Introduction to Image Processing

Transcription

1 Introduction to Image Processing The First Semester of Class 2546 Dr. Nawapak Eua-Anant Department of Computer Engineering Khon Kaen University

2 Course Syllabus Date and Time : MW.-2. EN 45, LAB TU7-2, LAB2 TH7-2 Assessments: Attendance & Homework 5% Lab and Homework 35% Midterm 3% Final 3% Grading: 85-% A, 75-85% B+, 7-75% B, 65-7% C+, 6-65% C, 55-6% D+, 5-55% D, -5% F References:.Rafael C. Gonzalez and Richard E. Woods, Digital Image Processing, Addison Wesley, Anil K. Jain, Fundamentals of Digital Image Processing, Prentice-Hall, Inc., William K. Pratt, Digital Image Processing, 2 nd Edition, Wiley & Sons, Inc., 99.

3 Course Outline. Introduction 2. Digital Image Fundamentals 3. Image Transforms 4. Image Enhancement 5. Image Segmentation 6. Image Compression 7. Image Morphology

4 Chapter Introduction to Image Processing

5 What is Digital Image Processing? Processing of a multidimensional pictures by a digital computer การประมวลผลส ญญาณร ปภาพโดยใช ด จ ตอลคอมพ วเตอร Why we need Digital Image Processing?.เพ อบ นท กและจ ดเก บภาพ 2.เพ อปร บปร งภาพให ด ข นโดยใช กระบวนการทาง คณ ตศาสตร 3.เพ อช วยในการว เคราะห ร ปภาพ 4.เพ อส งเคราะห ภาพ 5.เพ อสร างระบบการมองเห นให ก บคอมพ วเตอร

6 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)

7 Visual Perception: Human Eye (Picture from Microsoft Encarta 2)

8 Chapter 2: Digital Image Fundamentals

9 Visual Perception: Human Eye (cont.).the lens contains 6-7% water, 6% of fat The iris diaphragm controls amount of light that enters the eye Light receptors in the retina - About 6-7 millions cones for bright light vision called photopic - Density of cones is about 5, elements/mm 2. - Cones involve in color vision. - Cones are concentrated in fovea about.5x.5 mm 2. - About 75-5 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.

10 Chapter 2: Digital Image Fundamentals

11 Image Formation in Human Eye

12 Chapter 2: Digital Image Fundamentals

13 Brightness Adaptation of Human Eye Intensity Position 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.

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

15 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.

16 Imaging Geometry: Perspective Transformation y, Image plane x, (,,) world coordinate (,,) z, (x,y) Lens center (x,y,z) Camera coordinate system focal length x y Eq..

17 Imaging Geometry: Perspective Transformation (cont.) Question: How can we project the real world object at (,,) onto the image plane (such as photographic film)? Answer: Relation between camera coordinate (x,y,z) and world coordinate (,,) are given by c x y z Eq..2 Since on the image plane z is always zero, z, we consider only (x,y) while z is neglected.

18 Imaging Geometry: Perspective Transformation (cont.) Equation.2 is not linear because of in the dividers so we introduce the homogeneous coordinate to solve this problem. Cartesian coordinate w Homogeneous coordinate w h k k k k 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.

19 ) ( k k k k k k k k Pw c h h Imaging Geometry: Perspective Transformation (cont.) P The perspective transformation matrix for the homogeneous coordinate: Perspective transformation becomes: Eq..3

20 ) ( k k k k c h Imaging Geometry: Perspective Transformation (cont.) z y x k k k k k k c ) ( ) ( ) ( From homogeneous coordinate We get camera coordinate in the image plane:

21 Imaging Geometry: Inverse Perspective Transformation P h c h P w where Eq..4

22 Inverse Perspective Transformation (cont.) For an image point (x,y ), since on the image plane z, we have We get the world coordinate : w h kx ky c h k kx x ky P c or h w y k??? Since the perspective transformation maps 3-D coordinates to 2-D Coordinates, we cannot get the inverse transform unless we have additional information.

