【摘要】：圖像采樣是計算機圖形學(xué)中的重要課題,當(dāng)今已經(jīng)產(chǎn)生了很多經(jīng)典的采樣理論與方法.圖像存儲與處理技術(shù)的廣泛需求,驅(qū)使著信號采樣到圖像采樣的發(fā)展.在經(jīng)典的Shannon采樣理論中,給出了保存離散信號完整信息的采樣頻率限制,而在更為復(fù)雜的圖像采樣中,這種采樣頻率在存儲空間與計算復(fù)雜度的限制中是無法保證的,所以產(chǎn)生了很多更加合理的圖像采樣方法.基于一維信號采樣的經(jīng)典方法,可以沿用于二維圖像采樣,例如均勻采樣、藍噪聲采樣和幾何特征匹配采樣等.它們均在圖像坐標(biāo)內(nèi)分布采樣點,有效利用圖像梯度、顯著度等特征,提高采樣效率。Shannon在非均勻采樣理論中指出,滿足平均采樣頻率閥值的非均勻采樣方法,也可以保存原始信號的完整信息,所以非均勻采樣方法可以更充分的利用圖像特征進而保存圖像信息。本文介紹了一種基于藍噪聲方法的圖像采樣,通過把灰度圖像看成具有密度的流形,參照廣義里奇曲率定義進行采樣.類似的采樣由前人提出過,但本文在其基礎(chǔ)上有了更多的擴展并引入離散Hessian陣的特征計算.這類方法的思路和結(jié)果也被廣泛的應(yīng)用于圖像和圖形的處理中.本文將其應(yīng)用于自然,深度和卡通等多種圖像,并且與其它采樣方法進行比較,顯現(xiàn)出本算法在采樣結(jié)果與還原結(jié)果的優(yōu)勢.而且進一步的實驗證明,對于灰度值變化頻率較大的圖像,采樣方法仍然可行,并且可以擴展至高維圖像,進一步的應(yīng)用將在未來的科研工作中繼續(xù)進行.
[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.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：TP391.41

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