The largest convex patches: a boundary-based method for obtaining object parts

Area of Science:

• Computer Vision
• Computational Geometry
• Artificial Intelligence

Background:

• Existing shape decomposition methods by Koenderink and van Doorn (1982) and Hoffman and Richards (1984) define part boundaries using parabolic contours or principal curvature extrema.
• These approaches have limitations in comprehensively decomposing complex shapes into meaningful components.

Purpose of the Study:

• To develop a new, robust method for shape decomposition into constituent parts.
• To leverage both global and local surface properties for accurate shape parcellation.
• To enhance object recognition and functional inference through improved shape decomposition.

Main Methods:

• The method decomposes shape boundaries into largest convex and smallest nonconvex surface patches.
• It involves building initial parts from locally convex patches, identifying essentially convex parts, and merging adjacent patches of similar sizes.
• The approach relies on global surface properties fully characterized by local surface properties.

Main Results:

• The proposed shape decomposition method effectively partitions both smooth and continuous shapes.
• Decomposition into largest convex patches maximizes perceived object integrity ('thingness') and minimizes concavities ('non-thingness').
• The method yields a natural parcellation of shapes into constituent parts.

Conclusions:

• This novel shape decomposition technique offers a more intuitive and effective way to segment objects.
• The resulting parcellation is highly beneficial for object recognition and inferring object function.
• The method provides a unified framework building upon previous boundary definitions in shape analysis.