![Point Operation
Point Operation
zero-memory operation
Map graylevel u∈[0,L] to graylevel v∈[0,L], through
transform relation v=f(u).
Contrast stretching, clipping, thresholding
α u, 0≤u<a
vb v γ
v = β ( u − a ) + va , a ≤ u < b
β
va γ ( u − b ) + vb , b ≤ u < L
α
u α and β determination is based on
a b L image histogram.](https://image.slidesharecdn.com/04imageenhancementedgedetection-120321101406-phpapp02/85/04-image-enhancement-edge-detection-4-320.jpg)
![Spatial Operation
Alternative method: every pixel is replaced by its 4-
closest neioghbors average intensity value :
v(m,n) = 0.5 [y(m,n) + 0.25{ y(m-1,n)
+ y(m+1,n) + y(m,n-1) + y(m,n+1)} ]
Averaging ‘ mask’:
¼ ¼ 1/9 1/9 1/9 0 1/8 0
¼ ¼ 1/9 1/9 1/9 1/8 ¼ 1/8
1/9 1/9 1/9 0 1/8 0
2×2 window 3×3 window 5-points weighted averaging](https://image.slidesharecdn.com/04imageenhancementedgedetection-120321101406-phpapp02/85/04-image-enhancement-edge-detection-17-320.jpg)
![High-boost Filtering (Unsharp Masking)
Substraction of amplified original image and low-pass fitered
original image:
g(m, n) = Af(m, n) – lowpass(f(m, n))
= (A-1)f(m, n) + [f(m, n)– lowpass(f(m, n))]
= (A-1)f(m, n) + higpass(f(m, n))
Produce an edge-enhanced version of original image.
Original Image High pass High boost](https://image.slidesharecdn.com/04imageenhancementedgedetection-120321101406-phpapp02/85/04-image-enhancement-edge-detection-29-320.jpg)
04 image enhancement edge detection
- 1. Image Enhancement & Edge Detection Tati R Mengko
- 2. Introduction Image Enhancement : accentuation and sharpening of image features (edges, boundaries, contrast) to improve image visual appearance and analysis. does not increase information content, but improves feature dynamic range to ease feature detection. Major challenge in image enhancement: quantification of the enhanced feature criterion.
- 3. Image Enhancement Techniques Image Enhancement Point Spatial Transform Pseudo Operation operation Operation Coloring •Contrast •Noise •Linear Filtering •False Coloring Stretching Smoothing •Root Filtering •Psudocoloring •Noise Clipping •Median Filtering •Homomorphic •Window Slicing •Unsharp Filtering •Histogram Masking Modeling •Low-, High-, Band-pass Filtering •Zooming
- 4. Point Operation Point Operation zero-memory operation Map graylevel u∈[0,L] to graylevel v∈[0,L], through transform relation v=f(u). Contrast stretching, clipping, thresholding α u, 0≤u<a vb v γ v = β ( u − a ) + va , a ≤ u < b β va γ ( u − b ) + vb , b ≤ u < L α u α and β determination is based on a b L image histogram.
- 5. Point Operation Contrast stretching Bad contrast: unadequate illumination, sensor non-linearity. In the contrast-stretched area, transforming gradient >1. Special contrast-stretching cases: Clipping: α=γ=0. Thresholding : α=γ=0 , a=b. v v vb v γ β va u u α u a b L stretching clipping tresholding
- 6. Thresholding Example: Binarization Red Blood Cells Grayscale Image Red Blood Cells Binary Image
- 7. Thresholding Example: Gamma Correction Original Image Gamma-corrected Image
- 8. Digital Negative Reversed graylevel scaling: 50 50 100 100 v = L-u 150 150 200 200 250 250 50 100 150 200 250 50 100 150 200 250 %MATLAB I=imread('cameraman.tif'); figure(1);imagesc(I);colormap(gray); figure(2);imagesc(255-double(I)); colormap(gray);
- 9. Intensity Level Slicing Segment a certain intensity level from the rest of the image. Without background: L, a ≤ u ≤ b v= 0, lainnya With background: L, a ≤ u ≤ b v= u , lainnya v v L u u a b a b L
- 10. Intensity Level Slicing Original image Without background With background
- 11. Range Compression and Digital Substraction Compress image intensity range: v = c log10(1+|u|) , c = scaling constant Digital Substraction: Detect difference/gradual intensity change between images. Example: Digital Substraction Angiography (DSA).
- 12. Example of Range Compression
- 13. Histogram Modeling Image histogram represents distribution of graylevel occurrence in an image. Histogram modeling: modification of an image histogram into a desired shape. Histogram Equalization: uniformly-distribute graylevel occurrence frequency distribution. I = imread('tire.tif');imshow(I); imhist(I,64) J = histeq(I);figure, imshow(J); figure; imhist(J,64) 2000 3000 1800 2500 1600 1400 2000 1200 1500 1000 1000 800 600 500 400 0 200 0 0 50 100 150 200 250 0 50 100 150 200 250 Before hist.equalization After hist.equalization
- 15. Histogram Equalization Histogram equalization is not appropriate for narrow intensity distribution images. Original Histeq Image Result
- 16. Spatial Operation Spatial Averaging Pixel intensity is replaced with weighted average of its neighborhood pixels intensity. v ( m, n ) = ∑ ∑ a (k,l ) y (m − k, n − l ) ( k ,l )∈W Spatial averaging: a(k,l) = constant 1 v ( m, n ) = ∑W ∑ y ( m − k , n − l ) NW ( k ,l )∈ a(k,l)=1/NW, NW = number of pixels within filtering window
- 17. Spatial Operation Alternative method: every pixel is replaced by its 4- closest neioghbors average intensity value : v(m,n) = 0.5 [y(m,n) + 0.25{ y(m-1,n) + y(m+1,n) + y(m,n-1) + y(m,n+1)} ] Averaging ‘ mask’: ¼ ¼ 1/9 1/9 1/9 0 1/8 0 ¼ ¼ 1/9 1/9 1/9 1/8 ¼ 1/8 1/9 1/9 1/9 0 1/8 0 2×2 window 3×3 window 5-points weighted averaging
- 18. Spatial Operation Spatial averaging: Smoothing Low-pass filtering Subsampling Noisy image: y(m,n) = u(m,n) + η(m,n) η(m,n) = white noise with variance= ση2 Output image: 1 v ( m, n ) = NW ∑ ∑ u ( m − k , n − l ) + η ( m, n ) ( k ,l )∈W η(m,n) = spatial average • If mean(η(m,n)) = 0, noise power suppression level is proportional to the number of pixels in the filtering window: ση2 = ση2/NW.
