A fast region segmentation algorithm on compressed gray images using Non-symmetry and Anti-packing Model and Extended Shading representation

Abstract

Image segmentation is one of the fundamental steps in image analysis for object identification. The main goal of image segmentation is to recognize homogeneous regions within an image as distinct and belonging to different objects. Inspired by the idea of the packing problem, in this paper, we propose a fast O(Nα(N))-time algorithm for image segmentation by using Non-symmetry and Anti-packing Model and Extended Shading representation, which was called the NAMES-based algorithm, where N is the number of homogenous blocks and α(N) is the inverse of the Ackerman’s function and it is a very slowly growing function. We first put forward four extended Lemmas and two extended Theorems. Then, we present a new scanning method used to process each NAMES block. Finally, we propose a novel NAMES-based data structure used to merge two regions. With the same experimental conditions and the same time complexity, our proposed NAMES-based algorithm, which extends the popular hierarchical representation model to a new non-hierarchical representation model, has about 86.75% and 89.47% average execution time improvement ratio when compared to the Binary Partition Tree (BPT)-based algorithm and the Quadtree Shading (QS)-based algorithm which has about 55.4% execution time improvement ratio when the QS-based algorithm itself is compared to the previous fastest region segmentation algorithm by Fiorio and Gustedt whose O(N2)-time algorithm is run on the original N×N gray image. Further, the NAMES can improve the memory-saving by 28.85% (5.04%) and simultaneously reduce the number of the homogeneous blocks by 49.05% (36.04%) more than the QS (the BPT) whereas maintaining the satisfactory image quality. Therefore, by comparing our NAMES-based algorithm with the QS-based algorithm and the BPT-based algorithm, the experimental results presented in this paper show that the former has not only higher compression ratio and less number of homogenous blocks than the latter whereas maintaining the satisfactory image quality, but also can significantly improve the execution speed for image segmentation, and therefore it is a much more effective algorithm for image segmentation.