 Open Access
 Total Downloads : 18
 Authors : Kailash Babu B.S, Mrs.Asha N
 Paper ID : IJERTCONV2IS13108
 Volume & Issue : NCRTS – 2014 (Volume 2 – Issue 13)
 Published (First Online): 30072018
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Prediction Based CFA Image Compression and Demosaicking Using Lagrange Interpolation.
Kailash babu B.S Mrs.Asha N
4th Sem M.tech, Asst. Prof, Dept of CSE
APSCE, Bangalore APSCE, Bangalore
ABSTRACT
In most digital cameras, Bayer CFA images are captured and demosaicing is generally carried out before compression. Recently, it was found that compressionfirst schemes outperform the conventional demosaicingfirst schemes in terms of output image quality. An efficient predictionbased lossless compression scheme for Bayer CFA images is proposed in this paper. It exploits a context matching technique to rank the neighboring pixels when predicting a pixel, an adaptive color difference estimation scheme to remove the color spectral redundancy when handling red and blue samples. CFA image compression is carried out first and in the later stage same compressed CFA image is interpolated using Lagrange interpolation
.Simulation results show that the proposed compression and interpolation scheme can achieve a better compression performance than the existing interpolation algorithm.
INTRODUCTION
To reduce cost, most digital cameras use a single image sensor to capture color images. A Bayer color filter array (CFA) as shown in Figure 1, is usually coated over the sensor in these cameras to record only one of the three color components at each pixel location. The resultant image is referred to as a CFA image in this paper hereafter. In general, a CFA image is first interpolated via a demosaicing process to form a full color image before being compressed for storage. Figure 2a shows the workflow of this imaging chain. Recently, some reports indicated that such a demosaicingfirst processing sequence was inefficient in a way that the demosaicing process always introduced some redundancy which should eventually be removed in the following compression step. As a result, an alternative processing sequence which carries out compression before demosaicing as shown in Figure 2b has been proposed lately. Under this new strategy, digital cameras can have a simpler design and lower power consumption as computationally heavy processes like demosaicing can be carried out in an offline
powerful personal computer. This motivates the demand of CFA image compression schemes. There are two categories of CFA image compression schemes: lossy and lossless. Lossy schemes compress a CFA image by discarding its visually redundant information. These schemes usually yield a higher compression ratio as compared with the lossless schemes. Schemes presented in are some examples of this approach. In these schemes, different lossy compression techniques such as discrete cosine transform, vector quantization subband coding with symmetric short kernel filters , transform followed by JPEG or JPEG 2000 and lowpass filtering followed by JPEGLS or JPEG 2000 (lossless mode) are used to reduce data redundancy. In some highend photography applications such as commercial poster production, original CFA images are required for producing high quality full color images directly. In such cases, lossless compression of CFA images is necessary. Some lossless image compression schemes like JPEGLS and JPEG2000 can be used to en code a CFA image but only a fair performance can be attained. Recently, an advanced lossless CFA image compression scheme (LCMI) was proposed. In this scheme, the mosaic data is decorrelated by the Mallat wavelet packet transform, and the coefficients are then compressed by Rice code.
In this paper, a predictionbased lossless CFA compression scheme as shown in Figure 3 is proposed. It divides a CFA image into 2 subimages: a green subimage which contains all green samples of the CFA image and a nongreen subimage which holds the red and the blue samples. The green subimage is coded first and the non green subimage follows based on the green subimage as a reference. To reduce the spectral redundancy, the non green subimage is processed in the color difference domain whereas the green subimage is processed in the intensity domain as a reference for the color difference content of the nongreen subimage. Both subimages are processed in raster scan sequence with our proposed context matching based prediction technique to remove the spatial dependency. The prediction residue planes of the
two subimages are then entropy encoded sequentially with our proposed realization scheme of adaptive Rice code.
Experimental results show that the proposed compression scheme can effectively and efficiently reduce the redundancy in both spatial and color spectral domains. As compared with the existing lossless CFA image coding schemes such as [1012], the proposed scheme provides the best compression performance in our simulation study.
CONTEXT MATCHING BASED PREDICTION
The proposed prediction technique handles the green plane and the nongreen plane separately in a raster scan manner. It weights the neighboring samples such that the one has higher context similarity to that of the current sample contributes more to the current prediction. Accordingly, this prediction technique is referred to as context matching based prediction (CMBP) in this paper. The green plane (green subimage) is handled first as a CFA image contains double number of green samples to that of red/blue samples and the correlation among green samples can be exploited easily as compared with that among red or blue samples. Accordingly, the green plane can be used as a good reference to estimate the color difference of a red or blue sample when handling the nongreen plane (nongreen sub image).
Prediction on the green plane
As the green plane is raster scanned during the prediction and all prediction errors are recorded, all processed green
samples are known and can be exploited in the prediction of the pixels which have not yet been processed. Assume that we are now processing a particular green sample g(i,j) as shown in Figure 4a. The four nearest processed neighboring green samples of g(i,j) form a candidate set g(i,j)={g(i,j2), g(i1,j1), g(i2,j), g(i1,j+1)}. The candidates are ranked by comparing their support regions (i.e. context) with that of g(i,j). The support region of a green sample at position (p,q), Sg(p,q), is defined as shown in Figure 5a. In formulation, we have Sg(p,q)={(p,q2), (p 1,q1), (p2,q), (p1,q+1)}. The matching extent of the support region of g(i,j) and the support region of g(m,n) for g(m,n)g(i,j) is then measured by
Though a higher order distance such as Euclidian distance can be used instead of eqn.(1) to achieve a better matching performance, we found in our simulations that the improvement was not significant enough to for its high realization complexity.
Figure 4. Positions of the pixels included in the candidate set of (a) a green sample and (b) a red/blue
Sample
Figure 5. The support region of (a) a green sample and (b) a red/blue sample
Let g(mk,nk)g(i,j) for k=1,2,3,4 be the 4 ranked candidates of sample g(i,j) such that
D(Sg (i,j) , Sg (mu ,nu ) ) <= D(Sg (i,j) , Sg (mv ,nv ) ) for 1u<v4. The value of g(i,j) can then be predicted with a prediction filter as
where wk for k=1,2,3,4 are normalized weighting coefficients such that
