper, we will mathematically define the concept of weak symmetry, including topological symmetry, which serves as a basis for quantizing asymmetry. The methodology is based on non-rigid registration in the sense that the "size" of a diffeomorphism describes the amount of asymmetry. We will define this size in terms of the minimum biological work needed. That is, we evaluate how much work the biological system must carry out in order to make the object symmetrical; or identically, how much work has been carried out in order to make the ideal symmetrical object into the current (slightly) asymmetrical object. The quantization of asymmetry is validated on a set of normal (assumed near symmetrical) mandibles, and a set of pathological assumed non-symmetric mandibles exhibiting a statistically significant increase of asymmetry.

U2 - 10.1117/12.535325

DO - 10.1117/12.535325

M3 - Article in proceedings

T3 - Medical Imaging 2004: Image Processing

SP - 274

EP - 282

BT - Proceedings of SPIE

Y2 - 29 November 2010

ER -