How to Efficiently Identify and Outline Concave Holes within a 2D Point Set?

Identifying and Outlining Concave Holes in 2D Point Sets

This problem involves identifying and outlining concave regions (holes) within a 2D point cloud, a common task in various fields like agriculture (as described), astronomy, and image processing. The challenge lies in the need for an algorithm that's robust to varying point densities and allows for adjustable sensitivity to define the concavity of the resulting polygons.

The difficulty in finding readily available algorithms stems from the fact that a universally accepted, single "best" solution doesn't exist. The optimal approach depends heavily on the specific characteristics of your data and the desired level of accuracy and computational efficiency.

Search Terms and Approaches:

Instead of searching for a specific algorithm name, focus on these search terms:

• "Concave hull algorithm": This is a more accurate term than "concave polygon" as it directly addresses the problem of finding the boundary of a concave region.
• "Alpha shapes": Alpha shapes are a well-established technique for constructing a shape from a point set, allowing for control over the concavity through a parameter (alpha). They are particularly suitable for identifying holes.
• "Constrained Delaunay triangulation": This technique can be used to create a triangulation of the point set, and then identify holes by examining the triangles that are not connected to the exterior boundary.
• "Voronoi diagram": While not directly identifying holes, the Voronoi diagram can provide useful information about the spatial distribution of points, which can be used as a preprocessing step for hole detection.
• "Point cloud hole filling": Although focused on filling holes, algorithms in this area often use techniques that can be adapted to identify the hole boundaries.
• "Region growing": This is a general image processing technique that could be adapted to identify connected regions of empty space within your point cloud.

Algorithm Suggestions (Conceptual):

1. Alpha Shapes Approach: This is likely the most suitable starting point. Implement an alpha shape algorithm. Experiment with different alpha values to control the sensitivity. Smaller alpha values will result in more detailed shapes, capturing smaller holes, while larger values will smooth out the shapes, potentially merging small holes. Holes will appear as separate polygons within the overall alpha shape.

2. Delaunay Triangulation and Hole Detection:

   • Create a Delaunay triangulation of your point set.
   • Identify boundary edges (edges that only belong to one triangle).
   • The triangles not connected to the exterior boundary edges define the holes.
   • To create concave polygons from these triangles, you might need a post-processing step, potentially involving a concave hull algorithm on the vertices of these inner triangles.

3. Distance-Based Approach:

   • For each point, calculate its distance to its nearest neighbor.
   • Points with significantly larger distances to their nearest neighbors might indicate the boundary of a hole.
   • Apply a clustering or contouring algorithm to group these points and form the polygon representing the hole.

Implementation Notes (C#):

Several C# libraries provide implementations of Delaunay triangulation and alpha shapes. Research libraries like:

• Computational Geometry Algorithms Library (CGAL) (though it might require some interfacing with C ).
• AForge.NET (offers image processing capabilities that could be adapted).

Remember that you'll likely need to adapt and combine different techniques to achieve the best results for your specific application. Start with the alpha shapes approach, as it's relatively straightforward to implement and offers good control over the sensitivity. If performance becomes an issue with very large datasets, consider optimizing the algorithm or using more sophisticated spatial indexing techniques.

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