An efficient region expansion algorithm for regular triangulated meshes

Area of Science:

• Computer Vision
• Computational Geometry
• Image Processing

Background:

• Region expansion is a fundamental image processing operation.
• Exact region expansion is computationally expensive.
• Existing efficient methods rely on square quadtrees and the L∞-norm, limiting applicability.

Purpose of the Study:

• To adapt the L∞-norm metric and region expansion algorithm for regular triangulated meshes.
• To enable efficient approximation of region expansion on non-square grids.

Main Methods:

• Adapted the L∞-norm metric for triangulated meshes.
• Modified existing quadtree-based algorithms for triangular nodes.
• Developed an efficient approximation algorithm for region expansion.

Main Results:

• Achieved sublinear time complexity with respect to the expansion radius.
• Demonstrated efficient region expansion approximation on triangulated meshes.
• Enabled region expansion for applications like spherical surface approximation.

Conclusions:

• The adapted algorithm efficiently approximates region expansion on triangulated meshes.
• This method overcomes limitations of square quadtree approaches.
• Offers a faster solution for region expansion in image processing and surface approximation.