COMPRESSION ALGORITHM,S BY
USING WAVELETS
*Chakresh kumar, **Chandra Shekhar,**Seema Das,**Shampy Bhandari
* Department of Electronics and communication Engineering, Galgotias College of Engineering and Technology, Greater Noida-201306
**Deptt of Electronics & Communication Engineering, Dronacharya College of Engineering Gurgaon-123506, India
Abstract— Large volumes of fingerprints are collected and stored every day in a wide range of applications,
including forensics, access control etc. In this digital world, police forces use Automated Fingerprint Identification Systems (AFIS) to match fingerprints. The database of Federal Bureau of Investigation (FBI) which contains more than 70 million finger prints. In these systems, fingerprint image compression is essential. Wavelet based Algorithms for image compression are the most successful, which result in high compression ratios compared to other compression techniques. Then set partitioning in hierarchical trees (SPIHT) which is applied to get better quality, i.e., high peak signal to noise ratio (PSNR).
We present optimized biorthogonal and orthonormal wavelets for embedded zero tree wavelet compression of fingerprint images.
I. INTRODUCTION
FINGERPRINTS are the ridge and furrow patterns on the tip of the finger and are used for personal identification of the people [1]. An automatic recognition of people based on fingerprints requires that the input fingerprint be matched with candidates within a large number of fingerprints. The FBI Identification Division collected 25 millions fingerprint cards by 1992[2]. Each fingerprint card requires approximately 10 MB of storage .Thus; the 25 million fingerprint cards require 245,000 GB of storage. To reduce the storage requirements, the captured data must be compressed. The minutiae and their relations in a fingerprint are the key features for identification.That means any
reconstructed image must preserve these features.
One of the main difficulties in developing compression algorithms for fingerprints resides preserving the ridge endings and bifurcations. Compression can be achieved by applying various transformation techniques. To avoid redundancy, which hinders compression, the transform must be at least biorthogonal and in order to save CPU time, the corresponding algorithm must be fast In this paper we focus on 2-D wavelet coding technique because it satisfies all the above conditions well and moreover every function in a wavelet basis is a dilated and translated version of one mother wavelet. That allows transformation to be carried out more successfully than other techniques such as DST, DCT and DFT.
II. WAVELET CODING AND SPIHT
Initialization n = log2 (max |coeff|)
LIP = All elements in H LSP = Empty
LIS = D’s of Roots
Sorting Pass
Process LIP
for each coeff (i,j) in LIP Output Sn(i,j)
If Sn(i,j)=1
O/p sign of coeff(i,j): 0/1 = -/+ Move (i,j) to the LSP
Endif
End loop over LIP
Process LIS
for each set (i,j) in LIS if type D Send Sn(D(i,j)) If Sn(D(i,j))=1
for each (k,l) O(i,j)
output Sn(k,l)
if Sn(k,l)=1, then add (k,l) to the LSP and output sign of coeff: 0/1 = -/+ if Sn(k,l)=0, then add (k,l) to the end of the LIP
endfor endif
else (type L ) Send Sn(L(i,j))
If Sn(L(i,j))=1
add each (k,l) O(i,j) to the end of the LIS as an entry of type D. remove (i,j) from the LIS
end if on type
End loop over LIS
Refinement Pass
Process LSP
for each element (i,j) in LSP – except those just added above Output the nth most significant bit of coeff
End loop over LSP
Update
Decrement n by 1 Go to sorting pass.
Where:
O(i,j): set of coordinates of all offspring of node (i,j); children only
D (i,j): set of coordinates of all descendants of node (i,j); children, grandchildren, great-grand, etc. H (i,j): set of all tree roots (nodes in the highest pyramid level); parents
L (i,j): D (i,j) – O(i,j) (all descendents except the offspring); grandchildren, great-grand, etc.
FIGURE 1
III. OPTIMIZATION OF WAVELETS
A basis that spans a space does not have to be orthogonal. In order to gain greater flexibility in the construction of wavelet bases, we resort to relaxing the orthogonality condition and allowing non-orthogonal wavelet bases[7]. For example, it is well-known that the Haar wavelet is the only known wavelet that is compactly supported, orthogonal, and symmetric. In many applications, the symmetry of the filter coefficients is often desirable since it results in linear phase of the transfer function. So in order to construct more families of compactly supported, symmetric wavelets, in this section we forego the requirement of orthogonality, and, in particular, we introduce the so-called biorthogonal wavelets[8].
