A Fast Alpha-Tree Algorithm for Extreme Dynamic Range Pixel Dissimilarities

The
$\alpha$
-tree algorithm is a useful hierarchical representation technique which facilitates comprehension of images such as remote sensing and medical images. Most
$\alpha$
-tree algorithms make use of priority queues to process image edges in a correct order, but because traditional priority queues are inefficient in
$\alpha$
-tree algorithms using extreme-dynamic-range pixel dissimilarities, they run slower compared with other related algorithms such as component tree. In this paper, we propose a novel hierarchical heap priority queue algorithm that can process
$\alpha$
-tree edges much more efficiently than other state-of-the-art priority queues. Experimental results using 48-bit Sentinel-2 A remotely sensed images and randomly generated images have shown that the proposed hierarchical heap priority queue improved the timings of the flooding
$\alpha$
-tree algorithm by replacing the heap priority queue with the proposed queue: 1.68 times in 4-N and 2.41 times in 8-N on Sentinel-2 A images, and 2.56 times and 4.43 times on randomly generated images.