對(duì)傅立葉變換后圖像空間域與頻率域中垂直現(xiàn)象的研究.ppt

對(duì)傅立葉變換后圖像空間域與 頻率域中垂直現(xiàn)象的研究,學(xué)生：楊誠(chéng),目錄,現(xiàn)象與疑惑 數(shù)學(xué)證明 推廣 物理意義 研究現(xiàn)狀與意義 待解決問(wèn)題,現(xiàn)象與疑惑,現(xiàn)象與疑惑,輸入圖像為xy平面內(nèi)任意一條水平線，幅度值為1,數(shù)學(xué)證明水平線,以前面提到的直線為輸入圖像,數(shù)學(xué)證明水平線,數(shù)學(xué)證明水平線,推廣任意斜線,推廣任意斜線,推廣任意直線,當(dāng)直線上的灰度值不是一常量時(shí)，如下圖：,物理意義,物理意義,物理意義：與 方向垂直的直線上的點(diǎn)(x,y)頻率相同,物理意義,輸入圖像取特定的fringe patterns時(shí)：,物理意義實(shí)例,以前面提到的fringe patterns：sin(x+y)為例。 當(dāng)把圖像向u=v(或者說(shuō)是x=y)方向投影并以f(x,y)灰度值為縱坐標(biāo)時(shí)，可以近似得到右下角的圖，可以看出f(x,y)在u=v這個(gè)方向上有固定頻率 物理意義就是：輸入函數(shù)sin(x+y)的所有點(diǎn)在u=v(或x=y)方向的投影所得到的函數(shù)只有一個(gè)頻率為 的正弦分量，也就是說(shuō)所有的點(diǎn)在u=v方向上只能在 上有值。這樣就會(huì)產(chǎn)生“疊加”的效果，我們就可以在u-v平面上看見(jiàn)兩個(gè)亮點(diǎn)。,研究現(xiàn)狀與意義,The Scientist and Engineers Guide to Digital Signal Processing By Steven W. Smith, Ph.D. chapter24-Linear Image Processing 1.convolution to multiplication 2.Fourier Slice Theorem A two-dimensional fast Fourier transform method for measuring the inclination angle of parallel fringe patterns. S. De Nicola a, *, P. Ferraro . Optics & Laser Technology 30 (1998) 167173 “The line joining these two peaks in the frequency space is perpendicular to the inclination angle of the interference fringe pattern”,研究現(xiàn)狀與意義,Detecting regular patterns using frequency domain self-filtering D.G. Bailey, Dept. of Phys., Massey Univ., Palmerston North, New Zealand Image Processing, 1997. Proceedings., International Conference on Download from IEEE “The direction of the peak from the origin corresponds to the direction of the sinusoidal variation.”,研究現(xiàn)狀與意義,Analysis of the Superposition of Periodic Layers and Their Moire Effects through the Algebraic Structure of Their Fourier Spectrum Journal of Mathematical Imaging and Vision 8, 99130 (1998),待解決問(wèn)題,很多文章中提到當(dāng)圖像為有規(guī)律的Regular Patterns (or Regular Image)時(shí)會(huì)出現(xiàn)這樣的垂直現(xiàn)象，但是推廣時(shí)很困難，因?yàn)闊o(wú)法硬性的用數(shù)學(xué)表達(dá)式把Regular Patterns規(guī)定下來(lái)。只有“Detecting irregularities in regular patterns”提到“Defining regular pattern”但是作者是以Bravais lattice(布拉維點(diǎn)陣)為具體例子，所以