Related Experiment Video
Updated: May 29, 2026

Morphometric Analyses of Shape: The Analysis Software Toolbox for Craniofacial Shape Quantification in Zebrafish
Published on: February 27, 2026
An extremum principle for shape from contour
1Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139.
Abstract:
An extremum principle is developed that determines three-dimensional surface orientation from a two-dimensional contour. The principle maximizes the ratio of the area to the square of the perimeter, a measure of the compactness or symmetry of the three-dimensional surface. The principle interprets regular figures correctly and it interprets skew symmetries as oriented real symmetries. The maximum likelihood method approximates the principle on irregular figures, but we show that it consistently overestimates the slant of an ellipse.
Related Concept Videos
Elevation of Intermediate Points on Vertical Curves
Absolute and Local Extreme Values
First Derivatives and the Shape of a Graph
Second Derivatives and the Shape of a Graph
Plastic Deformations
Plastic Deformations