Let Dir(i,j){W, NW, N, NE} be a direction vector associated with sample g(i,j). It is defined as the direction pointed from sample g(i,j) to g(i,j)s 1st ranked candidate g(m1,n1). Figure 6 shows its all possible values. This definition applies to all green samples in the green sub image. As an example, Figure 7 shows the direction map o a testing image shown in Figure 8. If the direction of g(i,j) is identical to the directions of all green samples in Sg(i,j), pixel (i,j) will be considered in a homogenous region and g (i, j) will then be estimated to be g(m1,n1) directly. In formulation, we have
Figure 6. The four possible directions associated with a green pixel
Which implies {w1, w2, w3, w4} = {1,0,0,0}. Otherwise, g(i,j) is considered to be in a heterogeneous region and a predefined prediction filter is used to estimate g(i,j) with eqn.(2) instead.
In our study, wk are obtained by quantizing the training result derived by linear regression with a set of training images covering half of the test images shown in Figure 8. They are quantized to reduce the realization effort of eqn.(2). After all, when g(i,j) is not in a homogeneous region, the coefficients of the prediction filter used to obtain the result presented in this paper are given by {w1, w2, w3, w4}={5/8, 2/8, 1/8, 0}, which allows the realization of eqn.(2) to be achieved with only shift and addition operations as follows.
The prediction error is determined with g(i, j) g(i, j) . Figure 9 summaries how to generate the prediction residue of the green plane of a CFA image.
In CMBP, a green sample is classified according to the homogeneity of its local region to improve the prediction performance. Figure 10 shows the effect of this classification step. By comparing Figures 10a and 10b, one can see that the approach with classification can handle the edge regions more effectively and more edge details can be eliminated in the corresponding prediction residue planes. Another supporting observation is the stronger decorrelation power of the approach using classification. Figure 11 shows the correlation among prediction residues in the green plane of testing image 8 under the two different conditions. The correlation of the residues
obtained with region classification is lower, which implies that the approach is more effective in data compression. Besides, the entropy of the prediction residues obtained with region classification is also lower. As far as testing image 8 is concerned, their zeroorder entropy values are, respectively, 6.195 and 6.039 bpp.
Prediction on the nongreen plane
of all green samples in Sc(i,j) are identical, pixel (i,j) can also be considered as in a homogenous region.
Prediction based CFA image compression
As for the case when the sample being processed is a red or blue sample in the nongreen plane, the prediction is carried out in the color difference domain instead of the green intensity domain as in the green plane. This is done to remove the interchannel redundancy. Since the nongreen plane is processed after the green plane, all green samples in a CFA image are known and can be exploited when
Image compression
Figure 7 CFA
processing the nongreen plane. Besides, as the nongreen plane is raster scanned in the prediction, the color difference values of all processed nongreen samples in the CFA image should also be known and hence can be exploited when predicting the color difference of a particular nongreen sample.
Let d(p,q) be the greenred (or greenblue) color difference value of a nongreen sample c(p,q). Its determination will be discussed in detail in Section 3. For any nongreen sample c(i,j), its candidate set is c(i,j)={d(i,j2), d(i2,j2), d(i2,j), d(i2,j+2)}, and its support region (context) is defined as Sc(i,j)={(i,j1),(i1,j), (i,j+1), (i+1,j)}. Figure 4b and Figure 5b, show, respectively, the positions of the pixels involved in the definition of c(i,j) and Sc(i,j). The prediction for a nongreen sample is carried out in the color difference domain. Specifically, the predicted color difference value of sample c(i,j) is given by
where wk and d(mk,nk) are, respectively, the kth predictor coefficient and the kth ranked candidate in c(i,j) such that ( S c(i,j ) , Sc(mu ,nu )) <= ( S c(i,j ) , Sc(mu ,nv ),S for 1u<v
4, where
In the prediction carried out in the green plane, region homogeneity is exploited to simplify the prediction filter and improve the prediction result. Theoretically, similar idea can be adopted in handling a nongreen sample by considering the direction information of its neighboring samples. For any nongreen sample c(i,j), if the directions
Most of the earlier methods were dealing with normal image compression, but CFA image compression is the new technique .the compression of a image results in loss of data and lead to low quality of image and leads to zipper effect and many other effects, in the proposed system we carry out a CFA image compression and later the same CFA is interpolated using lagrange interpolation this method results in better quality and low memory of a high resolution Image.
Lagrange interpolation
INPUT: vector x; vector y = f(x); a point to evaluate z OUTPUT: P z Lagrange polynomial P(x) evaluated at z Step 1 Initialize variables. Set P z equal zero. Set n to the number of pairs of points (x; y). Set
L to be the all ones vector of length n.
Step 2 For i = 1 to n do . . .
Step 3 For j = 1 to n do Step 4.
Step 4 If i 6= j then Li = (z xj)=(xi xj) Li
Step 5 P z = Li yi + P z
Step 6 Output P z. Stop
The two missing colors are estimated using the green and blue measurements made by neighboring pixels. This process is called interpolation. Each pixel will have three values the actual value of the color it measures through its filter, as well as two interpolated values for the two missing colors. The interpolation is applied to each and every pixel to obtain a full color image. The color interpolation process is known as demosaicing Lagrange interpolation results in better quality picture with reduced image size Overcomes fringe effects and false colors. Physical size of a digital camera can be reduced by using a single sensor.
EXPERIMENTAL RESULTS
A set of 6, 500 Ã— 500 (or 512 Ã— 768) Kodak color images is used to train the statistical model parameters of the proposed algorithm. Another set of 18 different Kodak color images is used to evaluate the performance of the algorithm. For performance comparison
For performance comparison we used different
interpolation methods such as bilinear interpolation, gradientbased interpolation
Fig. 8 shows the demosaic results. Fig. 8(a) shows a color image input Fig. 8(b) shows compressed CFA image 8(c) shows the interpolated image generated using lagrange interpolation. The proposed algorithm has the best overall PSNR average, outperforming the nearest method(bilinear interpolation) by 0.16 dB andgradient based method by
0.68 dB.
demosaicing solutions in terms of objective PSNR comparison. The performance of the proposed algorithm might be improved by using adaptive size lters in green channel inter polation stage instead of a xed lter. Introducing a gentle post processing step might also improve its results. However, additional computational cost and quality tradeoff is always a concern with post processing steps.
Original image
CFA image
Demosaick image
Figure 8 a )shows a color image input, b) compressed CFA image and c) image generated using lagrange interpolation
CONCLUSION
In this paper, we presented an easy to implement, noniterative, prediction based compression and interpolation demosaicing algorithm. Experimental results show that proposed algorithm outperforms other avail able
.
REFERENCES

