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Image Transforms

Explore image processing and computer vision techniques such as point transforms, brightness/contrast adjustments, histogram manipulation, thresholding, and local transforms for enhancing and refining image quality seamlessly.

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Image Transforms

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  1. 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 Image Processing and Computer Vision: 2

  3. Point Transforms • Manipulating individual pixel values • Brightness adjustment • Contrast adjustment • Histogram manipulation • equalisation • Image magnification Image Processing and Computer Vision: 2

  4. Grey Scale Manipulation • Brightness modifications • Contrast modifications • Histogram manipulation Image Processing and Computer Vision: 2

  5. Brightness Adjustment Add a constant to all values g’ = g + k (k = 50) Image Processing and Computer Vision: 2

  6. Contrast Adjustment Scale all values by a constant g’ = g*k (k = 1.5) Image Processing and Computer Vision: 2

  7. Image Histogram • Measure frequency of occurrence of each grey/colour value Image Processing and Computer Vision: 2

  8. Histogram Manipulation • Modify distribution of grey values to achieve some effect Image Processing and Computer Vision: 2

  9. Equalisation/Adaptive Equalisation • Specifically to make histogram uniform Image Processing and Computer Vision: 2

  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. Image Processing and Computer Vision: 2

  11. Thresholding • Transform grey/colour image to binary if f(x, y) > T output = 1 else 0 • How to find T? Image Processing and Computer Vision: 2

  12. Threshold Value • Manual • User defines a threshold • P-Tile • Mode • Other automatic methods Image Processing and Computer Vision: 2

  13. P-Tile • If we know the proportion of the image that is object • Threshold the image to select this proportion of pixels Image Processing and Computer Vision: 2

  14. Mode Threshold at the minimum between the histogram’s peaks. Image Processing and Computer Vision: 2

  15. Average l Average h Automated Methods Find a threshold  such that (Start at  = 0 and work upwards.) Image Processing and Computer Vision: 2

  16. Image Magnification • Reducing • new value is weighted sum of nearest neighbours • new value equals nearest neighbour • Enlarging • new value is weighted sum of nearest neighbours • add noise to obscure pixelation Image Processing and Computer Vision: 2

  17. Local Transforms • Convolution • Applications • smoothing • sharpening • matching Image Processing and Computer Vision: 2

  18. Convolution Definition Place template on image Multiply overlapping values in image and template Sum products and normalise (Templates usually small) Image Processing and Computer Vision: 2

  19. Example Image Template Result … . . . . . ... … 3 5 7 4 4 … … 4 5 8 5 4 … … 4 6 9 6 4 … … 4 6 9 5 3 … … 4 5 8 5 4 … … . . . . . ... … . . . . . ... … . . . . . ... … . 6 6 6 . … … . 6 7 6 . … … . 6 7 6 . … … . . . . . ... … . . . . . ... 1 1 1 1 2 1 1 1 1 Divide by template sum Image Processing and Computer Vision: 2

  20. Separable Templates • Convolve with n x n template • n2 multiplications and additions • Convolve with two n x 1 templates • 2n multiplications and additions Image Processing and Computer Vision: 2

  21. Example 0 –1 0 -1 4 –1 0 –1 0 • Laplacian template • Separated kernels -1 2 -1 -1 2 -1 Image Processing and Computer Vision: 2

  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 Image Processing and Computer Vision: 2

  23. Applications • Usefulness of convolution is the effects generated by changing templates • Smoothing • Noise reduction • Sharpening • Edge enhancement • Template matching • A later lecture Image Processing and Computer Vision: 2

  24. Smoothing • Aim is to reduce noise • What is “noise”? • How is it reduced • Addition • Adaptively • Weighted Image Processing and Computer Vision: 2

  25. Noise Definition • Noise is deviation of a value from its expected value • Random changes • x  x + n • Salt and pepper • x  {max, min} Image Processing and Computer Vision: 2

  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 Image Processing and Computer Vision: 2

  27. Adaptive Smoothing • Compute smoothed value, s Output = s if |s – x| > T x otherwise Image Processing and Computer Vision: 2

  28. Median Smoothing Median is one value in an ordered set: 1 2 3 4 5 6 7  median = 4 2 3 4 5 6 7  median = 4.5 Image Processing and Computer Vision: 2

  29. Original Smoothed Median Smoothing Image Processing and Computer Vision: 2

  30. Gaussian Smoothing • To reduce ringing • Weighted smoothing • Numbers from Gaussian (normal) distribution are weights. Image Processing and Computer Vision: 2

  31. Sharpening • What is it? • Enhancing discontinuities • Edge detection • Why do it? • Perceptually important • Computationally important Image Processing and Computer Vision: 2

  32. Edge Definition Image Processing and Computer Vision: 2

  33. Edge Types • Step edge • Line edge • Roof edge • Real edges Image Processing and Computer Vision: 2

  34. First Derivative, Gradient Edge Detection • If an edge is a discontinuity • Can detect it by differencing Image Processing and Computer Vision: 2

  35. Roberts Cross Edge Detector • Simplest edge detector • Inaccurate localisation Image Processing and Computer Vision: 2

  36. Prewitt/Sobel Edge Detector Image Processing and Computer Vision: 2

  37. Edge Detection • Combine horizontal and vertical edge estimates Image Processing and Computer Vision: 2

  38. Problems • Enhanced edges are noise sensitive • Scale • What is “local”? Image Processing and Computer Vision: 2

  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) Image Processing and Computer Vision: 2

  40. Example Results Image Processing and Computer Vision: 2

  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 Image Processing and Computer Vision: 2

  42. Example Results Image Processing and Computer Vision: 2

  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 Image Processing and Computer Vision: 2

  45. Cosine/Sine • A halfway solution to the Fourier Transform • Used in image coding Image Processing and Computer Vision: 2

  46. Fourier • All periodic signals can be represented by a sum of appropriately weighted sine/cosine waves Image Processing and Computer Vision: 2

  47. Transformed section of BT Building image. Image Processing and Computer Vision: 2

  48. Frequency Domain Filtering • Convolution Theorem: Convolution in spatial domain is equivalent to Multiplication in frequency domain Image Processing and Computer Vision: 2

  49. Smoothing Suppress high frequency components Image Processing and Computer Vision: 2

  50. Sharpening Suppress low frequency components Image Processing and Computer Vision: 2

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