分形编码在图像处理中的应用研究
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摘要
随着多媒体通信技术的快速发展,人们迫切需要高效的图像压缩技术来满足日常工作生活的需要。分形图像编码是一种新颖且有很大发展潜力的图像压缩技术,自Jacquin提出第一个实用的分形图像编码算法以来,国内外学者对其产生了浓厚的研究兴趣。经过多年的发展,分形编码已经广泛应用到图像压缩以及其他图像处理任务中。本文对分形编码及其在其他图像处理任务中的应用进行了研究,主要包括如下内容：
(1)快速分形图像编码算法的研究。分形编码过程是分形图像压缩的基础,因此加速分形编码是首先需要解决的问题,基于特征量最近邻搜索的快速分形编码是解决该问题的有效途径之一。在分析和研究图像灰度分布结构特性的基础上,提出结构信息特征和相关信息特征的定义,推导并证明了上述两个特征作为最近邻搜索特征是子块满足最佳匹配的必要条件。实验表明,在相同压缩比和编码时间情况下,本文算法较同类算法能够得到更好的解码图像质量。
(2)基于快速分形编码的混合图像压缩算法。分形图像编码算法具有潜在高压缩比的特点,与一定分形码相对应的图像子块尺寸越大,则压缩比就越大。对输入图像进行四叉树分割,通过分析和对比快速分形编码算法与JPEG算法可知,快速分形编码算法适用于32×32和16×16子块,而JPEG算法则适用于剩余8×8子块。实验表明,在相同压缩比情况下,本文算法较JPEG算法能够得到更好的解码图像质量。最后,对本文算法在实际中应用进行了分析。
(3)分形解码图像质量的可预测性。由拼贴定理可知,在已知拼贴误差的情况下,我们只能得到解码图像的误差上限。本文在大量实验基础上,总结出平均拼贴误差与解码图像质量之间的对数关系,然后据此提出分形解码图像质量的预测算法。通过该预测算法我们可以在分形编码过程中对解码图像质量进行实时预测,当解码图像质量不能达到特定要求时能够及时停止编码并更换编码算法,不必进行剩余部分的分形编码和分形解码操作,节省了时间和资源。
(4)分形编码在压缩以外的其他图像处理任务中的应用研究。主要包括三个方面：(ⅰ)基于模型约束的分形图像去噪算法。经过分析可知,噪声图像的局部在分形编码去噪前后具有均值不变的特点,根据该约束模型对分形图像去噪的结果进行修正。实验表明,本文算法能够进一步改善分形图像去噪效果。(ⅱ)基于无损无搜索分形编码的图像放大算法。分形图像解码的分辨率无关性使其能够对编码图像进行放大。本文采用无搜索算法实时对低分辨率图像进行分形编码,然后增加一个误差补偿向量消除分形编码过程中的拼贴误差,实现无损无搜索分形图像编码,该算法能够在快速完成分形编码的同时,消除分形编码过程带来的信息损失。最后将该分形编码算法与其他分形图像放大技术相结合。实验表明,本文算法较传统和其他分形图像放大算法在达到较好性能的同时,具有更好的视觉效果。(ⅲ)分形图像编解码的整体快速实现算法。在分形编解码操作需要连续完成的应用场合,例如分形图像去噪和分形图像放大,分形编码过程的有用信息将有助于进一步加快分形解码,本文提出采用拼贴图像作为分形解码的初始迭代图像。实验表明,本文算法比单独进行分形编码和解码能够在更短的时间内完成。
(5)基于结构方向信息的图像质量评价算法。在结构相似度的基础上进一步挖掘图像中包含的方向信息,将像素邻域中包含的方向信息作为图像相似度评价的因素之一,提出局部结构方向相似度的概念。采用局部结构方向相似度对图像的不同频率分量进行评价并加权求和。实验表明,本文算法能够更好地与人的主观感受相一致。
With the rapid development of multimedia communication technology, there is an urgent need for efficient image compression technology to meet people's daily life. Fractal image coding is a novel and promising image compression technology. Since Jacquin proposed the first block based fractal image coding algorithm, researchers worldwide have had a strong interest in the study. After many years'development, fractal image coding has been successfully applied in image compression as well as other image processing applications. In our research, the fractal image coding itself and its applications to other aspects of image processing are studied. The main contributions of the dissertation are as follows:
(1) Research of the fast fractal image coding. Since the fractal encoding process is the first step of the fractal image coding, acceleration of fractal coding is the first issue to be resolved and the fast fractal coding algorithm based on feature vector's nearest search is a promising method. By analyzing the configuration of the image intensity, the definitions of structural information feature and correlation information feature are proposed. We can proof that the nearest neighbor search result for one range block in the feature space is a requirement for the best matched domain block. Experiments show that compared with similar fast fractal encoding algorithms, the proposed algorithm can provide better decoded image quality in the case of the same compression ratio and encoding time.
