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Morphometric Analyses of Shape: The Analysis Software Toolbox for Craniofacial Shape Quantification in Zebrafish

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An extremum principle for shape from contour.

M Brady¹, A Yuille

¹Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This summary is machine-generated.

A new principle determines 3D surface orientation from 2D contours by maximizing area-to-perimeter ratio for symmetry. This method accurately interprets regular shapes but may overestimate slant in irregular figures like ellipses.

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Area of Science:

Computer Vision
Computational Geometry
Perception

Background:

Determining 3D surface orientation from 2D contours is a fundamental challenge in computer vision.
Existing methods may struggle with irregular shapes and symmetries.

Purpose of the Study:

To develop a novel extremum principle for inferring 3D surface orientation from 2D contours.
To establish a measure of surface compactness/symmetry for this inference.

Main Methods:

Formulated an extremum principle maximizing the ratio of surface area to the square of its perimeter.
Applied the principle to regular and irregular figures, including ellipses.
Compared results with the maximum likelihood method.

Main Results:

The principle accurately determines 3D surface orientation for regular figures.
Skew symmetries are interpreted as real, oriented symmetries.
The maximum likelihood method was found to consistently overestimate ellipse slant.

Conclusions:

The proposed extremum principle offers a robust method for 3D surface orientation inference.
It provides a new perspective on interpreting symmetries in visual perception.
Limitations regarding slant estimation for irregular shapes were identified.