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Distance transform for images represented by quadtrees.

¹Department of Computer Science, University of Maryland, College Park, MD 20742.

IEEE Transactions on Pattern Analysis and Machine Intelligence

|August 27, 2011

Summary

This study adapts image processing distance metrics to quadtree representations, introducing a chessboard distance transform. This new method efficiently calculates distances from black nodes to white nodes in quadtrees.

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Area of Science:

Computer Science
Image Processing
Computational Geometry

Background:

Traditional image processing often uses binary array representations for distance calculations.
Quadtrees offer a hierarchical data structure for image representation, but adapting distance metrics can be challenging.

Purpose of the Study:

To adapt the concept of distance from binary array image representations to quadtree representations.
To define and compute a chessboard distance transform for quadtrees.

Main Methods:

The chessboard distance metric was adapted for quadtree structures.
A novel algorithm was developed to compute the chessboard distance transform by examining black nodes and their neighbors (including diagonal).
The algorithm's efficiency was analyzed in relation to the number of leaf nodes.

Main Results:

The chessboard distance metric is suitable for quadtree representations.
A chessboard distance transform for quadtrees was defined as the minimum distance from black nodes to the border of white nodes.
The presented algorithm efficiently computes this transform, requiring diagonal neighbor identification.

Conclusions:

The chessboard distance transform provides a new method for analyzing spatial relationships in quadtree-represented images.
The algorithm offers an efficient approach to computing this transform, with performance tied to the quadtree's leaf node count.
This work extends distance transform concepts to hierarchical image data structures.