1. Transforming images to images
Image Transforms
Transforming images to images

2. Classification of Image Transforms
Point transforms
modify individual pixels
modify pixels’ locations
Local transforms
output derived from neighbourhood
Global transforms
whole image contributes to each output value
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3. Point Transforms Manipulating individual pixel values
Brightness adjustment
Contrast adjustment
Histogram manipulation
equalisation
Image magnification
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4. Grey Scale Manipulation
Brightness modifications
Contrast modifications
Histogram manipulation
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5. Brightness Adjustment
Add a constant to all values
g’ = g + k
(k = 50)
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6. Contrast Adjustment Scale all values by a constant g’ = g*k (k = 1.5)
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7. Image Histogram
Measure frequency of occurrence of each grey/colour value
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8. Histogram Manipulation
Modify distribution of grey values to achieve some effect
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9. Equalisation/Adaptive Equalisation
Specifically to make histogram uniform
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10. Equalisation Transform
Equalised image has n x m/l pixels per grey level
Cumulative to level j
jnm/l pixels
Equate to a value in input cumulative histogram C[i]
C[i] = jnm/l
j = C[i]l/nm
Modifications to prevent mapping to –1.
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11. Thresholding Transform grey/colour image to binary
if f(x, y) > T output = 1
else 0
How to find T?
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12. Threshold Value Manual P-Tile Mode Other automatic methods
User defines a threshold
P-Tile
Mode
Other automatic methods
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13. P-Tile If we know the proportion of the image that is object
Threshold the image to select this proportion of pixels
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14. Mode Threshold at the minimum between the histogram’s peaks.
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15. Automated Methods Find a threshold  such that
(Start at  = 0 and work upwards.)
Average l
Average h
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16. Image Magnification Reducing Enlarging
new value is weighted sum of nearest neighbours
new value equals nearest neighbour
Enlarging
add noise to obscure pixelation
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17. Local Transforms Convolution Applications smoothing sharpening
matching
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18. Convolution Definition
Place template on image
Multiply overlapping values in image and template
Sum products and normalise
(Templates usually small)
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19. Example Image Template Result … . . . . . ... … 3 5 7 4 4 ……
… …
… …
… …
… … … …
… …
… … …
1 1 1
1 2 1
Divide by template sum
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20. Separable Templates Convolve with n x n template
n2 multiplications and additions
Convolve with two n x 1 templates
2n multiplications and additions
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21. Example Laplacian template Separated kernels 0 –1 0 -1 4 –1 -1 -1 2 -1
0 –1 0
-1 4 –1 -1 2
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22. Composite Filters Convolution is distributive
Can create a composite filter and do a single convolution
Not convolve image with one filter and convolve result with second.
Efficiency gain
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23. Applications
Usefulness of convolution is the effects generated by changing templates
Smoothing
Noise reduction
Sharpening
Edge enhancement
Template matching
A later lecture
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24. Smoothing Aim is to reduce noise What is “noise”? How is it reduced
Addition
Adaptively
Weighted
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25. Noise Definition Noise is deviation of a value from its expected value
Random changes
x  x + n
Salt and pepper
x  {max, min}
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26. Noise Reduction By smoothing S(x + n) = S(x) + S(n) = S(x)
Since noise is random and zero mean
Smooth locally or temporally
Local smoothing
Removes detail
Introduces ringing
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27. Adaptive Smoothing Compute smoothed value, s
Output = s if |s – x| > T
x otherwise
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28. Median Smoothing Median is one value in an ordered set:
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29. Original Smoothed Median Smoothing
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30. Gaussian Smoothing To reduce ringing Weighted smoothing
Numbers from Gaussian (normal) distribution are weights.
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31. Sharpening What is it? Why do it? Enhancing discontinuities
Edge detection
Why do it?
Perceptually important
Computationally important
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32. An edge is a significant local change in image intensity.
Edge Definition
An edge is a significant local change in image intensity.
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33. Edge Types Step edge Line edge Roof edge Real edges
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34. First Derivative, Gradient Edge Detection
If an edge is a discontinuity
Can detect it by differencing
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35. Roberts Cross Edge Detector
Simplest edge detector
Inaccurate localisation -1 1 -1 1
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36. Prewitt/Sobel Edge Detector-1 1 -1 1
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37. Edge Detection Combine horizontal and vertical edge estimates
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38. Problems Enhanced edges are noise sensitive Scale What is “local”?
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39. Canny/Deriche Edge Detector
Require
edges to be detected
accurate localisation
single response to an edge
Solution
Convolve image with Difference of Gaussian (DoG)
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40. Example Results
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41. Second Derivative Operators Zero Crossing
Model HVS
Locate edge to subpixel accuracy
Convolve image with Laplacian of Gaussian (LoG)
Edge location at crossing of zero axis
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42. Example Results
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43. Image Processing and Computer Vision: 2

44. Global Transforms
Computing a new value for a pixel using the whole image as input
Cosine and Sine transforms
Fourier transform
Frequency domain processing
Hough transform
Karhunen-Loeve transform
Wavelet transform
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45. Cosine/Sine A halfway solution to the Fourier Transform
Used in image coding
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46. Fourier
All periodic signals can be represented by a sum of appropriately weighted sine/cosine waves
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47. Transformed section of BT Building image.
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48. Frequency Domain Filtering
Convolution Theorem:
Convolution in spatial domain
is equivalent to
Multiplication in frequency domain
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49. Smoothing Suppress high frequency components
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50. Sharpening Suppress low frequency components
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51. Example
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52. Wavelet A hierarchical representation detail
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53. Hough Transform To detect curves analytically Example straight lines
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54. Straight Line y = mx + c c = -mx + y
gradient m, intercept c
c = -mx + y
gradient -x, intercept y
ALL points in (x, y) transform to a straight line in (c, m)
Can therefore detect collinear points
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55. Analytic Curve Finding
Alternative representation
to avoid infinities
Other curves
higher dimensional accumulators
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56. Performance Improvement Techniques
Look at pairs of points
Use edge orientation
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57. Karhunen-Loeve (Principal Component)
A compact method of representing variation in a set of images
PCs define a co-ordinate system
1st PC records most of variation
2nd PC records most of remainder
etc
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58. Method Take a set of typical images
Compute mean image and subtract from each sample
Transform images into columns
Group images into a matrix
Compute covariance matrix
Compute eigenvectors
these are the PCs
eigenvalues show their importance
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59. Uses Compact representation of variable data Object recognition
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60. Uses Hierarchical representation Multiresolution processing Coding
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61. Geometric Transformations
Definitions
Affine and non-affine transforms
Applications
Manipulating image shapes
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62. Affine Transforms Scale, Shear, Rotate, Translate
Length and areas preserved. x’ y’ 1 [ ]
a b c
d e f
g h i x y =
Change values of transform matrix elements according to desired effect.
a, e  scaling
b, d  shearing
a, b, d, e  rotation
c, f  translation
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63. Affine Transform Examples
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64. Warping Example Ansell Adams’ Aspens
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65. Image Resampling Moving source to destination pixels
x’ and y’ could be non-integer
Round result
can create holes in image
Manipulate in reverse
where did warped pixel come from
source is non-integer
interpolate nearest neighbours
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66. You Should Know… Point transforms Local transforms Global transforms
scaling, histogram manipulation,thresholding
Local transforms
edge detection, smoothing
Global transforms
Fourier, Hough, Principal Component, Wavelet
Geometrical transforms
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