23 To find the solution, let k kz ky kx c h Inverse Perspective Transformation (cont.) We get z z z y z x w z k kz ky kx c P w h h or ) ( Eq..5

24 Inverse Perspective Transformation (cont.) From Eq..5, z We get Eq..6 Substituting Eq..6 into Eq..5, we get x ( ) y ( ) Eq..7 Equations.7 show that inverse perspective transformation requires information of at least one component of the world coordinate of the point.

25 Inverse Perspective Transformation (cont.) x These equations: ( ) and y ( ) show that points on Line L in the world coordinate map to a single point in the image plane. y, Image plane x, ( 3, 3, 3 ) ( 2, 2, 2 ) (,, ) Line L (x,y) Lens center Points (,, ), ( 2, 2, 2 ), and ( 3, 3, 3 ) map to Point (x,y) in the image plane. z,

26 Stereo Imaging: How we get depth information from 2 eyes Image Image 2 y x B y x (x,y ) Left lens center Optical axis (x 2,y 2 ) right lens center World point (,,)

27 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,y ) 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 y 2 Image Origin of world coordinate system (x,y ) Image 2 B w (x 2,y 2 ) Plane of constant

28 Stereo Imaging: How we get depth information from 2 eyes (cont.). From the inverse perspective transform, we compute and 2 : x x2 ) and ( ) ( and 2 must be equal, we get 2 3. Since left and right lenses are separated by distance B, we have 2 + B 4. From, 2 and 3, we get x x2 ( ) and + B ( ) Solving yields B x 2 x

29 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: B x 2 x 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.

30 Imaging Geometry : Affine Transformations. Translation 2. Scaling 3. Rotating

31 Image Geometry: Translation of Object Displace the object by vector (,, ) with respect to its old position (+,+,+ ) (,,) (,, )

32 Image Geometry: Translation of Frame (,,) Translate the origin point of the frame by (,, ) with respect to the old frame (,, ) The object still stays at the same position. Only the frame is moved.

33 Image Geometry: Scaling Scale by factors S x, S y, S z along,, and axes. a b c d e f g A B C D E F G S S S z y x S S S z y x Note: Origin point is unchanged.

34 D Image Geometry: Rotating an object about -axis Rotate an object about -axis by x in a counterclockwise direction. x cos sin sin cos x x x x Note : In this case the object is moved. Only y and z are changed while x stills the same.

35 D Image Geometry: Rotating a frame about -axis Rotate the frame about -axis by x in a counterclockwise direction. x cos sin sin cos x x x x Note : In this case the object is not moved. The frame is rotated instead.

36 Image Geometry: Rotating an object about -axis Rotate an object about -axis by y in a counterclockwise direction. y cos sin sin cos y y y y Note : In this case the object is moved. Only x and z are changed while y stills the same. D

37 Image Geometry: Rotating a frame about -axis Rotate the frame about -axis by y in a counterclockwise direction. y Note : In this case the object is not moved. The frame is rotated instead. D cos sin sin cos y y y y

38 Image Geometry: Rotating an object about -axis Rotate an object about -axis by z in a counterclockwise direction. z Note : In this case the object is moved. Only x and y are changed while z stills the same. cos sin sin cos z z z z D

39 Image Geometry: Rotating a frame about -axis Rotate the frame about -axis by z in a counterclockwise direction. z Note : In this case the object is not moved. The frame is rotated instead. cos sin sin cos z z z z D

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

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

42 Image Geometry: Compute the camera coordinate from the world coordinate 3 z Steps from Gonzalez s book. Translate by w Camera Coordinate System x w World Coordinate System 4 r 2 Gimbal center y 2. Pan the camera (rotate about -axis) 3. Tilt the camera (rotate about -axis) 4. Translate by z r 5. Compute the perspective Tr. Note : perform on the frame

43 Image Geometry: Compute the camera coordinate from the world coordinate (cont.) Formula from Gonzalez s book Camera coordinate c P C R G h w h Perspective tr. World coordinate Translate to the image plane Center by z r Rotate by Pan ( z ) and Tilt ( x ) Translate to the gimbal center w

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

45 Image Geometry: Compute the camera coordinate from the world coordinate (cont.) General case Camera coordinate c P R T h w h Perspective tr. Rotate by Pan ( z ), Tilt ( x ), Twist ( y ) World coordinate Translate to the image plane center w