Morphological decomposition of 2-D binary shapes into convex polygons: a heuristic algorithm.

Area of Science:

• Computer Vision
• Image Processing
• Computational Geometry

Background:

• Existing morphological shape decomposition algorithms are often limited to simple component forms or require time-intensive search processes.
• Efficient and accurate shape decomposition is crucial for various applications in computer graphics and image analysis.

Purpose of the Study:

• To present a novel morphological shape decomposition algorithm for two-dimensional (2-D) binary shapes.
• To decompose shapes into a collection of convex polygonal components efficiently and accurately.

Main Methods:

• The algorithm first identifies a convex polygonal approximation using basic shape primitives selected at different scale levels.
• Subsequent components are found recursively from the difference image, with operations to repair concavities.
• A hierarchical structure is generated, describing the shape at multiple detail levels.

Main Results:

• The decomposition results align well with the natural structures of the input shapes.
• The algorithm demonstrates significantly lower computational cost compared to search-based convex decomposition methods.
• It provides accurate shape approximations at low coding costs, outperforming nonconvex decomposition algorithms.

Conclusions:

• The proposed algorithm offers an efficient and effective method for morphological shape decomposition into convex components.
• It achieves a good balance between decomposition accuracy, computational efficiency, and descriptive detail.
• This approach advances shape representation and analysis in digital imaging.