Finding neighbours on bincode-based images in O(n log log n) time

The interpolation-based bintree is a storage-saving encoding scheme for representing binary images. It represents the image by using a sequence of increasing positive integers, called bincodes. In this paper, an efficient algorithm for solving the problem of neighbor finding on bincodes is presented. The time complexity of the algorithm is O(n log log n), where n is the number of the bincodes. In addition, experimental results are included to confirm the theoretical analysis. These experimental values show that our algorithm is faster than the previous best known results (Huang and Chung, 1995a,b). Furthermore, by using the conversion algorithms, we can apply our algorithm for the neighbor-finding problem on images represented by other representations such as the locational codes, the DF-expression, the S-tree, and the Morton codes to achieve better performance.