共轭对称延拓计算全息与全息水印
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摘要
全息显示是真三维立体显示的最终解决方案,计算全息与传统的光学全息相比在信息的数字存储和光电再现方面具有更大的优势。对计算全息新算法的探索具有重要的学术意义,基于计算全息的显示技术在三维电视和多媒体展示等领域具有广泛的应用前景。计算全息和数字水印相结合的全息水印是一种信息隐藏新技术,由于全息图的不可撕毁性等特点,全息水印具有很强的鲁棒性,特别是抗几何攻击能力,为保护数字图像、视频和硬拷贝的知识产权提供新的有效手段。
本论文研究基于共轭对称延拓的Fourier计算全息新方法,提出将物光波进行共轭对称延拓,经快速Fourier变换直接生成实函数,对实函数进行适当的编码得到Fourier计算全息图,其中包含物光波的幅度和相位信息。与原先的基于干涉的计算全息不同之处在于,这里并不需要模拟物光和参考光的干涉,而是由物光波直接生成全息图,计算效率高。论文进行了理论推导,通过数字方法再现原始图像,并利用反射式电寻址LCD空间光调制器实现了光电再现。实验结果验证了共轭对称延拓Fourier计算全息算法的有效性和优良性能。
论文中提出基于彩色图像RGB分量的彩色图像计算全息方法,重点解决了彩色图像光电再现中因光源波长差异引起空间缩放的配准和空间位移的补偿问题,实现了光电再现。将彩色图像分解成RGB三个分量,基于共轭对称延拓的Fourier计算全息算法分别计算三基色全息图,合成彩色全息图。在数字再现中,只需对全息图的三基色分量分别进行数字再现即可合成彩色图像。而对于光电再现,则必须考虑不同波长的激光对光电再现图像的影响,通过对不同颜色分量图像的空间间隔进行适当缩放,调整三基色全息图的空间频率,使它们的光电再现图像严格配准。同时控制再现参数对不同再现光引起的再现图像空间位移进行补偿。论文导出了波长与再现图像配准和位移补偿的关系,根据这些原理交替投射RGB三种再现激光并由计算机控制空间光调制器的时分复用,实现彩色图像的再现。
论文将计算全息和数字水印技术相结合,在共轭对称延拓Fourier计算全息算法基础上提出了一种基于频谱分离的水印全息图空域嵌入的全息水印方法。为了实现水印的盲提取,将数字水印适当布局形成拓展的水印图像,由此生成水印全息图。根据其频谱特性对载体图像进行适当的预处理,在空域中将水印全息图嵌入。检测方不需要原始载体图像和水印信息即可提取水印。这种全息水印具有良好的透明性和很强的稳健性,能抵抗各种常见攻击如加噪声、锐化、平滑、灰度变化和JPEG压缩,以及包括剪切、缩放、旋转在内的几何攻击。尤为突出的是,能够抵抗喷墨打印-扫描攻击,以及对打印照片的剪切攻击,因此这种全息水印可用于图像硬拷贝版权归属的确认,对于平面媒体知识产权保护具有重要意义。全息水印还可用于判断图像是否受到攻击,以及攻击的性质和程度。论文中还提出了在载体图像的DCT域中采用量化调制法嵌入灰度的水印全息图。
Holography is considered one of the ultimate technologies for three-dimensional display. Compared to conventional methods, computer generated holography (CGH) is advantageous both in generation and reconstruction. CGH has applications in various areas. For example, CGH-based display techniques show a promising future of 3DTV and multimedia presentation. Combination of CGH and digital watermarking provides a novel method of information hiding.
As developing effective algorithms is significant to the development of CGH technology, this dissertation first proposes a CGH algorithm based on conjugate symmetric extension and Fourier transform. The complex amplitude of the light wave to be recorded is extended to produce a conjugate symmetric function. The function is then Fourier transformed to generate a real valued distribution containing both amplitude and phase information of the light wave. The obtained real distribution is encoded to give a gray-scale hologram, which can be used to reconstruct the original light wave. Unlike previous algorithms that are based on interference between the object and reference light waves, the proposed method does not need to simulate interference to produce a hologram. The new algorithm is highly efficient since it makes use of the fast Fourier transform. Theoretical derivation is given, and good reconstructions are obtained both digitally and electroholographically. Electroholographic reconstruction is realized by using an electronic addressing reflective LCD spatial light modulator. Experimental results validate the proposed algorithm and show its good performance.
