1. UNIT-I Digital Image Fundamentals and Transforms 1

2. Outline Image-An Introduction History of Digital Image Processing Applications of DIP Elements of Visual Perception Sampling and Quantization 2D Mathematical Preliminaries Image Transforms

3. “One picture is worth more than ten thousand words” Anonymous

4. What is an Image? An image is an array, or a matrix, of square pixels (picture elements) arranged in columns and rows. An image — an array or a matrix of pixels arranged in columns and rows.

5. Black and white image In a (8-bit) greyscale image each picture element has an assigned intensity that ranges from 0 to 255. A grey scale image is what people normally call a black and white image, but the name emphasizes that such an image will also include many shades of grey.

6. An example:8-bit greyscale image Each pixel has a value from 0 (black) to 255 (white). The possible range of the pixel values depend on the colour depth of the image, here 8 bit = 256 tones or greyscales.

7. What is a Digital Image? A digital image is a representation of a two- dimensional image as a finite set of digital values, called picture elements or pixels

8. What is a Digital Image? (cont…) Pixel values typically represent gray levels, colours, heights, opacities etc Remember digitization implies that a digital image is an approximation of a real scene 1 pixel

9. What is a Digital Image? (cont…) Common image formats include: –1 sample per point (B&W or Grayscale) –3 samples per point (Red, Green, and Blue) –4 samples per point (Red, Green, Blue, and “Alpha”, a.k.a. Opacity)

10. What is Digital Image Processing? Digital image processing focuses on two major tasks –Improvement of pictorial information for human interpretation –Processing of image data for storage, transmission and representation for autonomous machine perception

11. What is DIP? (cont…) The continuum from image processing to computer vision can be broken up into low-, mid- and high-level processes Low Level Process Input: Image Output: Image Examples: Noise removal, image sharpening Mid Level Process Input: Image Output: Attributes Examples: Object recognition, segmentation High Level Process Input: Attributes Output: Understanding Examples: Scene understanding, autonomous navigation

12. History of Digital Image Processing Early 1920s: One of the first applications of digital imaging was in the news- paper industry –The Bartlane cable picture transmission service –Images were transferred by submarine cable between London and New York –Pictures were coded for cable transfer and reconstructed at the receiving end on a telegraph printer Early digital image

13. History of DIP (cont…) Mid to late 1920s: Improvements to the Bartlane system resulted in higher quality images –New reproduction processes based on photographic techniques –Increased number of tones in reproduced images Improved digital image Early 15 tone digital image

14. History of DIP (cont…) 1960s: Improvements in computing technology and the onset of the space race led to a surge of work in digital image processing –1964: Computers used to improve the quality of images of the moon taken by the Ranger 7 probe –Such techniques were used in other space missions including the Apollo landings A picture of the moon taken by the Ranger 7 probe minutes before landing

15. History of DIP (cont…) 1970s: Digital image processing begins to be used in medical applications –1979: Sir Godfrey N. Hounsfield & Prof. Allan M. Cormack share the Nobel Prize in medicine for the invention of tomography, the technology behind Computerised Axial Tomography (CAT) scans Typical head slice CAT image

16. History of DIP (cont…) 1980s - Today: The use of digital image processing techniques has exploded and they are now used for all kinds of tasks in all kinds of areas –Image enhancement/restoration –Artistic effects –Medical visualisation –Industrial inspection –Law enforcement –Human computer interfaces

17. Examples: Image Enhancement One of the most common uses of DIP techniques: improve quality, remove noise etc

18. Examples: The Hubble Telescope Launched in 1990 the Hubble telescope can take images of very distant objects However, an incorrect mirror made many of Hubble’s images were useless Image processing techniques were used to fix this

19. Examples: Artistic Effects Artistic effects are used to make images more visually appealing, to add special effects and to make composite images

20. Examples: Medicine Take slice from MRI scan of canine heart, and find boundaries between types of tissue –Image with gray levels representing tissue density –Use a suitable filter to highlight edges Original MRI Image of a Dog Heart Edge Detection Image

21. Examples: GIS Geographic Information Systems –Digital image processing techniques are used extensively to manipulate satellite imagery –Terrain classification –Meteorology

22. Examples: GIS (cont…) Night-Time Lights of the World data set –Global inventory of human settlement –Not hard to imagine the kind of analysis that might be done using this data

23. Examples: Industrial Inspection Human operators are expensive, slow and unreliable Make machines do the job instead Industrial vision systems are used in all kinds of industries

