docCamera Models and Imaging
download 
Report Transcription
Camera Models and Imaging
Leow Wee Kheng CS4243 Computer Vision and Pattern Recognition Camera Models and Imaging CS4243 Camera Models and Imaging 1 Through our eyes… CS4243 Through our eyes we see the world. Camera Models and Imaging 2 cornea focus light lens retina captures image transmit image optic nerves iris pupil control amount of light entering the eye CS4243 Camera Models and Imaging 3 Through their eyes… CS4243 Camera is computer’s eye. Camera Models and Imaging 4 Camera is structurally the same the eye. sensor | retina lens lens | cornea CS4243 Camera Models and Imaging 5 lens aperture | pupil lens | cornea CS4243 Camera Models and Imaging 6 aperture plates | iris aperture | pupil CS4243 Camera Models and Imaging 7 Imaging Images are 2D projections of real world scene. Images capture two kinds of information: Geometric: positions, points, lines, curves, etc. Photometric: intensity, colour. Complex 3D-2D relationships. Camera models approximate relationships. CS4243 Camera Models and Imaging 8 Camera Models Pinhole camera model Orthographic projection Scaled orthographic projection Paraperspective projection Perspective projection CS4243 Camera Models and Imaging 9 Pinhole Camera Model image plane 2D image pinhole virtual image plane 3D object focal length CS4243 Camera Models and Imaging 10 Math representation world frame / camera frame camera centre CS4243 image frame image centre Camera Models and Imaging projection line optical axis 11 CS4243 By default, use right-handed coordinate system. Camera Models and Imaging 12 3D point P = (X, Y, Z)T projects to 2D image point p = (x, y)T . By symmetry, i.e., CS4243 Simplest form of perspective projection. Camera Models and Imaging 13 Orthographic Projection 3D scene is at infinite distance from camera. All projection lines are parallel to optical axis. So, CS4243 Camera Models and Imaging 14 Scaled Orthographic Projection depth << distance to camera. Z is the same for all scene points, say Z0 Scene CS4243 Camera Models and Imaging 15 Perspective Projection camera frame image frame is parallel to camera’s X-Y plane world frame CS4243 Camera Models and Imaging 16 Intrinsic Parameters Pinhole camera model Camera sensor’s pixels not exactly square x, y : coordinates (pixels) k, l : scale parameters (pixels/m) f : focal length (m or mm) CS4243 Camera Models and Imaging 17 f, k, l are not independent. Can rewrite as follows (in pixels): So, Image centre or principal point c may not be at origin. Denote location of c in image plane as cx, cy. Then, Along CS4243 optical axis, X = Y = 0, and x = cx, y = cy. Camera Models and Imaging 18 Image frame may not be exactly rectangular. Let θ denote skew angle between x- and y-axis. Then, Combine all parameters yield Intrinsic parameter matrix homogeneous coordinates CS4243 Camera Models and Imaging 19 Denoting Some ρ = Z, we get books and papers absorb ρ into : giving Be careful. A simpler form of K uses skew parameter s: CS4243 Camera Models and Imaging 20 Extrinsic Parameters Camera frame is not aligned with world frame. Rigid transformation between them: frame object Coordinates of 3D scene point in camera frame. Coordinates of 3D scene point in world frame. Rotation matrix of world frame in camera frame. Position of world frame’s origin in camera frame. CS4243 Camera Models and Imaging 21 Translation matrix Rotation matrix CS4243 Camera Models and Imaging 22 Rotation matrix is orthonormal: So, In particular, let . Then, CS4243 Camera Models and Imaging 23 Combine intrinsic and extrinsic parameters: Simpler notation: CS4243 Camera Models and Imaging 24 Lens Distortion Lens can distort images, especially at short focal length. barrel CS4243 pin-cushion Camera Models and Imaging fisheye 25 Radial distortion is modelled as distorted coordinates with CS4243 undistorted coordinates distortion parameters . Actual image coordinates Camera Models and Imaging 26 Camera Calibration Compute intrinsic / extrinsic parameters. Capture calibration pattern from various views. CS4243 Camera Models and Imaging 27 Detect inner corners in images. Run calibration program (available in OpenCV). CS4243 Camera Models and Imaging 28 Homography A transformation between projective planes. Maps straight lines to straight lines. CS4243 Camera Models and Imaging 29 Homography equation: image point homography image point Affine is a special case of homography: CS4243 Camera Models and Imaging 30 Scaling H by s does not change equation: Homography is defined up to unspecified scale. So, can set h33 = 1. Expanding homography equation gives CS4243 Camera Models and Imaging 31 Assembling equations over all points yields System of linear equations. Easy to solve. CS4243 Camera Models and Imaging 32 Example Circles: input corresponding points. Black dots: computed points, match input points. CS4243 Camera Models and Imaging 33 Before homographic transform CS4243 Camera Models and Imaging 34 After homographic transform CS4243 Camera Models and Imaging 35 Summary Simplest camera model: pinhole model. Most commonly used model: perspective model. Intrinsic parameters: Focal length, principal point. Extrinsic parameters: Camera rotation and translation. Lens distortion Homography: maps lines to lines. CS4243 Camera Models and Imaging 36 Further Reading Camera models: [Sze10] Section 2.1.5, [FP03] Section 1.1, 1.2, 2.2, 2.3. Lens distortion: [Sze10] Section 2.1.6, [BK08] Chapter 11. Camera calibration: [BK08] Chapter 11, [Zha00]. Image undistortion: [BK08] Chapter 11. CS4243 Camera Models and Imaging 37 References Bradski and Kaehler. Learning OpenCV. O’Reilly, 2008. D. A. Forsyth and J. Ponce. Computer Vision: A Modern Approach. Pearson Education, 2003. R. Szeliski. Computer Vision: Algorithms and Applications. Springer, 2010. Z. Zhang. A flexible new technique for camera calibration. IEEE Trans. PAMI, 22(11):1330–1334, 2000. CS4243 Camera Models and Imaging 38