(2) Hybrid image compression algorithm based on fast fractal coding. Fractal image coding algorithm has the potential of high compression ratio. If the size of the range block is bigger, the compression ratio will be higher. Firstly, the input image is segmented by the quadtree algorithm. By comparing the fast fractal image coding algorithm and the JPEG algorithm, we can see that the fast fractal image coding algorithm is suitable for the blocks of 32×32 and 16×16 pixels and the remain blocks of pixels can be coded by the JPEG algorithm. Experiments show that in the case of the same compression ratio, the proposed algorithm can obtain better decoded image quality. Lastly, the possibility of applying our algorithm in the practical applications is discussed.
(3) Estimation of the decoded image quality in the fractal image coding. According to the collage theorem, we can only obtain the error limit of the decoded image from the collage error in the encoding process. Based on large amounts of experiments, we find that there exists a logarithmic relationship between the average collage error and the decoded image quality. Since the decoded image quality can be estimated by the average collage error, we can estimate the decoded image quality temporally in the fractal encoding process. For some images that are not suitable for fractal image coding, we can replace the fractal coding algorithm with other image compression methods without finishing the fractal encoding and decoding process completely.
(4) Fractal coding used in other aspects of image processing except image compression. (ⅰ) Fractal image de-noising algorithm based on model constraint. Since the mean value will remain a constant for the local parts of the noisy image and restored image, the restored image quality can be further improved by the above constraint model. Experiments show that we can obtain better restored image quality. (ⅱ) Fractal image magnification based on no search lossless fractal image coding. Because of the resolution independence in the fractal decoding process, fractal image coding can be used to image magnification. Firstly, the no search fractal image coding is adopted to encode the low resolution image, then an error compensation vector is added to the block matching process in the fractal encoding and the collage error can be removed. According to the collage theorem, the fractal decoded image can be obtained losslessly. Lastly, the no search lossless fractal encoding algorithm is combined with some other existing fractal image magnification technique. Experiments show that the proposed algorithm can provide better performance than other similar fractal image magnification methods and the conventional ones. (ⅲ) Acceleration of the fractal image encoding and decoding process. Under some circumstances such as fractal image de-noising and fractal image magnification, the fractal encoding and decoding process will be completed continuously. Some useful information in the fractal encoding process can be used to help the fractal decoding process. We find that if the collage image is selected as the initial image, the fractal image decoding process can be completed in a shorter time.
(5) Image quality assessment based on structural orientation information. The structural Similarity (SSIM) method can achieve better image assessment result compared with conventional Peak Signal to Noise Ratio (PSNR) method, but the structural information in SSIM is not completely extracted. In our research, the orientation information was further extracted and the Local Structural Orientation Similarity (LSOS) was proposed. Different frequencies of the image are assessed with LSOS and the results are summed with different weights. Experiments show that compared with other methods, the proposed method can be more consistent with the human visual system.
(1)快速分形图像编码算法的研究。分形编码过程是分形图像压缩的基础,因此加速分形编码是首先需要解决的问题,基于特征量最近邻搜索的快速分形编码是解决该问题的有效途径之一。在分析和研究图像灰度分布结构特性的基础上,提出结构信息特征和相关信息特征的定义,推导并证明了上述两个特征作为最近邻搜索特征是子块满足最佳匹配的必要条件。实验表明,在相同压缩比和编码时间情况下,本文算法较同类算法能够得到更好的解码图像质量。
(2)基于快速分形编码的混合图像压缩算法。分形图像编码算法具有潜在高压缩比的特点,与一定分形码相对应的图像子块尺寸越大,则压缩比就越大。对输入图像进行四叉树分割,通过分析和对比快速分形编码算法与JPEG算法可知,快速分形编码算法适用于32×32和16×16子块,而JPEG算法则适用于剩余8×8子块。实验表明,在相同压缩比情况下,本文算法较JPEG算法能够得到更好的解码图像质量。最后,对本文算法在实际中应用进行了分析。
(3)分形解码图像质量的可预测性。由拼贴定理可知,在已知拼贴误差的情况下,我们只能得到解码图像的误差上限。本文在大量实验基础上,总结出平均拼贴误差与解码图像质量之间的对数关系,然后据此提出分形解码图像质量的预测算法。通过该预测算法我们可以在分形编码过程中对解码图像质量进行实时预测,当解码图像质量不能达到特定要求时能够及时停止编码并更换编码算法,不必进行剩余部分的分形编码和分形解码操作,节省了时间和资源。
(4)分形编码在压缩以外的其他图像处理任务中的应用研究。主要包括三个方面：(ⅰ)基于模型约束的分形图像去噪算法。经过分析可知,噪声图像的局部在分形编码去噪前后具有均值不变的特点,根据该约束模型对分形图像去噪的结果进行修正。实验表明,本文算法能够进一步改善分形图像去噪效果。(ⅱ)基于无损无搜索分形编码的图像放大算法。分形图像解码的分辨率无关性使其能够对编码图像进行放大。本文采用无搜索算法实时对低分辨率图像进行分形编码,然后增加一个误差补偿向量消除分形编码过程中的拼贴误差,实现无损无搜索分形图像编码,该算法能够在快速完成分形编码的同时,消除分形编码过程带来的信息损失。最后将该分形编码算法与其他分形图像放大技术相结合。实验表明,本文算法较传统和其他分形图像放大算法在达到较好性能的同时,具有更好的视觉效果。(ⅲ)分形图像编解码的整体快速实现算法。在分形编解码操作需要连续完成的应用场合,例如分形图像去噪和分形图像放大,分形编码过程的有用信息将有助于进一步加快分形解码,本文提出采用拼贴图像作为分形解码的初始迭代图像。实验表明,本文算法比单独进行分形编码和解码能够在更短的时间内完成。
(5)基于结构方向信息的图像质量评价算法。在结构相似度的基础上进一步挖掘图像中包含的方向信息,将像素邻域中包含的方向信息作为图像相似度评价的因素之一,提出局部结构方向相似度的概念。采用局部结构方向相似度对图像的不同频率分量进行评价并加权求和。实验表明,本文算法能够更好地与人的主观感受相一致。
