Tham khảo tài liệu 'handbook of industrial automation - richard l. shell and ernest l. hall part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Figure 6 Images at various gray-scale quantization ranges. Figure 8 Color cube shows the three-dimensional nature of color. basic operations like linear filtering and modulations are easily described in the Fourier domain. A common example of Fourier transforms can be seen in the appearance of stars. A star lools like a small point of twinkling light. However the small point of light we observe is actually the far-field Fraunhoffer diffraction pattern or Fourier transform of the image of the star. The twinkling is due to the motion of our eyes. The moon image looks quite different since we are close enough to view the near-field or Fresnel diffraction pattern. While the most common transform is the Fourier transform there are also several closely related trans forms. The Hadamard Walsh and discrete cosine transforms are used in the area of image compression. The Hough transform is used to find straight lines in a binary image. The Hotelling transform is commonly used to find the orientation of the maximum dimension of an object 5 . Fourier Transform The one-dimensional Fourier transform may be written as F u f x e iux dx 5 9 9 9 0 9 9 0 0 9 9 0 0 0 9 9 0 0 9 9 0 0 0 9 9 0 0 9 9 0 0 0 9 0 9 9 9 0 0 9 9 0 0 9 9 0 9 9 0 0 9 9 0 9 9 0 0 9 9 0 0 9 0 0 0 Figure 7 Digitized image. Figure 9 Image surface and viewing geometry effects. Copyright 2000 Marcel Dekker Inc. Figure 10 Diffuse surface reflection. In the two-dimensional case the Fourier transform and its corresponding inverse representation are F u v f x dx dy . x 6 f x y F u du dv The discrete two-dimensional Fourier transform and corresponding inverse relationship may be written as F V E E-t v x 0 7 0 f .x ỳ F u - U G V G 7 for X 0 1 . N 1 y 0 1 . N 1 and u 0 1 . N - 1 V 0 1 . N - 1. Convolution Algorithm The convolution theorem that the input and output of a linear position invariant system are related by a convolution is an important principle. The basic idea of convolution is that if we have two
