Camera Calibration. Schedule. Jesus J Caban. Note: You have until next Monday to let me know. ! Today:! Camera calibration


 Candace Shaw
 1 years ago
 Views:
Transcription
1 Camera Calibration Jesus J Caban Schedule! Today:! Camera calibration! Wednesday:! Lecture: Motion & Optical Flow! Monday:! Lecture: Medical Imaging! Final presentations:! Nov 29 th : W. Griffin! Dec 1 st : F. Zafar, Y. Wang, and N. Chhaya! Dec 6 th : J. Dandois! Dec 8 th :! Dec 13 th :! Dec 20 th : +5 bonus points +3 bonus points +2 bonus points +1 bonus points +0 bonus points +0 bonus points Note: You have until next Monday to let me know
2 Camera Calibration: Motivation! Images are obtained from 3D scenes! The exact position and orientation of the camera sensing device are often unknown! Camera needs to be related to some global frame / reference to be able to:! Get accurate measurements! Inspect materials! Etc Camera Model! Camera model:! from world to camera (coordinate systems)! from camera (3D) to image frame (2D) x im (x im,y im ) O y x y im p P P w Z w X w Y w
3 Camera Calibration! Goal: build the geometric relations between a 3D scene and its 2D images.! 3D transformation that represents the viewpoints and viewing directions of the camera! The perspective projection that maps 3D points into 2D images Camera Model: Parameters! Camera Parameters! Intrinsic Parameters (of the camera): link the frame coordinates of an image point with its corresponding camera coordinates! Extrinsic parameters: define the location and orientation of the camera coordinate system with respect to the world coordinate system x im (x im,y im ) O y x y im p P P w Z w X w Y w
4 Transformations 2D Rotation (x, y ) (x, y)! x = x cos(!)  y sin(!) y = x sin(!) + y cos(!)
5 2D Rotation! Rotation by angle! (about the origin)!"#"%!"#"%!% &()%*+%),%*.,/+,0% 12/%/2)(32+4% Scaling! Scaling operation:! Or, in matrix form: " x % " = a 0 %" # y & # 0 b& x % # y & scaling matrix S
6 Scaling! Scaling a coordinate means multiplying each of its components by a scalar! Uniform scaling means this scalar is the same for all components: " 2 Scaling! Uniform scaling by s:!"#"%!"#"%
7 Nonuniform Scaling! Nonuniform scaling: different scalars per component: X " 2, Y " 0.5 2x2 Matrices! What types of transformations can be represented with a 2x2 matrix? 2D Mirror about Y axis? 2D Mirror over (0,0)?
8 All 2D Linear Transformations! Linear transformations are combinations of! Scale,! Rotation,! Shear, and! Mirror! Properties of linear transformations:! Origin maps to origin! Lines map to lines! Parallel lines remain parallel! Ratios are preserved! Closed under composition What about 2D Translation? 56%7/(+8(320%! Translation is not a liner operation on 2D coordinates! Homogeneous coordinates
9 Homogeneous coordinates 7/*9:4%%(;;%2,%<2/,%922/;*(),4% B%!%#%&#%% 2<2=,,2>+%F8(,% 2<2=,,2>+%*<(=,%% 922/;*(),+% A% Homogeneous Coordinates! Add a 3rd coordinate to every 2D point! (x, y, w) represents a point at location (x/w, y/w)! (x, y, 0) represents a point at infinity! (0, 0, 0) is not allowed y 2 (2,1,1) or (4,2,2) or (6,3,3) Convenient coordinate 1 system to represent many useful x transformations 1 2
10 2D Translation?! Solution: homogeneous coordinates to the rescue Translation! Example of translation Homogeneous Coordinates " x % " 1 0 t x %" x% y = 0 1 t y y # 1 & # & # 1& " x + t x % = y + t y # 1 & t x = 2 t y = 1
11 Affine transformations (A%)/(+G2/<(32%B*)%% 8(+)%/2B%H%"%"%D%I%B,%9(88%(%% )*+,%)/(+G2/<(32 Basic affine transformations Translate Scale 2D inplane rotation Shear
12 3D Rotations & ) X " = & 0 cos" #sin") %& 0 sin" cos" () cos" 0 sin" & ) Y " = & ) %& #sin" 0 cos" () cos" #sin" 0 & ) Z " = & sin" cos" 0) %& 0 0 1( ) Where do we go from here? (J,%)/(+G2/<(32% B()%(FF,+%B,%B,% 9(=,%)*+%/2B0
13 Projective Transformations?(88,;%(%.##/")0.&%%!2/%01)+)"0,"20,345,)0 Image warping with homographies image plane in front image plane below black area where no pixel maps to
14 Camera Calibration Camera Model: Parameters! Camera Parameters! Intrinsic Parameters (of the camera): link the frame coordinates of an image point with its corresponding camera coordinates! Extrinsic parameters: define the location and orientation of the camera coordinate system with respect to the world coordinate system x im (x im,y im ) O y x y im p P P w Z w X w Y w
15 Camera coordinate system Principal axis: line from the camera center perpendicular to the image plane Principal point (p): point where principal axis intersects the image plane (origin of normalized coordinate system) Perspective Projection Equations (XZ Plane) X x f Z "x f = X Z "x = f X Z Notice: Position on the image plane is related to depth. (u,v) are scaled equally based on focal length and depth
16 Equivalent Image Geometries! Consider case with object on optical axis! More convenient geometry, with an upright image! Both are equivalent mathematically x = f X Z (X,Y,Z)! ( f X Z, f Y Z ) X Y Z 1 " # % &! f X f Y Z " # % & Pinhole camera model X Y Z 1 " # % & f 0 f " # % & =
17 Principal point offset principal point: Camera coordinate system: origin is at the principal point Image coordinate system: origin is in the corner Principal point offset principal point: (X,Y,Z)! ( f X Z + p x, f Y Z + p y )
18 Pixel size Pixel size:! m x pixels per meter in horizontal direction, m y pixels per meter in vertical direction pixels/m m pixels Skew The camera coordinate system may be skewed due to some manufacturing error.