24. Examples: PCB Inspection Printed Circuit Board (PCB) inspection –Machine inspection is used to determine that all components are present and that all solder joints are acceptable –Both conventional imaging and x-ray imaging are used

25. Examples: Law Enforcement Image processing techniques are used extensively by law enforcers –Number plate recognition for speed cameras/automated toll systems –Fingerprint recognition –Enhancement of CCTV images

26. Examples: HCI Trying to make human computer interfaces more natural –Face recognition –Gesture recognition

27. Fundamental Steps in Image Processing Image Acquisition Image Acquisition Preprocessing (Enhancement & Restoration) Preprocessing (Enhancement & Restoration) Segmentation Representation & Description Representation & Description Recognition & Interpretation Recognition & Interpretation Problem Domain Knowledge Base Knowledge Base Result

28. Monochromatic Digital Imagec x y Gray Level f(x,y)

29. R+G+B R G B R G B R G B R G B R G B R G B

30. Image Formation in Human Eye

31. Electromagnetic Spectrum

32. Key Stages in Digital Image Processing Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

33. Key Stages in Digital Image Processing: Image Aquisition Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

34. Key Stages in Digital Image Processing: Image Enhancement Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

35. Key Stages in Digital Image Processing: Image Restoration Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

36. Key Stages in Digital Image Processing: Morphological Processing Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

37. Key Stages in Digital Image Processing: Segmentation Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

38. Key Stages in Digital Image Processing: Object Recognition Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

39. Key Stages in Digital Image Processing: Representation & Description Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

40. Key Stages in Digital Image Processing: Image Compression Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

41. Key Stages in Digital Image Processing: Colour Image Processing Image Acquisition Image Restoration Morphological Processing Segmentation Representation & Description Image Enhancement Object Recognition Problem Domain Colour Image Processing Image Compression

42. Components of an image processing system

43. Elements of Visual Perception- Structure of Human Eye

44. Distribution of Cones and Rods in the Retina

45. Structure of human eye Cornea-tough transparent tissue Schlera-opaque membrane-enclosing the remainder of optic globe Choroid-n/w of blood vessels -major source of nutrition to eye -Ciliary body: contracts or expands -Iris: Diameter of pupil approx 2 to 8 mm Lens-Concentric layers of fibrous cells & is suspended by fibers attached to ciliary body

46. Structure of human eye Lens-Slightly yellow pigmentation - Excessive clouding-Cataracts Retina-Posterior position - Light receptors over the surface of retina Receptors-Cones & Rods Cones-Located in the central position of retina -Fovea,Sensitive to color -Each cone is connected to its own nerve end - Photopic or Bright-light vision Rods-Larger in number - Several rods connected to single nerve end -overall picture of the field of view - not involved in color vision but sensitive to low levels of illumination - Scotopic or Dim-Light vision

47. Subjective Brightness The intensity as perceived by the human visual system It is a logarithmic function of the light intensity incident on the eye Luminance-Measure of the amount of light energy, an observer perceives from the light.

48. Brightness Adaptation HVS cannot operate over a large dynamic range Overall sensitivity current sensitivity level of visual system Ba to Bb Total range of distinct intensity levels,it can discriminate simultaneously < total adaptation range

49. Brightness Discrimination ability to discriminate changes in intensity level ∆I/Ic=Weber ratio ∆Ic =increment of illumination discriminable 50% of the time with background illumination I

50. Weber ratio Weber ratio: small-good brightness discrimination Weber ratio: large-poor brightness discrimination Rods Cones

51. Mach Band Effect Increases contrast b/w two surfaces with different luminance Spatial interaction of luminance from an object & its surrounding Brightness is not a monotonic function of luminance Light receptors-draw light sensitive chemical compounds from adjacent regions

52. Simultaneous Contrast

53. Optical Illusions

54. Image Formation f(x,y) = reflectance(x,y) * illumination(x,y) Reflectance in [0,1], illumination in [0,inf]

55. Sampling and Quantization

57. What is an image? An image is a function, f –f( x, y ) gives the intensity at position ( x, y ) –Realistically, the image can only be defined over a rectangle, with a finite range: f: [a,b]x[c,d]  [0,1] A color image is just three functions pasted together.

58. Images as functions

59. What is a digital image? On digital (discrete) images: –Sample the 2D space on a regular grid –Quantize each sample (round to nearest integer) If our samples are D apart, we can write this as: f[i,j] = Quantize{ f(i D, j D) } The image can now be represented as a matrix of integer values

60. Gray Scale image In a (8-bit) greyscale image each picture element has an assigned intensity that ranges from 0 to 255. A grey scale image is what people normally call a black and white image, but the name emphasizes that such an image will also include many shades of grey.