Properties of orthogonal & Bi-orthogonal Wavelets that make them important tool for image compression are: 1.Compactly supporting:
On the basis of compacltly supporting the bi-orthogonal & Orthogonal wavelets are more compactly supported than any other wavelets.
2. Symmetry:
Symmetric scaling functions and wavelets are important because they are used to build bases of regular wavelets over an interval, rather than the real axis. Daubechies has proved that, for a wavelet to be symmetric or antisymmetric, its filter must have a linear complex phase, and the only symmetric compactly supported conjugate mirror filter is the Haar filter, which corresponds to a discontinuous wavelet with one vanishing moment. Besides the Haar wavelet, there is no symmetric compactly supported orthogonal wavelet.
Unlike the orthogonal case, it is possible to synthesize biorthogonal wavelets and scaling functions, which are symmetric or antisymmetric.
We optimize wavelets for fingerprint image compression by searching the space of wavelet filter coefficients to minimize an error metric. Optimizations were done for filter lengths of 8 and 10 taps, corresponding to 3 and 4 annealed variables respectively. For an orthonormal 2n-tap wavelet there are also n-1 free coefficients, due to the normalization condition and the n orthogonality conditions
hihi2k k 0.
Type of Wavelet
No of taps Rms error
Biorthogonal 10 6.876(best)
Biorthogonal 8 6.937
Biorthogonal 7 7.128(Worst)
Orthogonal 10 8.349
Orthogonal 8 8.873
The above table shows the comparative analysis of type of wavelet filter used with variable no of taps. Their respective rms error can be calculated. We can select the best filter for different images because no single filter can be proved best for all the images.
By using optimized wavelet with SPIHT algorithm compression ratio upto 20:1 can be achieved.
IV. RESULTS
Using optimized Biorthogonal and Orthogonal wavelets with SPIHT algorithm does the compression. The compression ratio of 20:1 is achieved by using our technique and gives better results than any other compression technique. The figure 2 shows the original and compressed image of fingerprint. This compressed fingerprint can be analyzed by experts for fingerprint matching and can be transmitted by wireless connections using lesser bandwidth and airtime.
Original image FIGURE 2 (a)
V. REFRENCES
[1] C. H. Park, J. J. Lee, M. J. T. Smith, S. I. Park, and K. H. Park, "Directional filter bank-based fingerprint feature extraction and matching," IEEE Trans. on Circuits and Systems for Video Technology., vol. 14, no. 1, pp. 74-84, Jan. 2004.
[2] Federal bureau of investigation ‘WSQ gray scale fingerprint image compression specification’.document IAFIS-IC-0110v2 Februry 1993. [3] Shaprio, J.M; ‘Embedded image coding zerotree of wavelet coefficients, IEEE transactions on signal processing Vol 41, No 12, pp
3445-3462, December 1993.
[4] Sherlock B.G, Monro D.M and millard; ‘Fingerprint enhancemet by directional fourier filtering’, IEEE proceeding-vision, image & signal processing vol 141, No 2 ,pp 87-94,April 1994.
[5] C. H. Park, J. J. Lee, M. J. T. Smith, S. I. Park, and K. H. Park,"Directional filter bank-based fingerprint feature extraction and matching," IEEE Trans. on Circuits and Systems for Video Technology., vol. 14, no. 1, pp. 74-84, Jan. 2004.
[6] A. Said and W. A. Pearlman, "A New fast and efficient image codec based on set partitioning in hierarchical trees", IEEE Trans. On Circuits and Systems for Video Technology, vol. 6, no.3 pp 243-250, Jun. 1996.
[7] Daubechies “orthonormal bases of compactly supported wavelets,’ Comm pure Appl. Mtah Vol 41, pp 909-966, 1998.
[8] S. M. Phoong, C. W. Kim, P. P. Vaidyanathan, and R. Ansari, "A new class of two-channel biorthogonal filter banks and wavelet bases", IEEE Trans. on signal Processing, vol. 43, no.3, pp. 649-665, Mar. 1995
