2. ISAN-DSP GROUP 168 442 Introduction to Image Processing The First Semester of Class 2546 Dr. Nawapak Eua-Anant Department of Computer Engineering Khon Kaen University

3. ISAN-DSP GROUP Course Syllabus Date and Time : MW 11.00-12.00 EN 4510, LAB1 TU17-20, LAB2 TH17-20 Assessments: Attendance & Homework5% Lab and Homework35% Midterm30% Final30% Grading: 85-100% A, 75-85% B+, 70-75% B, 65-70% C+, 60-65% C, 55-60% D+, 50-55% D, 0-50% F References: 1.Rafael C. Gonzalez and Richard E. Woods, “Digital Image Processing”, Addison Wesley, 1992. 2. Anil K. Jain, “Fundamentals of Digital Image Processing”, Prentice-Hall, Inc., 1989. 3.William K. Pratt, “Digital Image Processing”, 2 nd Edition, Wiley & Sons, Inc., 1991.

4. ISAN-DSP GROUP Course Outline 1. Introduction 2. Digital Image Fundamentals 3. Image Transforms 4. Image Enhancement 5. Image Segmentation 6. Image Compression 7. Image Morphology

5. ISAN-DSP GROUP Chapter 1 Introduction to Image Processing

6. ISAN-DSP GROUP What is Digital Image Processing ? Processing of a multidimensional pictures by a digital computer การประมวลผลสัญญาณรูปภาพโดยใช้ดิจิตอลคอมพิวเตอร์ Why we need Digital Image Processing ? 1. เพื่อบันทึกและจัดเก็บภาพ 2. เพื่อปรับปรุงภาพให้ดีขึ้นโดยใช้ กระบวนการทางคณิตศาสตร์ 3. เพื่อช่วยในการวิเคราะห์รูปภาพ 4. เพื่อสังเคราะห์ภาพ 5. เพื่อสร้างระบบการมองเห็นให้กับ คอมพิวเตอร์

7. ISAN-DSP GROUP Digital Image Digital image = a multidimensional array of numbers (such as intensity image) or vectors (such as color image) Each component in the image called pixel associates with the pixel value (a single number in the case of intensity images or a vector in the case of color images).

8. ISAN-DSP GROUP Visual Perception: Human Eye (Picture from Microsoft Encarta 2000)

9. ISAN-DSP GROUP Chapter 2: Digital Image Fundamentals

10. ISAN-DSP GROUP Visual Perception: Human Eye (cont.) 1.The lens contains 60-70% water, 6% of fat. 2.The iris diaphragm controls amount of light that enters the eye. 3.Light receptors in the retina - About 6-7 millions cones for bright light vision called photopic - Density of cones is about 150,000 elements/mm 2. - Cones involve in color vision. - Cones are concentrated in fovea about 1.5x1.5 mm 2. - About 75-150 millions rods for dim light vision called scotopic - Rods are sensitive to low level of light and are not involved color vision. 4. Blind spot is the region of emergence of the optic nerve from the eye.

11. ISAN-DSP GROUP Chapter 2: Digital Image Fundamentals

12. ISAN-DSP GROUP Image Formation in Human Eye

13. ISAN-DSP GROUP Chapter 2: Digital Image Fundamentals

14. ISAN-DSP GROUP Brightness Adaptation of Human Eye Position Intensity Intensities of surrounding points effect perceived brightness at each point. In this image, edges between bars appear brighter on the right side and darker On the left side.

15. ISAN-DSP GROUP In area A, brightness perceived is darker while in area B is brighter. This phenomenon is called Mach Band Effect. Brightness Adaptation of Human Eye (cont.) Position Intensity A B

16. ISAN-DSP GROUP Brightness Adaptation of Human Eye (cont.) Simultaneous contrast. All small squares have exactly the same intensity but they appear progressively darker as background becomes lighter.

