The $\alpha $ -tree is an effective hierarchical image representation used for connected filtering or segmentation in remote sensing and other image applications. The $\alpha $ -tree constructs a tree based on the dissimilarities of the pixels in an image. Compared to other hierarchical image representations such as the component tree, the $\alpha $ -tree provides a better representation of the granularity of images and is easier to apply to multichannel images. The major drawback of the $\alpha $ -tree is its processing speed, due to the large amount of data to be processed and the lack of studies on an efficient algorithms, especially on multichannel and high dynamic range images. In this study, we introduce a novel adaptation of the hybrid component tree algorithm on the $\alpha $ -tree for fast parallel $\alpha $ -tree construction in any dynamic range of pixel dissimilarity. We tested the hybrid $\alpha $ -tree algorithm on Sentinel-2 remote sensing images from the European Space Agency (ESA) as well as randomly generated images, on the Hábrók high performance computing cluster. Experimental results show that the hybrid $\alpha $ -tree algorithm achieves the processing speed of 10-30Mpix/s and the speedup of 10-30 on a 128-core computer, proving the efficiency of the first parallel $\alpha $ -tree algorithm in high dynamic range, to the best of our knowledge.

The α-tree algorithm is a useful hierarchical representation technique which facilitates comprehension of images such as remote sensing and medical images. Most α-tree algorithms make use of priority queues to process image edges in a correct order, but because traditional priority queues are inefficient in α-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 α-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 α-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.

Estimation of the background is an essential step in automated extraction of faint, extended objects from large-scale, optical surveys in astronomy. In this paper we present an improvement on the background estimation method of a commonly used tool in this field: Source Extractor (SEx-tractor). We show that the original method suffers from bias caused by presence of extended sources, and present an alternative which greatly reduces this effect, leading to much better preservation of faint extended structures.