In this work a lossless wavelet-fractal image coder is proposed. The process starts by compressing and decompressing the original image using wavelet transformation and fractal coding algorithm. The decompressed image is removed from the original one to obtain a residual image which is coded by using Huffman algorithm. Simulation results show that with the proposed scheme, we achieve an infinite peak signal to noise ratio (PSNR) with higher compression ratio compared to typical lossless method. Moreover, the use of wavelet transform speeds up the fractal compression algorithm by reducing the size of the domain pool. The compression results of several welding radiographic images using the proposed scheme are evaluated quantitatively and compared with the results of Huffman coding algorithm.
EdwardG., Inspection of welded joints, In ASM Handbook Welding6(1993), 1081–1088.
2.
SchwartzC., Automatic evaluation of welded joints using image processing on radiographs, Proceeding of American Institute of Physics657 (2003), 689–694.
3.
VilarR., ZapataJ. and RuizR., An automatic system of classification of weld defects in radiographic images, NDT&E International42(5) (2009), 467–476.
4.
MekhalfaF. and NacereddineN., Multiclass Classification of Weld Defects in Radiographic Images based on Support Vector Machines, In Proceedings of The 10th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS)2014, 1–6.
5.
HuffmanD.A., A method for the construction of minimum redundancy codes, Proceeding of The Institute of Radio Engineers40 (1952) 1098–1101.
6.
WelchT., A technique for high performance data compression, IEEE on Computer17(6) (1984), 8–19.
7.
GershoA. and GrayR.M., Vector Quantization and Signal Compression, Kluwer Academic Publishers1993, 309–343.
8.
AndrewsH.C. and PrattW.K., Transform image coding, Processing Communication1969, 63–84.
9.
SalomonD. and MottaG., Handbook of data compression, Springer, 5th edition, 2009.
10.
BarnsleyM.F. and SloanA.D., A better way to compress images, Byte Magazine13(1) (1988), 215–223.
11.
JacquinA.E., A fractal theory of iterated Markov operators with applications to digital image coding, Ph. D. Dissertation, Georgia Institute of Technology, Atlanta, GA, 1989.
12.
KoliN.A. and AliM.S., A survey on the Fractal Image Compression Key Issues, Information Technology Journal7(8) (2008), 1085–1095.
13.
WohlbergB. and de JagerG., A review of the fractal image coding literature, IEEE Trans on Image Processing8 (1999), 1716–1728.
14.
MallatS.G., A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans Pattern Anal Machine Intel11 (1989), 674–693.
15.
AntoniniM., BarlaudM., MathieuP. and DaubechiesI., Image coding using wavelet transform, IEEE Trans on Image Processing5 (1992), 205–220.
16.
ResnikoffL.H., RaymondO. and WellsJr., Wavelet Analysis: The scalable Structure of Information, Springer, 2nd edition, 2002.
17.
RehnaV.J. and Jeya KumarM.K., Hybrid approaches to image coding: A review, International Journal of Advanced Computer Science and Applications2(7) (2011), 108–115.
18.
PentlandA. and HorowitzB., A practical approach to fractal based image compression, Proceeding of Data Compression Conference, Snowbird, Utah, April 8–11 (1991), 1976–1985.
19.
BarahavZ. and MalahD., Hierarchical interpretation of fractal image coding and its application to fast decoding, Proceeding of IEEE International Conference on Digital Signal Processing1993, 190–195.
20.
DubridgeF., Fast image coding by hierarchical fractal construction, In Preprint of The UCSD, San Diego1995.
21.
DavisG.M., Self-quantized wavelet subtrees: A wavelet based theory of fractal image compression. In SZUH.H. editor, Wavelet Applications II of SPIE Proceedings2491 (1995), 141–152.
22.
KrupnikH., MalahD. and KarninE., Fractal representation of images via the discrete wavelet transform, In Proceeding of The 18th IEEE Convention of Electrical and Electronics Engineers (1995), 2.2.2./1–5.
23.
Van De WalleA., Merging fractal image compression and wavelet transform methods, In Nato ASI on Fractal Image Encoding and Analysis1995, 8–17.
24.
SimonB., Explicit link between local fractal transform and multiresolution transform, IEEE International Conference on Image Processing1 (1995), 278–281.
25.
RinaldoR. and CalvagnonG., Image Coding by Block Prediction of Multiresolution Subimages, IEEE Transactions on Image Processing7 (1995), 1–11.
26.
DavisG.M.and WaveletA., Based Analysis of Fractal Image Compression, IEEE Transaction on Image Processing7(2) (1998), 141–154.
27.
LiJ. and Jay KuoC.C., Hybrid Wavelet-Fractal Image Compression Based on A rate-Distortion Criterion, Proc. SPIE 3024, Visual Communications and Image Processing3024 (1997), 1014–1025.
28.
ZhangL. and XiL., Hybrid image compression using fractal-wavelet prediction, In Proceedings of The 5th WSEAS International Conference on Information Security and Privacy Table of Contents2006, 112–117.
29.
KimT., DyckR.E. and MillerD.J., Hybrid Fractal Zerotree Wavelet Image Coding, Signal Processing, Image Communication17 (2002), 347–360.
30.
ShapiroJ.M., Embedded image coding using zerotrees of wavelet coefficients, IEEE Trans On Signal Processing41(12) (1993), 3445–3462.
31.
IanoY., Da SilvaF.S. and CrusA.L., A fast and Efficient Hybrid Fractal-Wavelet Image Coder, IEEE Transaction Image Processing15(1) (2006), 98–105.
SaidA. and PearlmanW.A., A new fast and efficient image codec based on set partitioning in hierarchical trees, IEEE Trans On Circuits Systems Video Technology6(3) (1996), 243–250.
34.
DuraisamyR., ValarmathiL. and AyyappanJ., Iteration Free Hybrid Fractal-Wavelet Image Coder, International Journal of Computational Cognition6(4) (2008), 34–40.
35.
ChangH.T. and KuoC.J., Iteration free fractal image coding based on efficient domain pool design, IEEE Trans On Image Process9(3) (2000), 329–339.
36.
JacquinA.E., Image coding based on a fractal theory of iterated contractive image transformation, IEEE Trans On Image Processing1(1) (1992), 18–30.
37.
AvanakiM.R.N., AberA. and EbrahimpourR., Compression of cDNA Microarray Images based on pure-fractal and wavelet-fractal techniques, ICGST-GVIP Journal11(1) (2011), 43–52.
38.
HaarA., Zur Theorie der orthogonalen Funktionen Systeme, Mathematische Annalen69 (1910), 331–371.
39.
AhmadA., KrillB., AmiraA. and RabahH., 3D Haar wavelet transform with Dynamic partial Reconfiguration for 3D medical image compression, IEEE Biomedical Circuits and Systems Conference2009, 137–140.
40.
MekhalfaF. and BerkaniD., Hybrid Wavelet-Fractal Image Coder Applied, Radiographic Images of Weld Defects, Communications in Computer and Information Science166 (2011), 753–761.
41.
PujarJ.H. and KadlaskarL.M., A new lossless Method of Image Compression and Decompression Using Huffman Coding Techniques, Journal of Theoretical and Applied Information Technology15 (2005), 18–22.