17. ISAN-DSP GROUP Imaging Geometry: Perspective Transformation Lens center x,X y,Y (x,y)(x,y) z,Z (X,Y,Z) = world coordinate (x,y,z) = Camera coordinate system (X,Y,Z) = focal length Image plane Eq. 1.1

18. ISAN-DSP GROUP Imaging Geometry: Perspective Transformation (cont.) Question: How can we project the real world object at (X,Y,Z) onto the image plane (such as photographic film)? Answer: Relation between camera coordinate (x,y,z) and world coordinate (X,Y,Z) are given by Since on the image plane z is always zero, z=0, we consider only (x,y) while z is neglected. Eq. 1.2

19. ISAN-DSP GROUP Imaging Geometry: Perspective Transformation (cont.) Equation 1.2 is not linear because of Z in the dividers so we introduce the homogeneous coordinate to solve this problem. Cartesian coordinate Homogeneous coordinate k = nonzero constant To convert from the homogeneous coordinate w h to the Cartesian coordinate w, we divide the first 3 components of w h by the fourth component.

20. ISAN-DSP GROUP Imaging Geometry: Perspective Transformation (cont.) The perspective transformation matrix for the homogeneous coordinate: Perspective transformation becomes: Eq. 1.3

21. ISAN-DSP GROUP Imaging Geometry: Perspective Transformation (cont.) From homogeneous coordinate We get camera coordinate in the image plane:

22. ISAN-DSP GROUP Imaging Geometry: Inverse Perspective Transformation where Eq. 1.4

23. ISAN-DSP GROUP For an image point (x 0,y 0 ), since on the image plane z=0, we have Inverse Perspective Transformation (cont.) We get the world coordinate : Since the perspective transformation maps 3-D coordinates to 2-D Coordinates, we cannot get the inverse transform unless we have additional information.

24. ISAN-DSP GROUP To find the solution, let Inverse Perspective Transformation (cont.) We get Eq. 1.5

25. ISAN-DSP GROUP Inverse Perspective Transformation (cont.) From Eq. 1.5, We get Eq. 1.6 Substituting Eq. 1.6 into Eq.1.5, we get Eq. 1.7 Equations 1.7 show that inverse perspective transformation requires information of at least one component of the world coordinate of the point.

26. ISAN-DSP GROUP Inverse Perspective Transformation (cont.) These equations: show that points on Line L in the world coordinate map to a single point in the image plane. Lens center x,X y,Y z,Z (x,y)(x,y) Image plane (X 2,Y 2,Z 2 ) (X 3,Y 3,Z 3 ) Points (X 1,Y 1,Z 1 ), (X 2,Y 2,Z 2 ), and (X 3,Y 3,Z 3 ) map to Point (x,y) in the image plane. (X 1,Y 1,Z 1 ) Line L

27. ISAN-DSP GROUP y x Stereo Imaging: How we get depth information from 2 eyes Left lens center (x2,y2)(x2,y2) Image 2 y x right lens center B World point (X,Y,Z) Optical axis Image 1 (x1,y1)(x1,y1)

28. ISAN-DSP GROUP Stereo Imaging: How we get depth information from 2 eyes (cont.) Problem: we know camera coordinates of the object on left and right image planes (x 1,y 1 ) and (x 2,y 2 ) and want to how far from the camera the object is located. Note: when y-axis is parallel to the ground, we have y 1 = y 2 (x2,y2)(x2,y2) (x1,y1)(x1,y1) B w Z Image 2 Image 1 Plane of constant Z X Origin of world coordinate system

29. ISAN-DSP GROUP 1. From the inverse perspective transform, we compute X 1 and X 2 : 3. Since left and right lenses are separated by distance B, we have 2. Z 1 and Z 2 must be equal, we get Stereo Imaging: How we get depth information from 2 eyes (cont.) 4. From 1, 2 and 3, we get Solving Z yields

30. ISAN-DSP GROUP Stereo Imaging: How we get depth information from 2 eyes (cont.) We can locate the object if we know positions of the object in left and right image planes using Equation: Question: While the equation is so simple but why it is very difficult to built an automatic stereo vision system that can reconstruct 3-D scene from images obtained from 2 cameras? Answers: for a computer, locating the corresponding points on left and right images is the most difficult task.

31. ISAN-DSP GROUP Imaging Geometry : Affine Transformations 1. Translation 2. Scaling 3. Rotating

32. ISAN-DSP GROUP Image Geometry: Translation of Object Y Z X Displace the object by vector (X 0,Y 0,Z 0 ) with respect to its old position. (X+X0,Y+Y0,Z+Z0)(X+X0,Y+Y0,Z+Z0) (X,Y,Z)(X,Y,Z) (X0,Y0,Z0)(X0,Y0,Z0)

33. ISAN-DSP GROUP Image Geometry: Translation of Frame Y Z X (0,0,0) Translate the origin point of the frame by (X 0,Y 0,Z 0 ) with respect to the old frame Y  ZZ X  (X0,Y0,Z0)(X0,Y0,Z0) The object still stays at the same position. Only the frame is moved.

