Reduction of Blocking Artifacts in Images by Michael Rauch & Benjamin Hofstetter

2002-05-30

Motivation The JPEG image compression standard is based on the DCT (Discrete Cosinus Transform) of the image. The quantization of the DCT coefficients results in blocking artifacts at high compression levels. This sheet gives an overview of different approaches to reduce those artifacts to enhance image quality and threats one of them in further detail. Fig 1: Blocking artifacts on the left image. Enhanced image on the right

Overview The basic idea for the reduction of artifacts is to smooth the image at the block boundaries where the blocking effect is highly visible. Pixels that are part of an image detail or edges in the image itself should be left untouched. Different Approaches: apply a space-variant low-pass filter (complex) exploit the cross-scale correlation among wavelet coefficients use anisotropic diffusion (complex, i guess) estimate the maximum-likelihood of the quantization noise (to smooth or not to smooth) use rational filtering, this approach is detailed in the next section

Algorith Details: Rational Filtering Basic Idea: In uniform areas where the brightness changes only slightly artifacts are seen as abrupt change of luminance at the block boundaries. This can be resolved by simply smoothing with a linear operator. In detailed areas the artifact removal has to be done more carefully to avoid losing image details. Details have to be recognized and the smoothing has to be done with a directional filtering which preserves the textures across the block boundaries. The entire procedure can be done with a local operator. The main issue is then to bias the behaviour between linear and directional filtering according to the local image characteristics.

A B C D E F G H I Fig 2: Filter window

Rational Filter: The rational filter modulates the coefficients of a linear low pass filter in order to limit its action in presence of image details. The numerator in Formula 1 has a low pass behaviour while the denominator is a function of the difference between couples of pixels within the filtering mask. Letters A-I in Formula 1 represent the pixel values shown in Fig 2. If the difference between two pixels is large, chances are good that the mask is located across a signal transition and the frequency response is automatically made less selective in the given direction. A I w 4 2 1 k' w A I D F w 4 2 1 k' w D F G C w 4 2 1 k'w G C w w 4 4 I 1 k'w D F 1 k'w G 

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2 L 





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Formula 1: Filter Output



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Formula 2: Bias determining parameter

Formula 2 shows the calculation of paramter k' which determines the biasing between linear and directional filtering. The proportion between the variance in the 3x3 window σL2 and the average variance of the entire image σΤη2 is used to decide upon the filtering behaviour. An external parameter k is used to further tweak the filtering degree to the desire outcome. The value of weight w is 0,25, which becomes obvious if we set k'=0. This corresponds to a linear filter.

References 'A simple algorithm for the reduction of blocking artifacts in images and its implementation' by Roberto Castagno, Stefano Marsi and Gianni Ramponi [http://ipl.univ.trieste.it/ipl/publications/itce98.ps.gz]