基于广义里奇曲率的图像采样和重建
发布时间：2018-11-07 09:45
【摘要】：图像采样是计算机图形学中的重要课题,当今已经产生了很多经典的采样理论与方法.图像存储与处理技术的广泛需求,驱使着信号采样到图像采样的发展.在经典的Shannon采样理论中,给出了保存离散信号完整信息的采样频率限制,而在更为复杂的图像采样中,这种采样频率在存储空间与计算复杂度的限制中是无法保证的,所以产生了很多更加合理的图像采样方法.基于一维信号采样的经典方法,可以沿用于二维图像采样,例如均匀采样、蓝噪声采样和几何特征匹配采样等.它们均在图像坐标内分布采样点,有效利用图像梯度、显著度等特征,提高采样效率。Shannon在非均匀采样理论中指出,满足平均采样频率阀值的非均匀采样方法,也可以保存原始信号的完整信息,所以非均匀采样方法可以更充分的利用图像特征进而保存图像信息。本文介绍了一种基于蓝噪声方法的图像采样,通过把灰度图像看成具有密度的流形,参照广义里奇曲率定义进行采样.类似的采样由前人提出过,但本文在其基础上有了更多的扩展并引入离散Hessian阵的特征计算.这类方法的思路和结果也被广泛的应用于图像和图形的处理中.本文将其应用于自然,深度和卡通等多种图像,并且与其它采样方法进行比较,显现出本算法在采样结果与还原结果的优势.而且进一步的实验证明,对于灰度值变化频率较大的图像,采样方法仍然可行,并且可以扩展至高维图像,进一步的应用将在未来的科研工作中继续进行.
[Abstract]:Image sampling is an important subject in computer graphics. Nowadays, many classical sampling theories and methods have been produced. The extensive demand of image storage and processing technology drives the development of signal sampling to image sampling. In the classical Shannon sampling theory, the sampling frequency limit is given to preserve the complete information of discrete signal. In more complex image sampling, the sampling frequency is not guaranteed in the limitation of storage space and computational complexity. So there are many more reasonable image sampling methods. The classical method based on one-dimensional signal sampling can be used for 2-D image sampling, such as uniform sampling, blue noise sampling, geometric feature matching sampling and so on. They all distribute sampling points in the image coordinates, effectively utilize the characteristics of image gradient and saliency, and improve the sampling efficiency. In the theory of non-uniform sampling, Shannon points out that the non-uniform sampling method satisfies the threshold of average sampling frequency. It can also save the complete information of the original signal, so the non-uniform sampling method can make full use of the image features and then save the image information. In this paper, an image sampling method based on blue noise is introduced. The grayscale image is regarded as a density manifold and sampled by referring to the generalized Ritchie curvature definition. Similar sampling has been proposed by predecessors, but on the basis of it, we have extended it more and introduced the characteristic calculation of discrete Hessian matrix. The ideas and results of this method are also widely used in image and graphics processing. In this paper, it is applied to many kinds of images, such as nature, depth, cartoon and so on, and compared with other sampling methods, it shows the superiority of this algorithm in sampling result and reducing result. Further experiments show that the sampling method is still feasible and can be extended to high-dimensional images, and further application will be carried out in the future scientific research work.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP391.41
本文编号：2315967
[Abstract]:Image sampling is an important subject in computer graphics. Nowadays, many classical sampling theories and methods have been produced. The extensive demand of image storage and processing technology drives the development of signal sampling to image sampling. In the classical Shannon sampling theory, the sampling frequency limit is given to preserve the complete information of discrete signal. In more complex image sampling, the sampling frequency is not guaranteed in the limitation of storage space and computational complexity. So there are many more reasonable image sampling methods. The classical method based on one-dimensional signal sampling can be used for 2-D image sampling, such as uniform sampling, blue noise sampling, geometric feature matching sampling and so on. They all distribute sampling points in the image coordinates, effectively utilize the characteristics of image gradient and saliency, and improve the sampling efficiency. In the theory of non-uniform sampling, Shannon points out that the non-uniform sampling method satisfies the threshold of average sampling frequency. It can also save the complete information of the original signal, so the non-uniform sampling method can make full use of the image features and then save the image information. In this paper, an image sampling method based on blue noise is introduced. The grayscale image is regarded as a density manifold and sampled by referring to the generalized Ritchie curvature definition. Similar sampling has been proposed by predecessors, but on the basis of it, we have extended it more and introduced the characteristic calculation of discrete Hessian matrix. The ideas and results of this method are also widely used in image and graphics processing. In this paper, it is applied to many kinds of images, such as nature, depth, cartoon and so on, and compared with other sampling methods, it shows the superiority of this algorithm in sampling result and reducing result. Further experiments show that the sampling method is still feasible and can be extended to high-dimensional images, and further application will be carried out in the future scientific research work.
【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TP391.41
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