Image Processing. Cosimo Distante. Lecture 6: Monochrome and Color processing

Transcription

1 Image Processing Cosimo Distante Lecture 6: Monochrome and Color processing

2 Pointwise operator: algorithms that execute simple operation on the single pixel without involving neighboring pixels I 0 (i,j)=o pointwise [I I (i,j)] If I I (i,j) > 150 then I O (i,j)=1 else I O (i,j)=0

3 Local Operator: algorithms that define the new value of a pixel based on the intensity values of the neighboring pixels I I input image, F(i,j) a window defined over the analysing pixel I 0 output image I 0 (i,j)=o locale {I I (i k,j l ); (i k,j l ) F(i,j)} Median filter with window size 3 3

4 Global Operator: algorithms that extract global information from the image They use all pixels of the image R=O global [I I (i,j)]

5 Histogram H(x) is the frequency of intensity value x The histogram H I (x) can be seen as the results of the global operatorfor the input image I With the histogram we loose spacial information

6 Original Dark Light R. S. Gaborski 6

7 Contrast manipulation Given: x gray level of input image I I (i,j), y gray level of output image I 0 (i,j), T(x) the gray level transform (manipulation) y=t(x)

8 Linear with x a x x b and β = Δ y Δ x y=β(x-x a ) the stretching coefficient obtained by the ratio of the output gray level range and input gray level range Δx=x b -x a. Example: the interval of the most frequent levels in the image is [ ] Then Δx=50 different levels That can be stretched to 256 levels (Δy) to have a better quality

9 Linear stretching

10 Linear with multiple paths α = y x a a a b a b x x y y = β ) ( ) ( max max b b x x L y y L = δ y a and y b are constants used to increase or decrease the global illumination

11 Linear with multiple paths special case If α=0 and δ=0 Then stretching is related to interval (x a,x b ) While are excluded (clipping) gray levels less than x a and greater than x b background object This is useful when we know the object is in (x a,x b ) in order to segment it. IF x a =x b x T, the output image is named Binary Image.

12 Non Linear Quadratic transformation: y=x Expand high gray level and compress lower gray level 300 Square root transf. Opposite behavior as previous transf. y = x Log transform y = log ( 1+ x) e log [ 1+ max( x)] e Applied when the range of gray levels in input image is much wider than the wanted range in output image (in Fourier representation)

13 Negative Complementing with respect to the maximum gray level of the input image Inverse y = L max x y = 1 with x > 0 x Useful to visualize very dark details of an image Imm. Original Negative Inverse

14 Histogram EqualizaGon The histogram equalizagon transformagon generates an image with equally likely intensity values The intensity values in the output image cover the full range, [0 1] The resulgng image has higher dynamic range Recall the values in the normalized histogram are approximately the probability of occurrence of those values The histogram equalizagon transform is the cumulagve distribugon funcgon (CDF) R. S. Gaborski 14

15 CUMULATIVE DISTRIBUTION FUNCTION Histogram CDF R. S. Gaborski 15

16 Histogram equalization

17 Histogram equalization

18 Histogram equalization Algorithm Given NxM tha image size and L max the maximum gray levels First step is to create the histogram of the image H I Then build the cumulagve histogram H c Then compute the mapping funcgon H c (x) and remap every pixel

19 Histogram EqualizaGon Input Image Output Image R. S. Gaborski 19

20 Histogram EqualizaGon Example g = histeq(f, nlev) where f is the original image and nlev number of intensity levels in output image R. S. Gaborski 20

21 Adaptive Histogram Equalization (AHE) Since our eyes adapt to local regions instead of engre image, it is useful to opgmize image enhancement locally The image is divided in a grid of non-overlapping regions histogram equalizagon applied in each region

22 Contrast Limited Adaptive Histogram Equalization (CLAHE) Operate a clip on the equalized histogram Compute the cumulagve histogram Nota%on change N is the number of gray levels M the total number of pixels in Image ß is the clip limit and α clip factor s max maximum allowed slope For X-ray images s max =4 Perform histogram equalizagon locally and operate a clipping redistribugng the pixels

23 Contrast Limited Adaptive Histogram Equalization (CLAHE) h(n) β h(n)-β Nota%on change N is the number of gray levels M the total number of pixels in Image n

24 Contrast Limited Adaptive Histogram Equalization (CLAHE) Original Image Histogram Equalization CLAHE