In the next part of the dissertation, we study electroholographic reconstruction of color images. CGH algorithms of color images are developed based on the RGB components. Each color component is treated using the method of conjugate symmetric extension and Fourier transform. Digital reconstruction is straightforward, that is, to reconstruct the three color components and combine them to form the color image. In electroholographic reconstruction, however, there is a scaling and alignment problem due to different wavelengths of the three laser sources. Alignment of the reconstructed RGB components is achieved by matching the spatial size and compensating for the spatial offset. Holograms of RGB components are recalculated according to the wavelengths of the light sources, resulting in relevant sizes and offsets. Specifically, spatial spacing of each color component is properly scaled to adjust the spatial frequency of the corresponding hologram so that the reconstructed RGB images can match with each other. Compensation of spatial offset is achieved by controlling reconstruction parameters in the software. A color image is reconstructed using time division switching of reference lights and time division multiplexing of a spatial light modulator.
As an application of CGH, we propose a new watermarking technique based on computer generated holography. A hologram of the watermark image is first generated by using the proposed conjugate symmetric extension and Fourier approach. The hologram is embedded into the cover image in the spatial domain. To ensure blind extraction, the spectral components of the embedded hologram and the cover image must be made separable. This is achieved by properly arrange the watermark in an extended mask and perform a slight frequency-domain filtering of the cover image prior to the embedding. The watermarked image has good transparency and robustness. Experiments show that the watermark can survive not only normal image processing such as grayscale transform, smoothing, sharpening, noise contamination, and JPEG compression, but also geometrical attacks including cropping, re-sizing, and rotation. More importantly, the hologram-based watermark is capable of resisting inkjet printing and scanning so that it provides a means of protecting copyright of hardcopy photographs. The proposed watermarking is also useful in detecting tampering as it can reveal details of the geometric transformation of the watermarked image. In addition, we describe an alternative hologram watermarking approach, which uses the quantization index modulation technique to insert a hologram into a cover image in the DCT domain.
本论文研究基于共轭对称延拓的Fourier计算全息新方法,提出将物光波进行共轭对称延拓,经快速Fourier变换直接生成实函数,对实函数进行适当的编码得到Fourier计算全息图,其中包含物光波的幅度和相位信息。与原先的基于干涉的计算全息不同之处在于,这里并不需要模拟物光和参考光的干涉,而是由物光波直接生成全息图,计算效率高。论文进行了理论推导,通过数字方法再现原始图像,并利用反射式电寻址LCD空间光调制器实现了光电再现。实验结果验证了共轭对称延拓Fourier计算全息算法的有效性和优良性能。
论文中提出基于彩色图像RGB分量的彩色图像计算全息方法,重点解决了彩色图像光电再现中因光源波长差异引起空间缩放的配准和空间位移的补偿问题,实现了光电再现。将彩色图像分解成RGB三个分量,基于共轭对称延拓的Fourier计算全息算法分别计算三基色全息图,合成彩色全息图。在数字再现中,只需对全息图的三基色分量分别进行数字再现即可合成彩色图像。而对于光电再现,则必须考虑不同波长的激光对光电再现图像的影响,通过对不同颜色分量图像的空间间隔进行适当缩放,调整三基色全息图的空间频率,使它们的光电再现图像严格配准。同时控制再现参数对不同再现光引起的再现图像空间位移进行补偿。论文导出了波长与再现图像配准和位移补偿的关系,根据这些原理交替投射RGB三种再现激光并由计算机控制空间光调制器的时分复用,实现彩色图像的再现。
论文将计算全息和数字水印技术相结合,在共轭对称延拓Fourier计算全息算法基础上提出了一种基于频谱分离的水印全息图空域嵌入的全息水印方法。为了实现水印的盲提取,将数字水印适当布局形成拓展的水印图像,由此生成水印全息图。根据其频谱特性对载体图像进行适当的预处理,在空域中将水印全息图嵌入。检测方不需要原始载体图像和水印信息即可提取水印。这种全息水印具有良好的透明性和很强的稳健性,能抵抗各种常见攻击如加噪声、锐化、平滑、灰度变化和JPEG压缩,以及包括剪切、缩放、旋转在内的几何攻击。尤为突出的是,能够抵抗喷墨打印-扫描攻击,以及对打印照片的剪切攻击,因此这种全息水印可用于图像硬拷贝版权归属的确认,对于平面媒体知识产权保护具有重要意义。全息水印还可用于判断图像是否受到攻击,以及攻击的性质和程度。论文中还提出了在载体图像的DCT域中采用量化调制法嵌入灰度的水印全息图。
Holography is considered one of the ultimate technologies for three-dimensional display. Compared to conventional methods, computer generated holography (CGH) is advantageous both in generation and reconstruction. CGH has applications in various areas. For example, CGH-based display techniques show a promising future of 3DTV and multimedia presentation. Combination of CGH and digital watermarking provides a novel method of information hiding.
