Measuring Shapes with Desired Convex Polygons.

Area of Science:

• Computer Vision
• Image Analysis
• Geometric Modeling

Background:

• Traditional shape measures often rely on optimizing specific shape properties.
• Existing methods can be limited by the need to identify optimal shapes for defined properties.

Purpose of the Study:

• To develop a new family of shape measures based on predefined convex polygons.
• To introduce a flexible method for quantifying shape similarity to target polygons.

Main Methods:

• Developed a novel approach to shape measure design, starting from a desired convex polygon.
• Introduced a tuning parameter to control the behavior of the shape measures.
• Ensured measures are invariant to translation, rotation, and scaling.

Main Results:

• Created a 2-fold family of shape measures ranging from (0,1].
• Measures achieve a maximum value of 1 if and only if the shape matches the predefined polygon.
• Extended the method to generate new shape convexity measures.

Conclusions:

• The proposed shape measures offer a versatile tool for shape analysis and comparison.
• The invariance properties make these measures robust for various applications.
• The method provides a flexible framework for defining new shape descriptors.