3.2 Adaptive color decorrelation
3.2.1 Improving decorrelation process: multi component pixel classification
Different studies have been realized so that to lower the resulting bitrate. In particular, solutions based on classification processes have been designed. Indeed, classification can be used to improve the compression ratio of any codec thanks to the principle of conditional entropy. Let A, B and C be three statistical variables. Conditional entropy follows the relation
H(C) ≥ H(C|A) + H(C|B),
where A ∩ B = ∅, X ∩ A ∪ X ∩ B = X, H(X|A) being the entropy of X knowing A and H(X|B) being the entropy of X knowing B. Therefore if we can divide error values into different classes thanks to new information given by the context, it would lower the overall entropy and improve the
compression ratio. Classification requires then both context modeling tools as well as classification criteria.
Pixel spatial classification has been first defined in [143] and then is extended to multi-component images through a local activity based classification process [144][145], in the case of the Interleaved S+P framework.
In this document, we focus on the generic multi-component image -based solution.
3.2.1.1 Inter-component classification
As shown in [144], classification performed on pixels according to their neighborhood can improve the compression ratio. The same principle has been extended to multi component images, as for example color images. Such an algorithm tries to use the residual correlation between different components of an image to perform an accurate classification. Actually contours are more prone to have high error values whereas homogeneous areas produce low error values. Those areas tend to be located in the same position between the different image components, leading to propose a dedicated inter-component classification.
Inter-component classification is performed after the prediction scheme as shown on figure3.2. In this classification scheme, the goal is to classify (εZC)Q with information coming from (εZY)Q.
+ Prediction ++ - Y Z
Prediction Entropy Coding Entropy Coding Y compression C compression - + Entropy Coding Entropy Coding Classification 1 Cl 2 Cl 3 Cl Y Z C Z ZC ~ C Z
Y Z~Figure 3.2: Multi component classification scheme
The proposed inter-component classification is performed according to the following algorithm. Let Cl1, Cl2 and Cl3 be the three classes of the classification.
1. One of the three components is used as a reference Y to code another component C, Y coding process is thus not modified.
2. Histogram of absolute values of (εZY)Q is computed. 3. A first error threshold T 1 is set to the histogram mean.
5. Classification is then performed as follows: 6. Cl1= {(εZC)Q—abs((εZY)Q) < T 1}. 7. Cl2= {(εZC)Q—T 1 ≤ abs((εZY)Q) < T 2}. 8. Cl3= {(εZC)Q—T 2 ≤ abs((εZY)Q)}.
When considering the Interleaved S+P framework, as the 2G, 3M and 3G images present different characteristics in terms of error distribution, the inter component classification scheme is performed independently for each type of errors. It leads to three different classifications for both Flat and Texture coefficients. The aim of such a context modeling is to perform discriminations inside each type of errors. Thus, coefficients of a given type producing the same error distribution are gathered into one context class.
A set of three pictures has been used to evaluate the performances of the proposed solution. This set includes peppers, mandrill and lena pictures (table3.1). Each of them has different characteristics: mandrill image has high frequencies whereas peppers image features large areas of identical colour. Finally lena has both high frequencies and low frequencies respectively located in her hair and on the background. To obtain comparable results with other image coders such as JPEG2K, a simple arithmetic coder has been used. Four different color spaces were used for the compression, RGB, YCgCo-R [119], O1O2O3 [43] and the Reversible color transform used in JPEG2K [80]. All these color spaces are reversible and can therefore be used for lossless coding [144].
Except for peppers picture, performing colour space decorrelation improves compression results. The YCoCg-R, O1O2O3 and YDbDR colour spaces offer an average 4% gain on mandrill picture and an average 2.5% gain on lena image. The specificity of peppers picture in regard of colour spaces is due to the fact that this image has mainly two predominant colours, red and green. Therefore RGB colour space can, in this particular case, leads to better results. However, even if it produces the best improvement, compression using the RGB colour space remains less efficient in terms of compression ratio than the other colour spaces.
Despite the general use of color images, the development of image codecs such as JPEG, JPEG2K or the newly standardized JPEGXR has been primarily focused on giving the best performance on single component images. To handle color images, state of the art codecs usually rely on color transforms such as YUV, YCgCo and/or subsampling steps to achieve both good compression ratio and good visual quality. However after performing color transforms and/or subsampling, each color component is independently encoded.
When considering lossless coding, coding techniques rely on statistical analysis of the image to perform compression. As subsampling would cause losses, only reversible color transforms can be used. However, even after applying static color transforms, residual correlation still exists between components [144]. This underlaying correlation results in an suboptimal compression rate as decor- relation has been statically done without consideration of the statistics of the image itself. A critical application of lossless coding of colour images concerns cultural digital libraries [116]. Museums actually try to safely digitalize their belongings and thus to produce large quantities of lossless colour pictures. Moreover, current digital cameras are widespread and generate high resolution colour images. Professional photographers tend to prefer lossless compression of their pictures to avoid artifacts due to image compression.
To improve the compression ratio of color images for lossless coding as well as quality for lossy coding purposes, different approaches have been studied. In particular, performing adaptive inter
peppers Alone Classification
YCoCg-R 14.975 14.898
O1O2O3 14.968 14.896
YDbDr 15.048 14.960
RGB 14.907 14.767
mandrill Alone Classification
YCoCg-R 18.170 18.121
O1O2O3 18.106 18.065
YDbDr 18.122 18.084
RGB 18.948 18.705
lena Alone Classification
YCoCg-R 13.582 13.437
O1O2O3 13.536 13.392
YDbDr 13.577 13.422
RGB 13.914 13.662
Table 3.1: Compression results in bpp
component decorrelation was considered. Such an adaptive decorrelation differs from usual reverse color transforms by its automatical adaptivity to the image statistics.