1. Introduction Digital Image Processing Instructor: Dr. Cheng-Chien LiuCheng-Chien Liu Department of Earth Sciences National Cheng Kung University Last updated: 9 November 2003 Chapter 1

2. Image  Image A monochrome image  2D light intensity function f(x, y) A multicolor image  2D light intensity vector f(x, y) = f r (x, y) + f g (x, y) + …  Digital image An image that has been discretized both in spatial coordinates and in brightness Grey level (GL)  the digitized brightness value (2 m )  3D feature  illumination  sensor  relative intensity Pixel  the digitized spatial size (N 1  N 2 )  Picture element

3. Image (cont.)  Image resolution How much detail we can see in the image The number of bits need to store an image:  b = N 1  N 2  m Fig 1.1: checkerboard effect Fig 1.2: false contouring Fig 1.3:  A detailed image  false contouring is not that serious

4. Image processing  Why? Picture digitization and coding to facilitate transmission, printing and storage of pictures Picture enhancement and restoration in order, for example, to interpret more easily pictures of the surface of other planets taken by various probes Picture segmentation and description as an early stage in Machine Vision

5. Image processing (cont.)  How? Image  operators  image transform Linear operator: O[af + bg] = aO[f] + bO[g]  O[point source] = point spread function (PSF)  O[  (x- , y-  )] = h(x, , y,    (x- , y-  ) is a point source of brightness 1 centered at ( ,  ) Output image:  g( ,  ) =  x=0 N-1  y=0 N-1 f(x, y)h(x, , y,   Matrix form: g = Hf  [N  N] = [N 2  N 2 ] [N  N]  B1.2: Stacking operator [N  N]  [N 2  1]  Example 1.1  Example 1.2  2D convolution

6. Point Spread Function  PSF Meaning  h(x, , y,  expresses how much the input value at position (x, y) influences the output value at position ( ,  ) Shift invariant PSF  h(x, , y,  h(  -x,  -y) Separable PSF  h(x, , y,  h c (x,  )h r (y,  If PSF is both shift invariant and separable  g( ,  ) =  x=0 N-1 h c (  -x)  y=0 N-1 f(x, y)h r (  -y)  A cascade of two 1D convolutions  Matrix form: g = h c T f h r  B1.3: The formal derivation of the separable matrix equation  Example 1.3: H 23 = N 2 T HN 3

7. Purpose of Image Processing  Image enhancement (Fig 1.4 top) Given f choose h c and h r  g is “better” than f  Image compression (Fig 1.4 bottom) Given f choose h c and h r  g can be represented by fewer bits than f without much loss of detail  Image restoration (Fig 1.5 top) Given g and an estimate of h  recover f  Automatic vision (Fig 1.5 bottom) Given f choose h c and h r  g salienates certain features of f