doi:10.1016/S1568-4946(03)00039-5
Copyright © 2003 Elsevier B.V. All rights reserved.
Space partitioning based image compression using quality measures for subdivision decision
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Munaga V. N. K. Prasad
, 
, V. N. Mishra and K. K. Shukla
Department of Computer Engineering, Institute of Technology, Banaras Hindu University, Varanasi 221005, India
Received 24 July 2002;
revised 16 April 2003;
accepted 15 May 2003. ;
Available online 28 August 2003.
Abstract
This paper presents new partitioning methods for image compression using different image quality measures, which are improvements of the recently published Binary Tree Triangular Coding (BTTC) algorithm. The technique is based on recursive partitioning of the image domain into right-angled triangles arranged in a binary tree. All the partitioning methods proposed in this paper execute in O(n log n) time for encoding and θ(n) time for decoding, where n is the number of pixels in the image. Simulation results on standard test images show that the new methods produce significant improvement in quality as compared with conventional BTTC for comparable compression ratios.
Author Keywords: Image compression; Quality measures; Fuzzy compactness; Average difference; Entropy; Mean square error
Fig. 1. (a) Example of domain partition process; (b) tree representation of the decomposition.
Fig. 2. Possible domain partition and the resulting binary string
s.
Fig. 3. The Binary Tree Triangular Coding algorithm.
Fig. 4. Representation of adjacent pixels in the image.
Fig. 5. Pictorial representation of membership function.
Fig. 6. Original test images Lenna, Barbara, cameraman, baboon and World Trade Center from left to right.
Fig. 7. Domain triangulation for image Lenna using AD.
Fig. 8. Variation in peak signal to noise ratio for image Lenna.
Fig. 9. Variation in number of clock ticks for image Lenna.
Fig. 10. Comparative results of BTTC, AD, entropy, MSE and FC using test images cameraman, WTC, Lenna, Barbara, and baboon at similar compression ratio of 2.939: (a) variation in PSNR; (b) variation in number of clock ticks.
Fig. 11. Reconstructed Lenna images using AD at compression ratios of 1.85, 2.16, 2.46 and 2.70 from left to right.
Fig. 12. Distribution of triangulation with different quality factors. Subsampled Lenna image scaled by factor 4 (a) and domain triangulation of subsampled Lenna using BTTC (b), AD (c), entropy (d), MSE (e) and FC (f) at same number of triangles formed, i.e. 380.
Table 1. Distortion measures for the image Lenna
Table 2. Computing time statistics for the image Lenna
Corresponding author. Tel.: +91-542-2369-709; fax: +91-542-2369-709.
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