Efficient region segmentation on compressed gray images using quadtree and shading representation

Abstract Image segmentation, which partitions the image into homogeneous regions, is a fundamental operation in image processing. Suppose the input gray image with size N × N has been compressed into the compressed image via quadtree and shading representation. Assume that the number of blocks in the representation is B , commonly B N 2 due to the compression effect. This paper first derives some closed forms for computing the mean/variance of any block and for calculating the two statistical measures of any merged region in O (1) time. It then presents an efficient O ( Bα ( B ))-time algorithm for performing region segmentation on the compressed image directly where α ( B ) is the inverse of the Ackerman's function and is a very slowly growing function. With the same time complexity, our results extend the pioneering results by Dillencourt and Samet from the map image to the gray image. In addition, with four real images, experimental results show that our proposed algorithm has about 55.4% execution time improvement ratio when compared to the previous fastest region-segmentation algorithm by Fiorio and Gustedt whose O ( N 2 )-time algorithm is run on the original N × N gray image.