34. ISAN-DSP GROUP Image Geometry: Scaling Scale by factors S x, S y, S z along X, Y, and Z axes. a b c d e f g A B C DE F G Note: Origin point is unchanged.

35. ISAN-DSP GROUP  Image Geometry: Rotating an object about X-axis Rotate an object about X-axis by  x in a counterclockwise direction. Y Z X=X  xx Note : In this case the object is moved. Only y and z are changed while x stills the same.

36. ISAN-DSP GROUP  Image Geometry: Rotating a frame about X-axis Rotate the frame about X-axis by  x in a counterclockwise direction. Y Z xx Y  ZZ Note : In this case the object is not moved. The frame is rotated instead. X=X 

37. ISAN-DSP GROUP Image Geometry: Rotating an object about Y-axis Rotate an object about Y-axis by  y in a counterclockwise direction. Z X yy Note : In this case the object is moved. Only x and z are changed while y stills the same.  Y= Y 

38. ISAN-DSP GROUP Image Geometry: Rotating a frame about Y-axis Rotate the frame about Y-axis by  y in a counterclockwise direction. Y= Y  Z X yy Note : In this case the object is not moved. The frame is rotated instead.  ZZ X 

39. ISAN-DSP GROUP Image Geometry: Rotating an object about Z-axis Rotate an object about Z-axis by  z in a counterclockwise direction. Y Z X zz Note : In this case the object is moved. Only x and y are changed while z stills the same. 

40. ISAN-DSP GROUP Image Geometry: Rotating a frame about Z-axis Rotate the frame about Z-axis by  z in a counterclockwise direction. Y Z= Z  X zz Y  Note : In this case the object is not moved. The frame is rotated instead. X  

41. ISAN-DSP GROUP X Y Z World Coordinate System Image Geometry: How to compute a point on an image plane from the world coordinate Problem: we know the location of the object and want to know where it will be projected on the film (image plane). y z x Camera Coordinate System Answer: 1. Transform the world coordinate to the camera coordinate 2. Perform the perspective transformation

42. ISAN-DSP GROUP Image Geometry: How to compute a point on the image plane from the world coordinate (cont.) Lens center x y (x,y)(x,y) z (x,y,z) = Camera coordinate, (X,Y,Z) = World coordinate Image plane (z=0) Before using the perspective transformation, the world axes X-Y-Z must coincide with the camera axes x-y-z, (we need some transformations). (X,Y,Z) X Z Y

43. ISAN-DSP GROUP Image Geometry: Compute the camera coordinate from the world coordinate X Y Z World Coordinate System y z x Camera Coordinate System 2 3 Gimbal center 1. Translate* by w 0 Note : *perform on the frame 2. Pan the camera* (rotate about Z-axis) 4. Translate* by z = r Steps from Gonzalez’s book 3. Tilt the camera* (rotate about X-axis) 5. Compute the perspective Tr. 1 w0w0 4 r

44. ISAN-DSP GROUP Formula from Gonzalez’s book Perspective tr. Translate to the image plane Center by z = r Translate to the gimbal center w 0 World coordinate Camera coordinate Image Geometry: Compute the camera coordinate from the world coordinate (cont.) Rotate by Pan (  z ) and Tilt (  x )

45. ISAN-DSP GROUP X Y Z World Coordinate System y z x Camera Coordinate System 2 3 4 Gimbal center 1. Translate* by w 1 2. Pan the camera* 3. Tilt the camera* Note : *perform on the frame General case 4. Twist the camera* (rotate about Y-axis) 5. Compute the perspective Tr. w1w1 1 Image Geometry: Compute the camera coordinate from the world coordinate (cont.)

46. ISAN-DSP GROUP Image Geometry: Compute the camera coordinate from the world coordinate (cont.) General case Perspective tr. Translate to the image plane center w 1 World coordinate Camera coordinate Rotate by Pan (  z ), Tilt (  x ), Twist (  y )