With the rapid development of multimedia communication technology, there is an urgent need for efficient image compression technology to meet people's daily life. Fractal image coding is a novel and promising image compression technology. Since Jacquin proposed the first block based fractal image coding algorithm, researchers worldwide have had a strong interest in the study. After many years'development, fractal image coding has been successfully applied in image compression as well as other image processing applications. In our research, the fractal image coding itself and its applications to other aspects of image processing are studied. The main contributions of the dissertation are as follows:
(1) Research of the fast fractal image coding. Since the fractal encoding process is the first step of the fractal image coding, acceleration of fractal coding is the first issue to be resolved and the fast fractal coding algorithm based on feature vector's nearest search is a promising method. By analyzing the configuration of the image intensity, the definitions of structural information feature and correlation information feature are proposed. We can proof that the nearest neighbor search result for one range block in the feature space is a requirement for the best matched domain block. Experiments show that compared with similar fast fractal encoding algorithms, the proposed algorithm can provide better decoded image quality in the case of the same compression ratio and encoding time.
(2) Hybrid image compression algorithm based on fast fractal coding. Fractal image coding algorithm has the potential of high compression ratio. If the size of the range block is bigger, the compression ratio will be higher. Firstly, the input image is segmented by the quadtree algorithm. By comparing the fast fractal image coding algorithm and the JPEG algorithm, we can see that the fast fractal image coding algorithm is suitable for the blocks of 32×32 and 16×16 pixels and the remain blocks of pixels can be coded by the JPEG algorithm. Experiments show that in the case of the same compression ratio, the proposed algorithm can obtain better decoded image quality. Lastly, the possibility of applying our algorithm in the practical applications is discussed.
(3) Estimation of the decoded image quality in the fractal image coding. According to the collage theorem, we can only obtain the error limit of the decoded image from the collage error in the encoding process. Based on large amounts of experiments, we find that there exists a logarithmic relationship between the average collage error and the decoded image quality. Since the decoded image quality can be estimated by the average collage error, we can estimate the decoded image quality temporally in the fractal encoding process. For some images that are not suitable for fractal image coding, we can replace the fractal coding algorithm with other image compression methods without finishing the fractal encoding and decoding process completely.
(4) Fractal coding used in other aspects of image processing except image compression. (ⅰ) Fractal image de-noising algorithm based on model constraint. Since the mean value will remain a constant for the local parts of the noisy image and restored image, the restored image quality can be further improved by the above constraint model. Experiments show that we can obtain better restored image quality. (ⅱ) Fractal image magnification based on no search lossless fractal image coding. Because of the resolution independence in the fractal decoding process, fractal image coding can be used to image magnification. Firstly, the no search fractal image coding is adopted to encode the low resolution image, then an error compensation vector is added to the block matching process in the fractal encoding and the collage error can be removed. According to the collage theorem, the fractal decoded image can be obtained losslessly. Lastly, the no search lossless fractal encoding algorithm is combined with some other existing fractal image magnification technique. Experiments show that the proposed algorithm can provide better performance than other similar fractal image magnification methods and the conventional ones. (ⅲ) Acceleration of the fractal image encoding and decoding process. Under some circumstances such as fractal image de-noising and fractal image magnification, the fractal encoding and decoding process will be completed continuously. Some useful information in the fractal encoding process can be used to help the fractal decoding process. We find that if the collage image is selected as the initial image, the fractal image decoding process can be completed in a shorter time.
(5) Image quality assessment based on structural orientation information. The structural Similarity (SSIM) method can achieve better image assessment result compared with conventional Peak Signal to Noise Ratio (PSNR) method, but the structural information in SSIM is not completely extracted. In our research, the orientation information was further extracted and the Local Structural Orientation Similarity (LSOS) was proposed. Different frequencies of the image are assessed with LSOS and the results are summed with different weights. Experiments show that compared with other methods, the proposed method can be more consistent with the human visual system.
引文
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