1. Machine Vision ENT 273
Image Filters
Hema C.R.
Lecture 5

2. Why Filters are needed?
Image processing converts an input image into an enhanced image from which information about the image can be retrieved.
To enhance images any unwanted information or distortions called noise has to be removed.
Filtering is the process which removes noise from an image [which also includes lightening darker regions to enhance quality of the image or suppresses unwanted information /region]
Original Image
Image with Noise
Hema ENT 273 Lecture 5

3. Image Noise Images are formed by light falling on a sensor
Noises are introduced due to
Quantization – which reduces the light levels to 256
Imperfect sensors
Imperfect lighting conditions during acquisition
Compression formats
Hema ENT 273 Lecture 5

4. Features of Filter
Reduce the size of the data on which we want to build
our inferences
Reduction should retain most informative pieces
Edges and Corners
Texture
Mathematically/computationally
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6. Types of Noise Salt and Pepper Gaussian Noise Uniform Noise
Original Image
Types of Noise
Salt and Pepper
In salt and pepper noise pixels in the image are vastly different in color from their surrounding pixels.
The color of a noisy pixel bears no relation to the color of surrounding pixels.
Generally this type of noise will only affect a small number of image pixels.
When viewed, the image contains dark and white dots, hence the term salt and pepper noise. .
Gaussian Noise
In Gaussian noise (dependent noise), an amount of noise is added to every part of the picture.
Each pixel in the image will be changed from its original value by a (usually) small amount.
Taking a plot of the amount of distortion of a pixel against the frequency with which it occurs produces a Gaussian distribution of noise
Uniform Noise
Pixel values are usually close to their true values.
Average value is equal to the real one
Salt and Pepper Noise
Gaussian Noise
Uniform Noise
Hema ENT 273 Lecture 5

7. Noise Removal Most Noise removal processes are called filters
Applied to each point in an image [convolution]
Use information in the small local windows of a pixel
Noise removal Filters
Linear Filters
Non-Linear Filters
Gaussian filters
Mean Filter
Median Filter
Hema ENT 273 Lecture 5

8. Output impulse response
Linear Systems
Space Invariant System
A system whose response remains the same irrespective of the position of the input pulse
Output impulse response
Linear
Space
Invariant
System
Input impulse
Hema ENT 273 Lecture 5

9. Linear Space Invariant Systems
In LSI systems the output h(x,y) is a convolution of f(x,y) with impulse response g(x,y)
Linear
Space
Invariant
System
g(x,y)
Input Image
Output Image
Hema ENT 273 Lecture 5

10. Convolution Convolution
A neighborhood operation in which each output pixel is a weighted sum of neighboring input pixels. The weights are defined by the convolution kernel. Image processing operations implemented with convolution include smoothing, sharpening, and edge enhancement.
Convolution is a spatially invariant operation
Hema ENT 273 Lecture 5

11. Convolution (cont.) One of the most important processes on images.
Actually a class of operations allowing much variety.
Used in almost all Computer Vision programs as a starting point.
Used in many Computer Graphics processes.
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12. Example: horizontal differencing as convolution
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13. a combination of multiplication and addition
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14. Example: Image after convolution
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15. Convolution Mask A B C D E F G H I h [i,j] P1 P2 P3 P4 P5 P6 P7 P8 P9
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17. Mask The mask can contain any numbers. E.g. the mask below amounts to
averaging adjacent pixels and so produces a smoothing effect on the image.
The mask can be vertically oriented instead of horizontally. The
differencing mask will then be sensitive to horizontal edges.
Hema ENT 273 Lecture 5

18. The example below also combines smoothing and differencing, and is
The mask can be 2-dimensional—in fact, just like a small piece of image.
The example below also combines smoothing and differencing, and is
Hema ENT 273 Lecture 5

19. The mask can be 2-dimensional—in fact, just like a small piece of image. The example below also combines smoothing and differencing, and is used in practical applications. (It is referred to as a Sobel operator.)
Hema ENT 273 Lecture 5

