EECS 556 Image Processing W 09. Image enhancement. Smoothing and noise removal Sharpening filters

Transcription

1 EECS 556 Image Processing W 09 Image enhancement Smoothing and noise removal Sharpening filters

2 What is image processing? Image processing is the application of 2D signal processing methods to images Image representation and modeling Image enhancement Image restoration/image filtering Compression (computer vision)

3 Systems for 2D signals Image processing systems enhanced version of f Continuous Zoom lenses optical color filters photographic film analog photocopiers

4 Systems for 2D signals Continuous Zoom lenses optical color filters photographic film analog photocopiers Discrete scanner / digitizer, contrast enhancer, denoiser, image compressor edge detector

5 Image enhancement Accentuate certain desired features for subsequent analysis or display. Contrast stretching / dynamic range adjustment Color histogram normalization Noise reduction Sharpening Image interpolation / motion estimation Edge detection

6 Contrast stretched image

7 Histogram equalization

8 Edge detection

9 Image enhancement Accentuate certain desired features for subsequent analysis or display. Contrast stretching / dynamic range adjustment Color histogram normalization Noise reduction Sharpening Image interpolation / motion estimation Edge detection Tools: Filters 2D Fourier

10 LSI (linear shift invariant) systems An LSI system is completely specified by its impulse response. Discrete linear convolution

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12 Non linear operations Piecewise linear amplitude adjustment Histogram based transformations Edge detection methods

13 Image enhancement Notice: Objective goal is subjective and function of the human visual systems properties

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15 Image enhancement in Matlab edge - Find edges in intensity image. histeq - Enhance contrast using histogram equalization. imadjust - Adjust image intensity values or colormap. imnoise - Add noise to an image. medfilt2 - Perform 2 D median filtering. ordfilt2 - Perform 2 D order statistic filtering. wiener2 - Perform 2 D adaptive noise removal filtering.

16 Point and local processing Operations on single pixel at a time Operations on groups of pixels (neighborhoods) Pixel 4 Neighbors 8 Neighbors

17 Simplest form of processing: Point Processing Pixel T r = f ( m, n) s = T (r) 255 S=T(r) No change Thresholding Image negative : s=l r 0 r 255 Black 7

18 Simplest form of processing: Point Processing Pixel T r = f ( m, n) s = T (r) 255 Common Examples: γ = 0. Dynamic Range Compression T ( r) = c log( + r) s Gamma Correction γ = 0 0 r 255 Black T ( r) = γ cr Narrow range of dark gets mapped to broad range of gray 8

19 Gamma Correction: To compensate for nonlinearities in I/O devices like photographic film, scanners, printers, monitors, and the eye 9

20 Histogram Processing Distribution of gray levels can be judged by measuring a Histogram Histogram: 5 Graylevel 20

21 Example: 2

22 Transform histogram to desired histogram perceptually more pleasing 22

23 we will come back to this 23

24 Local processing Operations on groups of pixels (neighborhoods) Filtering Smoothing Noise smoothing Sharpening

25 Box (moving average) filter Kernel k with positive entries, that sum to. Notice: all weights are equal h[, ] smoothing Slide credit: David Lowe (UBC)

26 Box filter

27 Example: Smoothing with a box filter

28 Smoothing with a Gaussian Weight contributions of neighboring pixels by nearness x 5, σ = Constant factor at front makes volume sum to (can be ignored, as we should normalize weights to sum to in any case). Slide credit: Christopher Rasmussen

29 Smoothing with a Gaussian Rule of thumb: set filter half width to about 3 σ

30 Smoothing with a Gaussian

31 Why are they appealing? Remove high frequency components from the image (low pass filter) Convolution with self is another Gaussian Convolving two times with Gaussian kernel of width σ is same as convolving once with kernel of width sqrt(2) σ Separable kernel Factors into product of two D Gaussians Useful: can convolve all rows, then all columns Source: K. Grauman

32 Separability of the Gaussian filter Source: D. Lowe

33 Noise smoothing Often the power spectrum of an image hasless energy at high spatial frequencies. In contrast, noise power spectra are often flat (e.g., white noise) or approximately flat. SNR is poor for high spatial frequencies. Common to use a low pass filter to remove poor SNR components and preserve the good SNR components at low spatial frequencies.

34 Gaussian noise Noise: sum of many independent factors, with zero mean modeled by a gaussian:

35 Noise smoothing by gaussian filtering Smoothing reduces pixel noise: Each row shows smoothing with Gaussians of different width; each column shows different amounts of Gaussian noise.

36 Noise smoothing by Median filtering A median filter operates over a window by selecting the median intensity in the window Is median filtering linear? Source: K. Grauman

37 Median filter What advantage does median filtering have over Gaussian filtering? Robustness to outliers Remove salt & pepper noise Source: K. Grauman

38 Filter salt & pepper noise Salt-and-pepper noise Median filtered MATLAB: medfilt2(image, [h w]) Source: K. Grauman

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40 Median vs. Gaussian filtering 3x3 5x5 7x7 Gaussian Median

41 Sharpening sharpen an image by highpass filtering Extract fine details like edges

42 Sharpening

43 Sharpening & Highpass filtering Which filter can we use for sharpening? Does it work? No! We lose the DC component (uniform region)

44 Sharpening & Highpass filtering detail

45 = original smoothed (5x5) detail + α = original detail sharpened

46 Sharpening & Highpass filtering

47 Sharpening * = Original sharpened

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49 More Linear Operations: Sharpening Filters They are useful for highlighting or enhancing details and high frequency information (e.g. edges) They can (and often are) based on derivativetype operations in the image Recall: f x f (x+ h) h f (x) f ( x + ) f ( x) Continuous Discrete

50 Derivative type Filters [ ]

51 Derivative type Filters High pass filter: noise is amplified!

52 Derivative type Filters In 2D: Common design choice: Low pass filter along y

53 Derivative type Filters

54 Derivative type Filters Directional Derivatives Of A Binary Image Original Image 2D Kernel D Kernel D Kernel D Kernel

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57 Derivative type Filters ), ( ), ( 2 ), ( y ), ( ), ( 2 ), ( x y x f y x f y x f f y x f y x f y x f f [ ] 2 2 Laplacian: + = y x f f f [ ] 2 =

58 Variations of the Laplacian Filter Laplacian: + = y x f f f [ ] 2 = Same response in row/column directions = Isotropic filter

59 59 Sharpening Using the Laplacian Filter ), ( ), ( ), ( 2 y x f y x f A y x g = + 8 A Boosting High Frequencies Courtesy of Peyman Milanfar

60 Courtesy of Peyman Milanfar

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