- 19. Example of Spatial Operation Original Image Original Image + Noise
- 20. Example of Spatial Operation
- 21. Blurring Effect due to Averaging
- 22. Blurring Effect due to Averaging
- 23. Effects of Various Noise Energy
- 24. Effects of Various Noise Energy
- 25. Median Filter The last examples shows the weakness of averaging method Median filter overcome this problem
- 26. Median Filter
- 27. Image Sharpening Enhance missing delicate structures due to blurring effect. Sharpen graylevel difference between neighbouring pixels in an image. High-pass filtering Shift-invariant operator Convolution mask contains positive number surrounded by negative numbers. −1 −1 −1 1 −1 8 −1 9 −1 −1 −1
- 28. High Pass Filtering Relation between high-pass filtered image g, original image f, and its low-pass filtered version: g(m, n) = f(m, n) – lowpass(f(m, n))
- 29. High-boost Filtering (Unsharp Masking) Substraction of amplified original image and low-pass fitered original image: g(m, n) = Af(m, n) – lowpass(f(m, n)) = (A-1)f(m, n) + [f(m, n)– lowpass(f(m, n))] = (A-1)f(m, n) + higpass(f(m, n)) Produce an edge-enhanced version of original image. Original Image High pass High boost
- 30. Derivative Filter Sharpen image boundaries/edges, based on discrete spatial gradient operator: Implemented with 2-D convolution approach: hn = edge detector derivative filter convolution mask
- 31. Derivative Filter: Roberts Operator Original Image
- 32. Derivative Filter: Prewitt & Sobel Operator Sobel Prewitt
- 33. Frequency-domain Method Enhancement conducted in the transform domain, followed by an inverse transform to obtain the spatial domain enhanced image representation. For original image U = {u(m,n)} being transformed into V = {v(k,l)} : V = AUAT. Enhancement operation produces v’(k,l) = f(u(m,n)). Spatial domain enhanced image: U = A-1V’(AT)-1 . Generalized Filtering: zero-memory transformation Pixel-to-pixel multiplication: v’(k, l) = g(k, l) v(k, l). g(k, l) = zonal mask. u(m,n) Transformasi v(k,l) Operasi v’(k,l) Transformasi u’(m,n) Inverse Uniter AUAT Titik f(.) A-1 V’(AT)-1
- 34. Frequency-domain Method Frequency-domain processing is utilized to accelerate spatial image filtering. Time domain convolution is equivalent to fourier domain (FFT) pixel-to-pixel multiplication: g(m,n) = h(m,n)*f(m,n) ≈ G(u,v) = H(u,v) F(u,v)
- 35. Ideal Low-pass Filter Ideal low-pass filter: 1, jika u 2 + v 2 ≤ r r0=57 0 H ( u, v ) = 0, jika u 2 + v 2 > r0 Original Image LPF, r0 = 57 LPF, r0 = 36 LPF, r0 = 26 • Ringing effect: property of ideal filter.
- 36. Butterworth Low Pass Filter Butterworth low-pass filter: n: order filter, r0: cutoff freq. Original Image r0 = 18 r0 = 13 r0 = 10 •Removes ringing effects.
- 37. Butterworth Low-pass Filter False contouring removal and noise suppression. False False contour contour due removal with to LPF unadequate Butterworth quantization Original Image Noisy Image Filtered Image
- 38. Ideal High-pass Filter Ideal high-pass filter 0, jika u 2 + v 2 ≤ r r0 = 36 0 H ( u, v ) = 1, jika u 2 + v 2 > r0 Original Image HPF, r0 = 18 HPF, r0 = 36 HPF, r0 = 26 •Ringing effect: property of ideal filter
- 39. Butterworth High-pass Filter Butterworth high-pass filter r0=47, n=2 n: filter order, r0: cutoff freq. Citra asli r0 = 47 r0 = 36 r0 = 81 •Removes ringing effects.
- 40. Iterative based Edge Enhancement T.L.R. Mengko
- 41. Pyramid Edge Detection There may be a number of strong edges in the image that are not significant, because they are short or unconnected. Pyramid edge detection is used to enhance substantial (strong & long) edges, but to ignore the weak or short edges. repetitive shrinkage EDGE TRACKING 1. Cut down to quarter size by averaging 4 corresponding pixels 2. Repeat x times, keep each generated image 3. At the smallest image, perform edge detection (e.g Sobel) 4. Find edges ? (a threshold is needed) 5. If yes, perform edge detection on the group of 4 corresponding pixel in the next larger image. averaging 6. Continue to the next larger image till the largest image.