20. Example of 2-D convolution
Hema ENT 273 Lecture 5

21. Some special masks Horizontal differences Vertical differences
Diagonal differences
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22. Differencing masks may be more complex e.g. a horizontal bar mask
An arbitrary mask can be given this property by computing the mean of its weights, and subtracting the mean from each weight in turn to get a newweight.
Hema ENT 273 Lecture 5

23. A simple smoothing mask
This takes the average of each 3x3 region of the image.
The simple smoothing mask is not particularly good, because its point-spread function has sharp edges.
Hema ENT 273 Lecture 5

24. The Gaussian smoothing mask
A more effective smoothing mask falls off gently at the edges. One of the bestis the Gaussian mask. Its width is described by a parameter called (sigma).
Hema ENT 273 Lecture 5

25. Example on the effect of progressively increasing
Example on the effect of progressively increasing . Its values are 1, 2 and 4 in the 3 smoothed images.
Hema ENT 273 Lecture 5

26. Feature of Linear Filter
About modifying pixels based on neighborhood.
Linear means linear combination of neighbors.
Linear methods simplest
Can combine linear methods in any order to achieve same result
Maybe easier to undo
“Filter Banks”
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27. Mean Filter
Implemented by a local averaging operation where the value of each pixel is replaced by the average of all the values in the local neighborhood: where M is the total number of pixels in the neighborhood N
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28. 3x3 neighborhood about [i,j]
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29. Mean Filter
The mean filter is a simple sliding-window spatial filter that replaces the center value in the window with the average (mean) of all the pixel values in the window.
The window, or kernel, is usually square but can be any shape.
An example of mean filtering of a single 3x3 window of values is shown 5 3 7 2 6 4 8 1 9 * 5
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30. Example of mean filter using 3x3 neighborhood
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31. Another example of mean filter
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32. Median Filter
The median filter is also a sliding-window spatial filter, but it replaces the center value in the window with the median of all the pixel values in the window.
As for the mean filter, the kernel is usually square but can be any shape.
An example of median filtering of a single 3x3 window of values is shown
Median filter remove 'impulse' noise (outlying values, either high or low).
The median filter is also widely claimed to be 'edge-preserving' since it theoretically preserves step edges without blurring.
However, in the presence of noise it does blur edges in images slightly. 3 57 7 2 5 6 18 4 9
2,3,4,5,6,7,9,18,57 * 6
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33. Example of median filter using 3x3 neighborhood
Hema ENT 273 Lecture 5

34. Gaussian Filter
Gaussian filters removes noise by smoothing but also blurs the image,
The degree of smoothing is determined by the standard deviation of the Gaussian. (Larger standard deviation Gaussians, of course, require larger convolution masks in order to be accurately represented.)
The Gaussian outputs a `weighted average' of each pixel's neighborhood, with the average weighted more towards the value of the central pixels.
This is in contrast to the mean filter's uniformly weighted average.
Gaussian provides gentler smoothing and preserves edges better than a similarly sized mean filter
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36. 2D Gaussian function
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37. Gaussian Filter Can be constructed using binomial expansion Example
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38. We need to get the Gaussian mask, where c is a normalizing constant
By rewriting and choosing a value of the variance , we can find the nxn mask
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39. Example of Gaussian distribution for
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40. By choosingthe bottom right corner as the value of one
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41. To normalize the mask to ensure uniform intensity
Thus the convolution is
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42. Histogram Equalization
Histogram equalization is a common technique for enhancing the appearance of images. Suppose we have an image which is predominantly dark. Then its histogram would be skewed towards the lower end of the grey scale and all the image detail is compressed into the dark end of the histogram. If we could `stretch out' the grey levels at the dark end to produce a more uniformly distributed histogram then the image would become much clearer.
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46. Histogram Modification
Histogram equalization
Is a method for stretching contrast of unevenly distributed gray values by uniformly redistributing the gray values
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47. References Computer Vision – Linda G Shapiro & George Stockman
Mat lab reference notes
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48. Machine Vision
End of Lecture 5