B. E. Bayer, Color Imaging Array, U.S. Patent No. 3,971,065, July 20, 1976.

Y. T. Tsai, Color image compression for singlechip cameras, IEEE Trans. Electron
Devices, vol. 38, pp. 12261232, May 1991.

S.Y. Lee and A. Ortega, A novel approach of image compression in digital cameras with a
Bayer color filter array, Proc. IEEE Intl. Conf. Image Proc., vol. 3, pp. 482485, Oct. 2001.

C.C. Koh, J. Mukherjee, and S. K. Mitra, New efficient methods of image compression in

N. Zhang and X. Wu, Lossless compression of color mosaic images, IEEE Trans. Image
Proc., vol. 16, pp. 13791388, June 2006.

J. Shapiro, Embedded image coding using zerotrees of wavelet coefficients, IEEE Trans.
Signal Proc., vol. 41, pp. 34453462, Dec. 1993.

D. S. Taubman and M. W. Marcellin, JPEG2000: Image Compression Fundamentals,
Standards and Practice. Boston, MA: Kluwer Academic Publishers, 2002.

P. Schelkens, A. Skodras, and T. Ebrahimi (eds.), The JPEG 2000 Suite, Chichester, UK:
Wiley, 2009.

S. Srinivasan, C. Tu, S. L. Regunathan, and G. J. Sullivan, HD Photo: A New Image Coding
Technology for Digital Photography, Proc. SPIE Appl. Digital Image Proc. XXX, vol. 6696,
paper 669690, sequence number 6696 0A, pp. 119, Aug.
2007.

F. Dufaux, G. J. Sullivan, and T. Ebrahimi, The JPEG XR Image Coding Standard, IEEE
Signal Proc. Magazine, Standards in a Nutshell series, vol. 26, pp. 195199, Nov. 2009