Download presentation

Presentation is loading. Please wait.

Published byAnnabella Lovegrove Modified over 2 years ago

1
Last 4 lectures Camera Structure HDR Image Filtering Image Transform

2
Today Camera Projection Camera Calibration

3
Pinhole camera

4
Pinhole camera model (optical center) origin principal point P (X,Y,Z) p (x,y) The coordinate system –We will use the pin-hole model as an approximation –Put the optical center (Center Of Projection) at the origin –Put the image plane (Projection Plane) in front of the COP (Why?)

5
Pinhole camera model principal point

6
Pinhole camera model (optical center) origin principal point P (X,Y,Z) p (x,y) x y

7
Pinhole camera model (optical center) origin principal point P (X,Y,Z) p (x,y) x y

8
Intrinsic matrix non-square pixels (digital video) Is this form of K good enough?

9
Intrinsic matrix non-square pixels (digital video) skew Is this form of K good enough?

10
Intrinsic matrix non-square pixels (digital video) skew radial distortion Is this form of K good enough?

11
Distortion Radial distortion of the image –Caused by imperfect lenses –Deviations are most noticeable for rays that pass through the edge of the lens

12
Barrel Distortion No distortion Barrel Wide Angle Lens

13
Pin Cushion Distortion Pin cushion Telephoto lens No distortion

14
Modeling distortion To model lens distortion –Use above projection operation instead of standard projection matrix multiplication 2. Apply radial distortion 3. Apply focal length translate image center 1. Project (X, Y, Z) to “normalized” image coordinates Distortion-Free:With Distortion:

15
Camera rotation and translation extrinsic matrix

16
Two kinds of parameters internal or intrinsic parameters: focal length, optical center, skew external or extrinsic (pose): rotation and translation:

17
Other projection models

18
Orthographic projection Special case of perspective projection –Distance from the COP to the PP is infinite Image World –Also called “parallel projection”: (x, y, z) → (x, y)

19
Other types of projections Scaled orthographic –Also called “weak perspective” Affine projection –Also called “paraperspective”

20
Fun with perspective

21
Perspective cues

23
Fun with perspective Ames room

24
Forced perspective in LOTR Elijah Wood: 5' 6" (1.68 m)Ian McKellen 5' 11" (1.80 m)

25
Camera calibration

26
Estimate both intrinsic and extrinsic parameters Mainly, two categories: 1.Using objects with known geometry as reference 2.Self calibration (structure from motion)

27
Camera calibration approaches Directly estimate 11 unknowns in the M matrix using known 3D points (Xi,Yi,Zi) and measured feature positions (ui,vi)

28
Linear regression

30
Solve for Projection Matrix M using least- square techniques

31
Normal equation (Geometric Interpretation) Given an overdetermined system the normal equation is that which minimizes the sum of the square differences between left and right sides

32
Normal equation (Differential Interpretation) n x m, n equations, m variables

33
Normal equation Who invented Least Square? Carl Friedrich Gauss

34
Nonlinear optimization A probabilistic view of least square Feature measurement equations Likelihood of M given {(u i,v i )}

35
Optimal estimation Log likelihood of M given {(u i,v i )} It is a least square problem (but not necessarily linear least square) How do we minimize C?

36
Nonlinear least square methods

37
Least square fitting number of data points number of parameters

38
Nonlinear least square fitting

39
Function minimization It is very hard to solve in general. Here, we only consider a simpler problem of finding local minimum. Least square is related to function minimization.

40
Function minimization

41
Quadratic functions Approximate the function with a quadratic function within a small neighborhood

42
Function minimization

43
Computing gradient and Hessian Gradient Hessian

44
Computing gradient and Hessian Gradient Hessian

45
Computing gradient and Hessian Gradient Hessian

46
Computing gradient and Hessian Gradient Hessian

47
Computing gradient and Hessian Gradient Hessian

48
Searching for update h GradientHessian Idea 1: Steepest Descent

49
Steepest descent method isocontourgradient

50
Steepest descent method It has good performance in the initial stage of the iterative process. Converge very slow with a linear rate.

51
Searching for update h GradientHessian Idea 2: minimizing the quadric directly Converge faster but needs to solve the linear system

52
Recap: Calibration Directly estimate 11 unknowns in the M matrix using known 3D points (Xi,Yi,Zi) and measured feature positions (ui,vi) Camera Model:

53
Recap: Calibration Directly estimate 11 unknowns in the M matrix using known 3D points (Xi,Yi,Zi) and measured feature positions (ui,vi) Linear Approach:

54
Recap: Calibration Directly estimate 11 unknowns in the M matrix using known 3D points (Xi,Yi,Zi) and measured feature positions (ui,vi) NonLinear Approach:

55
Practical Issue is hard to make and the 3D feature positions are difficult to measure!

56
A popular calibration tool

57
Multi-plane calibration Images courtesy Jean-Yves Bouguet, Intel Corp. Advantage Only requires a plane Don’t have to know positions/orientations Good code available online! –Intel’s OpenCV library: http://www.intel.com/research/mrl/research/opencv/ http://www.intel.com/research/mrl/research/opencv/ –Matlab version by Jean-Yves Bouget: http://www.vision.caltech.edu/bouguetj/calib_doc/index.html http://www.vision.caltech.edu/bouguetj/calib_doc/index.html –Zhengyou Zhang’s web site: http://research.microsoft.com/~zhang/Calib/ http://research.microsoft.com/~zhang/Calib/

58
Step 1: data acquisition

59
Step 2: specify corner order

60
Step 3: corner extraction

62
Step 4: minimize projection error

63
Step 4: camera calibration

65
Step 5: refinement

Similar presentations

OK

Camera Calibration. Issues: what are intrinsic parameters of the camera? what is the camera matrix? (intrinsic+extrinsic) General strategy: view calibration.

Camera Calibration. Issues: what are intrinsic parameters of the camera? what is the camera matrix? (intrinsic+extrinsic) General strategy: view calibration.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on blue ocean strategy Ppt on water activity and microbial growth Ppt on retail marketing in india Ppt on construction of bridges in hilly areas Ppt on complex numbers class 11th result Ppt on review of related literature in research Ppt on idiopathic thrombocytopenia purpura genetic Ppt on relations and functions for class 11th accountancy Ppt on evolution of life Ppt on type 2 diabetes facts