61. Pixel Values, DN Pixel Values: The magnitude of the electromagnetic energy (or, intensity) captured in a digital image is represented by positive digital numbers. The digital numbers are in the form of binary digits (or 'bits') which vary from 0 to a selected power of 2 Image Type Pixel Value Color Levels 8-bit image 2 8 = 2560-255 16-bit image2 16 = 655360-65535 24-bit image2 24 = 167772160-16777215

62. Image processing An image processing operation typically defines a new image g in terms of an existing image f. Or the domain of f:

63. Spatial Resolution

66. Applications of Image Processing & Research Topics

67. Document Handling

68. Signature Verification

69. Biometrics

70. Fingerprint Verification / Identification

71. Fingerprint Identification Research at UNR Minutiae Matching Delaunay Triangulation

72. Object Recognition

73. Object Recognition Research reference view 1 reference view 2 novel view recognized

74. Indexing into Databases Shape content

75. Target Recognition Department of Defense (Army, Airforce, Navy)

76. Interpretation of aerial photography is a problem domain in both computer vision and registration. Interpretation of Aerial Photography

77. Autonomous Vehicles Land, Underwater, Space

78. Traffic Monitoring

79. Face Detection

80. Face Recognition

81. Facial Expression Recognition

82. Hand Gesture Recognition Smart Human-Computer User Interfaces Sign Language Recognition

83. Human Activity Recognition

84. Medical Applications skin cancer breast cancer

85. Morphing

86. An m×n (read "m by n") matrix, denoted by A, is a rectangular array of entries or elements (numbers, or symbols representing numbers) enclosed typically by square brackets, where m is the number of rows and n the number of columns. Matrix A gray-scale image is often represented by a matrix whose elements are intensity values of pixels Introduction to 2D Mathematical Preliminaries

87. Matrix Definitions (Con’t) A is square if m= n. A is diagonal if all off-diagonal elements are 0, and not all diagonal elements are 0. A is the identity matrix ( I ) if it is diagonal and all diagonal elements are 1. A is the zero or null matrix ( 0 ) if all its elements are 0. The trace of A equals the sum of the elements along its main diagonal. Two matrices A and B are equal iff the have the same number of rows and columns, and a ij = b ij.

88. Matrix Definitions (Con’t) The transpose A T of an m×n matrix A is an n×m matrix obtained by interchanging the rows and columns of A. A square matrix for which A T =A is said to be symmetric. Any matrix X for which XA=I and AX=I is called the inverse of A. Let c be a real or complex number (called a scalar). The scalar multiple of c and matrix A, denoted cA, is obtained by multiplying every elements of A by c. If c =  1, the scalar multiple is called the negative of A.

89. Block Matrix A block matrix is a matrix that is defined using smaller matrices, called blocks Example (Hadamard Matrix) Exercise

90. Block Matrix (con’t) H=256 W=256 divided into 1024 8  8 block matrices in JPEG compression

91. Row and Column Vectors A column vector is an m × 1 matrix: A row vector is a 1 × n matrix: A column vector can be expressed as a row vector by using the transpose:

92. Vector Norms There are numerous norms that are used in practice. In our work, the norm most often used is the so-called 2-norm, which, for a vector x in real  m, space is defined as which is recognized as the Euclidean distance from the origin to point x; this gives the expression the familiar name Euclidean norm. The expression also is recognized as the length of a vector x, with origin at point 0. From earlier discussions, the norm also can be written as

93. Some Basic Matrix Operations The sum of two matrices A and B (of equal dimension), denoted A + B, is the matrix with elements a ij + b ij. The difference of two matrices, A  B, has elements a ij  b ij. The product, AB, of m×n matrix A and n×q matrix B, is an m×q matrix C whose (i,j)-th element is formed by multiplying the entries across the ith row of A times the entries down the jth column of B; that is,

94. The inner product (also called dot product) of two vectors Note that the inner product is a scalar. Some Basic Matrix Operations (Con’t) is defined as

95. Orthogonality and Orthonormality From the preceding results, two vectors in  m are orthogonal if and only if their inner product is zero. Two vectors are orthonormal if, in addition to being orthogonal, the length of each vector is 1. From the concepts just discussed, we see that an arbitrary vector a is turned into a vector a n of unit length by performing the operation a n = a/||a||. Clearly, then, ||a n || = 1. A set of vectors is said to be an orthogonal set if every two vectors in the set are orthogonal. A set of vectors is orthonormal if every two vectors in the set are orthonormal.

96. IMAGE TRANSFORMS