Block Effect Reduction by the 1 D Grey Polynomial Interpolation Cheng Hsiung Hsieh1 and Ren Hsien Huang2 1 Department of Computer Science and Information Engineering Chaoyang University of Technology 2 Mars Semiconductor Corporation E mail chhsieh cyut edu tw Abstract In this paper the one dimensional grey polynomial interpolation 1 D GPI developed for image enlargement in 27 is applied to reduce the block effect in block discrete cosine transform BDCT image video coders Note that the block effect in BDCT coders results from insufficient bits for transform coefficients An interpolation approach is proposed to relieve the block effect problem The proposed approach consists of three stages First the input image is down sampled to reduce the amount of data Second the down sampled image is put into a BDCT coder such as JPEG and MPEG 2 Finally the 1 D GPI is applied to enlarge the decoded image Examples with the JPEG and MPEG 2 BDCT coder are provided to verify the proposed approach Simulation results indicate that the proposed scheme is able to effectively reduce the block effect significantly and therefore the subjective visual quality improved in the given examples Index Terms Grey 1 AGO Polynomial Interpolation Block Effect Block Discrete Cosine Transform Low Bit Rate Coding N I INTRODUCTION owadays image and video data are quite common in the network transmission Generally these data require large memory capacity and therefore large transmission bandwidth To relieve the problem image and video coding schemes are sought Among them the block discrete cosine transform BDCT is the most popular scheme for image and video compression because of its near optimum energy compaction and the availability of fast algorithms and hardwares Consequently the BDCT coder is extensively used by many current image video standards such as JPEG ITU T H 261 3 L and ISO MPEG 1 2 4 However one of problems in the BDCT coder is the block effect in low bit rate or high compression cases To deal with the problem several approaches have been reported recently For the still image coding standard JPEG several block effect reduction methods have been reported In 3 a low pass filter was applied to decoded image to smooth out the blockness However a blurred image resulted accordingly In 4 9 several types of de blocking filters and post processing were proposed Yet the improvement seemed not significant In 1115 the block effect reduction was performed in the wavelet domain which requires high computational cost generally In 1620 by the POCS Projection onto Convex Set the visual quality was enhanced significantly Nevertheless the computational complexity is quite high As for the video coding standard MPEG 2 several approaches to reduce block effect have been reported In 21 a lowpassfilter with Gaussian shaped impulse response was applied to the video sequence In 22 it utilized information obtained from the bitstream including DCT coefficients and motion vectors Based on the information each block was classified and detected for block effects To remove the block effect a filter was applied to the decoded images In 23 the slope measure was applied to the macro block MB boundaries to classify whether an MB was well compensated or not If it was not then the MB was adaptively quantized to reduce the block effect In this paper we propose a novel approach based on one dimension grey polynomial interpolation 1 D GPI to reduce the block effect in the BDCT coding When the JPEG and MPEG 2 are used in the proposed approach the coding systems are abbreviated as JPEG GPI and MPEG GPI respectively This paper is organized as follows In Section II 1 D polynomial interpolation is briefly reviewed Then the 1 D grey polynomial interpolation is described In Section III the proposed JPEGGPI and MPEG GPI coding systems are introduced In Section IV simulations are given to justify the proposed coding systems Finally conclusion is made in Section V II THE 1 D POLYNOMIAL INTERPOLATION In this section 1 D polynomial interpolation 1 D PI is briefly reviewed For details one may consult 24 Given x k the implementation steps for 1 D PI are described as follows Step 1 Assume x k is an L order polynomial as x k c L k L cL 1k L 1 c1k c0 Step 2 Substitute 1 k L 1 into 1 as x Vc L where elements of x c and V are x k c k and vkj k Step 3 1 2 j for 0 j L 1 k L 1 respectively Find the interpolated data x k 1 M as x k 1 M cL k 1 M L c1 k 1 M c0 3 where c k are the coefficients found in 2 Step 4 Obtain the final interpolated data as x k 1 M x k 1 M M 4 where M denotes an up sampling factor and is assumed an integer without the loss of generality III THE 1 D GREY POLYNOMIAL INTERPOLATION Note that randomness in data affects the performance of 1 D PI Therefore the performance can be improved by reducing the randomness in data And it is known that the preprocessing scheme in the grey system 25 the first order accumulated generating operation 1 AGO is able to reduce the randomness in data Consequently 1 AGO is incorporated into 1 D PI to improve the interpolation performance The new 1 D interpolation scheme is called 1 D grey polynomial interpolation 1 D GPI which is described as follows Given data x k 1 k L 1 the 1 AGO converted data is found as x 1 k k x i 5 i 1 for 1 k L 1 An example is depicted in Figure 1 where the original data x k is 1 4 2 5 3 and the 1 AGO converted data x 1 k is 1 5 7 12 15 It is easy to see the data after 1 AGO is smoother than the original data Thus it may improve the interpolation performance of 1 D PI In the 1 D GPI the 1 AGO is applied to preprocess data By the 1 D PI described in Section II the 1 AGO preprocessed data is interpolated Next interpolated pixels are found through the inverse of 1 AGO the first order inverse accumulated generating operation 1 IAGO which is defined as x k x 1 k x 1 k 1 for 2 k L 1 Finally an 6 filter is applied to interpolated pixels to further enhance the interpolation performance The 1 D GPI has been applied to image enlargement in 26 With less computational complexity the 1 D GPI has been shown having better performance than conventional 2 D interpolation schemes such as bilinear interpolation and bicubic interpolation in most of cases Thus it is used in the proposed coding systems described in Section IV The 1 D GPI is reviewed in the following Assume a color image O has YCbCr format and is down sampled by factor M M The down sampled image is denoted as OM Since YCbCr components are processed
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