Image Enhancement Digital Image Processing Instructor: Dr. Cheng-Chien LiuCheng-Chien Liu Department of Earth Sciences National Cheng Kung University Last updated: 16 September 2003 Chapter 4

Introduction  Image enhancement Subjectively look better  More details  Remove unwanted flickering  Enhance contrast Two approaches  Statistics of the gray values of the image  Manipulate the histogram  Principal component analysis  Rank order filtering  Spatial frequency content of the image

Histogram  Histogram Number(gray level) Normalized  probability density function Good or bad image  Good image  more spread of histogram  Bad image  narrow histogram Modification of histogram  p s (s)ds = p r (r)dr

Histogram (cont.)  Histogram equalization s = [  0 r p r (x)dx] / c  c = p s (s) Much more spread, but not flat (Figure 4.2 a – d)  Histogram equalization with random addition Randomly re-distribute the pixels with neighboring gray values  generate an absolutely flat histogram Figure 4.2 e – f

Histogram (cont.)  Histogram manipulation with function p s (s) p s (s)ds = p r (r)dr Three-step process  Equalization  Specify the histogram and obtain the transformation w = T 2 (s)  Apply the inversion to the equalized histogram Figure 4.3 Example 4.1  Locally manipulating histogram Scan the image with a window inside Modify the histogram but alter only the center pixel Figure 4.4 – 4.6  Flat black patch  receive too little light to record anything  Amplify non-existing information  look damaged

Histogram (cont.)  Alternative manipulation g(x,y) = m(x,y) + A[f(x,y)- m(x,y)]  m(x,y): the mean of the distribution of pixels inside a window   (x,y): the deviation of the distribution of pixels inside a window Transform  Areas with lower variance to be amplified most  A = kM /  (x,y)  k: constant  M: the average grey value of the image Example 4.4 (d)  Window size 5  5 with k = 3 Example 4.5 (d), 4.6 (d)  Window size 5  5 with k = 3  + post-processing of histogram equalization

Principal component analysis  Multi-spectral image (Fig 4.7) The pixels plotted in the multi-spectral space form a cluster  PCA (L-E transform) A linear transformation of the coordinate system  Three new axes coincide with the directions of the three largest spreads of the point distribution  The data are uncorrelated in the new set of axes  Processes Find the mean x i0 C(i,j) = (1/N 2 )  k  l [x i (k,l) - x i0 ][x j (k,l) - x j0 ]  k = 1, 2, …, N; l = 1, 2, …, N Find eigenvalues of C(i,j), form eigenvector matrix A Linear transform: y = Ax

Principal component analysis (cont.)  Advantages Convey the maximum information in a certain number of bits The 1 st principal component has the maximum contrast and information  Figure 4.8  Disadvantages Gray values have no physical meaning  connot be used for classification  e.g. water, trouser in Figure 4.8 (d) – (f)  Example 4.2 – 4.5

Rank order filtering  Types of noise Additive noise  Impulse noise, Gaussian noise, salt and pepper noise  e.g. additive zero-mean Gaussian noise  a zero-mean Gaussian probability function is added to the true value Multiplicative noise  e.g. variable illumination

Rank order filtering (cont.)  Median filter Principle  Choose a small window  take median value  force points with distinct intensities to be more like their neighbors  eliminate intensity spikes which appear isolated Remove the impulse noise almost completely  e.g. Figure 4.9 (c) Not good for additive Gaussian noise  e.g. Figure 4.9 (d)

Rank order filtering (cont.)  Smoothing the image Principle  Choose a small window  take median value  force points with distinct intensities to be more like their neighbors  eliminate intensity spikes which appear isolated Remove additive Gaussian noise  e.g. Figure 4.9 (f) Not good for the impulse noise  e.g. Figure 4.9 (e)

Rank order filtering (cont.)  Lowpass filter Principle  Signal and noise are uncorrelated  Flat spectrum of noise (Fig 4.11)  Use a lowpass filter  kill off all higher frequency noises Fig 4.12  The ideal lowpass filter in 2D in the frequency domain r 0 Drawback  Also kill off the useful information of the image buried in these high frequencies  clean but blurred image  Sharpening  enhance small fluctuations in the intensity of the image, noise included  High pass filter (Fig 4.13) Procedure  Fournier transform  Multiply with a filter function  Inverse Fournier transform

Rank order filtering (cont.)  Homomorphic filter f(x, y) = i(x, y)r(x, y)  i(x, y): illumination function  Uniform  low-frequency components  r(x, y): reflectance function  Sharp transitions in the intensity of an image  high-frequency components Principle  Separate i and r  take logarithm  ln f(x, y) = ln i(x, y) + ln r(x, y)  Enhance the high frequencies and suppress the low frequency  Fig 4.15  Fig 4.16