Asymmetry quantization and application to human mandibles
Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Standard
Asymmetry quantization and application to human mandibles. / Glerup, Nanna; Nielsen, Mads; Sporring, Jon; Kreiborg, Sven.
Proceedings of SPIE. 2004. p. 274-282 (Medical Imaging 2004: Image Processing, Vol. 5370).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
Harvard
APA
Vancouver
Author
Bibtex
}
RIS
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 -
ID: 5070561