As developing effective algorithms is significant to the development of CGH technology, this dissertation first proposes a CGH algorithm based on conjugate symmetric extension and Fourier transform. The complex amplitude of the light wave to be recorded is extended to produce a conjugate symmetric function. The function is then Fourier transformed to generate a real valued distribution containing both amplitude and phase information of the light wave. The obtained real distribution is encoded to give a gray-scale hologram, which can be used to reconstruct the original light wave. Unlike previous algorithms that are based on interference between the object and reference light waves, the proposed method does not need to simulate interference to produce a hologram. The new algorithm is highly efficient since it makes use of the fast Fourier transform. Theoretical derivation is given, and good reconstructions are obtained both digitally and electroholographically. Electroholographic reconstruction is realized by using an electronic addressing reflective LCD spatial light modulator. Experimental results validate the proposed algorithm and show its good performance.
In the next part of the dissertation, we study electroholographic reconstruction of color images. CGH algorithms of color images are developed based on the RGB components. Each color component is treated using the method of conjugate symmetric extension and Fourier transform. Digital reconstruction is straightforward, that is, to reconstruct the three color components and combine them to form the color image. In electroholographic reconstruction, however, there is a scaling and alignment problem due to different wavelengths of the three laser sources. Alignment of the reconstructed RGB components is achieved by matching the spatial size and compensating for the spatial offset. Holograms of RGB components are recalculated according to the wavelengths of the light sources, resulting in relevant sizes and offsets. Specifically, spatial spacing of each color component is properly scaled to adjust the spatial frequency of the corresponding hologram so that the reconstructed RGB images can match with each other. Compensation of spatial offset is achieved by controlling reconstruction parameters in the software. A color image is reconstructed using time division switching of reference lights and time division multiplexing of a spatial light modulator.
As an application of CGH, we propose a new watermarking technique based on computer generated holography. A hologram of the watermark image is first generated by using the proposed conjugate symmetric extension and Fourier approach. The hologram is embedded into the cover image in the spatial domain. To ensure blind extraction, the spectral components of the embedded hologram and the cover image must be made separable. This is achieved by properly arrange the watermark in an extended mask and perform a slight frequency-domain filtering of the cover image prior to the embedding. The watermarked image has good transparency and robustness. Experiments show that the watermark can survive not only normal image processing such as grayscale transform, smoothing, sharpening, noise contamination, and JPEG compression, but also geometrical attacks including cropping, re-sizing, and rotation. More importantly, the hologram-based watermark is capable of resisting inkjet printing and scanning so that it provides a means of protecting copyright of hardcopy photographs. The proposed watermarking is also useful in detecting tampering as it can reveal details of the geometric transformation of the watermarked image. In addition, we describe an alternative hologram watermarking approach, which uses the quantization index modulation technique to insert a hologram into a cover image in the DCT domain.
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