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Image Analysis

Image Analysis. Manipulate an image to extract information to help solve a problem. Preprocessing - get rid of unnecessary information Data reduction - transform the image to a useable form Feature analysis - make inferences about the image. Image Analysis. Preprocessing Noise reduction

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Image Analysis

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  1. Image Analysis • Manipulate an image to extract information to help solve a problem. • Preprocessing - get rid of unnecessary information • Data reduction - transform the image to a useable form • Feature analysis - make inferences about the image.

  2. Image Analysis • Preprocessing • Noise reduction • Gray level quantization • Spatial quantization • Finding regions of interest Reducing the number of bits

  3. Image Analysis • Data reduction process, in which the image(s) are transformed into a more convenient form. • RGB  HSL • Image subtraction • Histogram • Feature extraction

  4. Image Analysis • Feature analysis - Specific results • Blood cell counting • Tumor size and location • 3D model

  5. Image Analysis • Geometric • Resizing • Rotating • Noise Reduction • Image Smoothing • Median Filtering • Edge Detection • Searching for discontinuities • Histogram slicing • Blob detection

  6. Geometric Transformation

  7. Interpolation • Interpolation to determine image values at integer pixel locations of transformed image. • Numerous interpolation schemes exist • 2 simple methods are • Nearest neighbor: assign value of nearest known point • Bilinear interpolation: example on next slide Interpolation used to simplify data for further processing

  8. Nearest Neighbor Interpolation Interpolate this point To this value

  9. Linear Interpolation

  10. I(x’,y’) I(x,y) I(x+1,y) I(x,y+1) I(x+1,y+1) Bi-linear Interpolation 0 (a,b)  1 I(x’,y) = (1-a)I(x,y) + (a)I(x+1,y) I(x’,y+1) = (1-a)I(x,y+1) + (a)I(x+1,y+1) I(x’,y’) = (1-b)I(x’,y) + (b)I(x’,y+1) I(x’,y’) = (1-b)(1-a)I(x,y) + (1-b)(a)I(x+1,y) + (b)(1-a)I(x,y+1) + (a)(b)I(x,y)

  11. Bi-linear Interpolation I(x’,y’)

  12. Neighborhood Operations

  13. Objectives • Why are neighborhoods important? • What is linear convolution? • discrete • templates, masks or filters • algorithm mechanics • graphical interpretation • Describe non-linear operators • maximum • minimum • median • What is tiling?

  14. Why are neighbourhoods important? pixel

  15. Because… • Provide context for individual pixels. • Relationships between neighbors determine image features. • Neighborhood operations: • noise reduction • edge enhancement • zooming

  16. Noise reduction Edge Enhancement Zooming

  17. Neighbourhood Operations • Linear convolution (*) • A*B*C*D = B*C*D*A = …. • Non-linear operators • median, max, min, ...

  18. Convolution versus Spectral • We learnt two methods of processing images: • Convolution • Spectral • We analyzed and demonstrated how to build a processor (systolic, pipelined, parallel, cellular automaton) for 1D convolution. • 1D convolution is used in speech processing and in polynomial multiplication. • We will use visualized animations now to show in more detail how 2D convolution works for images. • This should convince you how important it is to do convolution quickly in modern Spectral Architectures, especially for 3D etc.

  19. 2D Convolution • Consists of filtering an image A using a filter (mask, template) B. • Mask is a small image whose pixel values are called weights. • Weights modify relationships between pixels. We will show more examples of convolution now, especially for 2D data

  20. A1,1 A3,2 A4,1 A3,4 A3,3 A2,2 A3,1 A2,4 A2,3 A4,3 A1,4 A1,3 A1,2 A4,2 A2,1 A4,4 C3,3 B2,2 C2,3 C2,2 C2,1 C3,1 C3,2 C1,2 C1,1 C1,3 B2,1 B1,2 B1,1 Input image Filter, mask or template Convolved Image A C B  = 2 2 3 3 4 4

  21. A1,1 A3,2 A1,2 A2,1 A2,2 A1,4 A2,3 A2,4 A3,1 A4,4 A1,3 A3,4 A4,1 A4,2 A4,3 A3,3 B1,1 B1,2 B2,1 B2,2 A1,1B1,1 A1,1B1,1 A1,2B1,2 A1,2B1,2 A2,1B2,1 A2,1B2,1 A2,2B2,2 A2,2B2,2 C1,1=   

