A Study on Fractal Image Compression Technique Using Discrete Cosine Transformation

• Main Authors: Der-Jyh Duh, 杜德智
• Other Authors: Shu-Yuan Chen
• Format: Others
• Language: en_US
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/97445595139086652610

博士 === 元智大學 === 資訊工程學系 === 94 === Fractal image compression has the advantages of the highly reconstructed image quality, high compression ratio and resolution independence. The basic idea of fractal image compression is utilizing the self-similarity between the sub-image blocks in the same image to achieve the purpose of image compression. Each sub-image block must be compared to the eight Dihedral transformations of all bigger sub-image blocks in the image to find the most similar block. A lot of time is spent for such full search mechanism. As a result, the encoding phase is very time consuming. In this dissertation, three methods are proposed to improve the encoding speed under fixed compression ratio using frequency information obtained from the Discrete Cosine Transformation (DCT) of each image block. Two of them are based on image block classification scheme in frequency domain. The third one proposes a prediction scheme to estimate the best Dihedral transformation used for best domain block search. The first method is to propose a fast fractal encoder based on a simple classification scheme. The classification scheme is based on the edge information of image block. During the encoding process, the classes of range blocks and domain blocks are determined first. Then, each range block is limited to search in the corresponding domain class to find the best match. Since the searching space is reduced, the encoding speed is improved. Three types of classes for image blocks are defined, which are smooth class, diagonal/sub-diagonal edge class and horizontal/vertical edge class. The classification is performed using only the lowest horizontal and vertical DCT coefficients of the given block. Therefore the classification scheme is simple and efficient. Since the classification mechanism is designed on the basis of edge properties and the intrinsic idea of fractal coding, the quality of the decoded image can be preserved. An adaptive threshold determination scheme, which is independent of the given image, is derived to guarantee a stable speedup ratio of three. The second method is to propose a mechanism for speed-quality control which is capable of speeding the encoder by a specified factor while maintaining reasonable image quality. The speedup is accomplished through a classification scheme in the frequency domain using only two DCT coefficients. Image qualities can be preserved as well since the mechanism uses edge property which incorporates fractal similarity, i.e., the Dihedral transformation into classification scheme. An adaptive threshold determination mechanism is also derived to guarantee a well speed-quality control performance. The Dihedral transformations of domain blocks are needed for fractal image compression in order to have better reconstructed image quality after compression. However, such transformations take approximately eight times longer than the standard encoding does. On the other hand, sacrificing Dihedral transformation to speedup the encoder will cause image quality decay since the codebook is not large enough. The third proposed method is to propose a direct estimating method to predict the best Dihedral transformation desired in domain block search. This estimation is accomplished by using only the three DCT coefficients of lower frequency part. The similarity measure for best domain block search in fractal image compression is then performed only on the predicted transformation. Simulation results show that the encoder is about 6 to 7 times faster than the full search method does. The encoding time is the same as that without performing transformations while the image quality is close to that of the full search method. In this dissertation, we propose a series of methods based on classification and prediction schemes for the speedup of fractal image compression. Both the classification and prediction are performed using only the lower few horizontal and vertical DCT coefficients of the given block, therefore they are simple and computationally efficient with little overhead. A stable speedup ratio can be well achieved since the classification schemes are adaptive to the image and prediction scheme can focus on only those best estimate blocks and transformation. Image qualities can be preserved as well since the schemes use edge property of image blocks. Finally, the efficiency and effectiveness of the proposed methods have been demonstrated by various experiments.