1. Linear Operations Using Masks
Masks are patterns used to define the weights used in averaging the neighbors of a pixel to compute some result at that pixel
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2. Expressing linear operations on neighborhoods
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3. Images as functions
Render with scanalyze????
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4. Neighborhood operations
Average neighborhood to remove noise or high frequency patterns
Detect boundaries at points of contrast using gradient computation
Can use median filtering to smooth while keeping boundaries sharp
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5. Image processing examples
Histogram equalization; gamma correction; median filtering
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6. Histogram equalization
Left image does not use all available gray levels. Image is recoded so that all gray levels are used and such that each gray level occurs in roughly the same number of pixels of the recoded image. (See algorithm in text, xv.)
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7. Histogram equalization can darken a bright image, perhaps improving contrast
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8. Can define mapping of input gray level to output level (xv)
Gamma correction: boost all gray levels
Boost low levels and reduce high
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9. Smoothing an image by averaging neighbors (boxcar)
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10. Output pixel is the dot product of the input neighborhood and the mask
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11. Properties of smoothing masks
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12. Types of ideal edges (in 1D)
These types are also present in 2D and 3D images and are complicated by orientation variations.
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13. Boxcar smoothing filter example
So, reducing noise will also degrade the signal.
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14. Linear smoothing smoothes noise and blurs signal
Blur: step is now ramp
Input image
Row after 5x5 mean filter
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15. Gaussian smoothing
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16. Median filter replaces center with neighborhood median, not mean
Median filter smoothes signal and preserves sharp boundary
Mean filtering smoothes signal and ramps the boundary
Noisy row of checkers image
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17. Median filter is not linear
Algorithm requires comparisons and is more expensive than using mask
Can sort all NxN pixel values and pick middle
Do not need totally sorted data: O(N) algorithm exists
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18. Scratches removed by using a median filter
Thin artifact removed, sharp boundaries preserved.
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19. Finding boundary pixels
Computing derivatives or gradients to locate region change.
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20. 2 rows of intensity vs difference
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21. Differencing used to estimate 1st and 2nd derivatives
Masks represent the first and 2nd differences
First differences
2nd differences
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22. Step edges X mask [-1, 0, +1]
Step edge is detected well, but edge location imprecise.
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23. Ramp and impulse X mask [-1, 0, +1]
Ramp edge now yields a broad weak response. Impulse response is a “whip”, first up and then down.
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24. 2nd derivative using mask [-1, 2, -1]
Response is zero on constant region and a “double whip” amplifies and locates the step edge.
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25. 2nd derivative using mask [-1, 2, -1]
Weak response brackets the ramp edge. Bright impulse yields a double whip with gain of 3X original contrast.
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26. Estimating 2D image gradient
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27. Gradient from 3x3 neighborhood
Estimate both magnitude and direction of the edge.
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28. Prewitt versus Sobel masks
Sobel mask uses weights of 1,2,1 and -1,-2,-1 in order to give more weight to center estimate. The scaling factor is thus 1/8 and not 1/6.
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29. Computational short cuts
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30. Alternative masks for gradient
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31. Computational shortcuts
Use MAX operation on 1D row and column derivatives.
Use OR operation on thresholded row and column derivatives.
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32. 2 rows of intensity vs difference
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33. Caption for Prewitt image
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34. Properties of derivative masks
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35. Next set of related slides
Interpret the properties of masks using the theory of vectors and dot products.
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