  22. A1,2B1,1 A3,3 A1,2 A2,1 A2,2 A1,3 A2,3 A2,4 A3,1 A3,2 A1,4 A3,4 A4,1 A4,2 A4,3 A4,4 B1,1 B1,2 B2,1 B2,2 A1,1 A1,2B1,1 A1,3B1,2 A1,3B1,2 A2,2B2,1 A2,2B2,1 A2,3B2,2 A2,3B2,2 C1,2=   

  23. A1,3B1,1 A3,3 A1,2 A2,1 A2,2 A1,3 A2,3 A2,4 A3,1 A3,2 A1,4 A3,4 A4,1 A4,2 A4,3 A4,4 B1,1 B1,2 B2,1 B2,2 A1,1 A1,3B1,1 A1,4B1,2 A1,4B1,2 A2,3B2,1 A2,3B2,1 A2,4B2,2 A2,4B2,2 C1,3=   

  24. A2,1B1,1 A3,3 A1,2 A2,1 A2,2 A1,3 A2,3 A2,4 A3,1 A3,2 A1,4 A3,4 A4,1 A4,2 A4,3 A4,4 B1,1 B1,2 B2,1 B2,2 A1,1 A2,1B1,1 A2,2B1,2 A2,2B1,2 A3,1B2,1 A3,1B2,1 A3,2B2,2 A3,2B2,2 C2,1=   

  25. A1,1 A1,2 A2,1 A2,2 A1,3 A1,4 A2,3 A2,4 A3,1 A3,2 A3,3 A3,4 A4,1 A4,2 A4,3 A4,4 B1,1 B1,2 B2,1 B2,2 B1,1 B1,2 B2,1 B2,2 B1,1 B1,2 B2,1 B2,2

  26. A1,1B1,1 A1,2B1,2 A2,1B2,1 A2,2B2,2 Mathematical Notation C1,1=   

  27. 2 4 4 7 9 4 3 8 9 3 5 9 9 3 6 10 9 -1 2 -1 Convolution Input image Filter, mask or template Convolved Image A C B 21 6 23  = 9 26 19 16 27 17 2 2 3 3 4 4

  28. N1 N2 N1-N2+1 Image size = M1 N1 Mask size = M2 N2 Convolution size = M1- M2 +1 N1-N2+1 Convolution size Typical Mask sizes = 33, 5 5, 77, 9 9, 1111 What is the convolved image size for a 128   128 image and 7  7 mask?

  29. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 * = We convolve with 9*9 averaging filter

  30. Nonlinear Neighbourhood Operations • Maximum • Minimum • Median We discussed already sorter architecture (three variants – pipelined, butterfly combinational and sequential controller). It can be used for all these operations, and also for other non-linear operators

  31. 61 62 57 60 59 65 63 58 59 55 55 56 49 59 57 63 59 63 62 45 53 60 1 1 1 1 Max and Min Operations C1,2= 63=max, 59=min

  32. 1 1 1 1 1 1 1 1 1 62 45 55 53 49 57 58 65 59 56 63 59 59 60 57 55 61 58 59 62 55 62 58 57 56 56 60 63 59 63 65 65 55 57 60 rank Median Operation 9 8 7 6 5 4 3 2 1 C1,2=

  33. 9x9 Median

  34. Edge Detection • What do we mean by edge detection? • What is an edge?

  35. What is Edge Detection? • Detects large intensity transitions between pixels • Redraws the image with only the edges showing 0 0 0 33 0 0 45 78 0 45 23 33 0 0 42 76 0 0 0 38

  36. Edge easy to find What is an Edge?

  37. What is an Edge? Where is edge? Single pixel wide or multiple pixels?

  38. What is an Edge? Noise is here Noise: have to distinguish noise from actual edge

  39. What is an Edge? Is this one edge or two?

  40. What is an Edge? Texture discontinuity

  41. Edge Detection – so what is an edge to be detected? • What is an edge • A large change in image brightness of a short spatial distance • Edge strength = (I(x,y)-I(x+dx,y))/dx But this general definition still allows for many theories, software implementation and hardware architectures.

  42. Now we will discuss and illustrate various kinds of filter operators

  43. Edge Detection Filters • High - Pass Filtering Eliminates Uniform Regions (Low Frequencies) • edge “detection” or “enhancement”

  44. Edge Detection Filters

  45. Edge Detection Filters Edge Detection Continued • Sum of Kernel Coefficients = 0 • differences in signs emphasize differences in pixel values • reduces average image intensity • Negative pixel values in output?

  46. Edge Direction vertical horizontal diagonal

  47. Directional High Pass Filters

  48. Convolution Edge Detection using Sobel and similar operators

  49. Sobel Operator Example of Sobel Operator

  50. Sobel Edge Detection

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