19 Lens distortion! Two main lens distortion:! Radial distortion: arise as a result of the shape of lens (e.g. fisheye)! Tangential distortion: arise from the assembly process of the camera as a whole. Radial Distortion! Zero at the optical center of the image! Increases as we move toward the periphery! Rays farther from the center of the lens are bent more than those closer in! Terms: k1, k2, k3
20 Intrinsic parameters! Principal point coordinates! Focal length! Pixel magnification factors! Skew (nonrectangular pixels)! Radial distortion Camera parameters Extrinsic parameters! Rotation and translation relative to world coordinate system Camera rotation and translation In general, the camera coordinate frame will be related to the world coordinate frame by a rotation and a translation ( ) X cam = R X  C coords. of point in camera frame coords. of a point in world frame (nonhomogeneous) coords. of camera center in world frame
21 Intrinsic parameters! Principal point coordinates! Focal length! Pixel magnification factors! Skew (nonrectangular pixels)! Radial distortion Camera parameters Extrinsic parameters! Rotation and translation relative to world coordinate system Camera Calibration Basic matrix: " % " t 1 %" R 11 R 12 R 13 0% " T 1 % G = PLRT = t 2 R 21 R 22 R T t 3 R 31 R 32 R T 3 # 0 0 1/ f 0& # &# & # & Intrinsic Parameters Extrinsic Parameters How to estimate those parameters?
22 Camera calibration Given n points with known 3D coordinates X i and known image projections x i, estimate the camera parameters X i x i Example Calibration Pattern Harris Corner Detector From Sebastian Thrun 44
23 Camera calibration Calibration: 2 steps! Step 1: Transform into camera coordinates " X C % " X W % Y C # Z C = f ( Y W & Z W,(,),*,T) # &! Step 2: Transform into image coordinates 46
24 Calibration Model (extrinsic) 47 Advantage of Homogeneous C s ith data point 48
25 Camera Calibration! Algorithm 1. Measure N 3D coordinates (Xi, Yi,Zi) 2. Locate their corresponding image points (xi,yi)  Edge, Corner, Hough 3. Build matrix A of a homogeneous system Av = 0 4. Compute SVD of A, solution v 5. Determine aspect ratio # and scale 6. Recover the first two rows of R and the first two components of T up to a sign 7. Determine sign s of by checking the projection equation 8. Compute the 3 rd row of R by vector product, and enforce orthogonality constraint by SVD 9. Solve Tz and fx using Least Square and SVD, then fy = fx / #% Y w Z w X w How Many Images Do We Need?! Assumption: K images with M corners each! 4+6K parameters! 2KM constraints! 2KM & 4+6K M>3 and K &2/(M3)! 2 images with 4 points, but will 1 images with 5 points work?! No, since points cannot be coplanar! 50
26 Calibration tools? Multiview Geometry
27 Twoview geometry Scene geometry (structure): Given corresponding points in two or more images, where is the preimage of these points in 3D? Correspondence (stereo matching): Given a point in just one image, how does it constrain the position of the corresponding point x in another image? Camera geometry (motion): Given a set of corresponding points in two images, what are the cameras for the two views? Parameters of a Stereo System! Intrinsic Parameters! Characterize the transformation from camera to pixel coordinate systems of each camera! Focal length, image center, aspect ratio P l P P r! Extrinsic parameters! Describe the relative position and orientation of the two cameras X l! Rotation matrix R and translation vector T p l Y l f l O l Z l R, T Z r X r p r Y r f r O r Bahadir K. Gunturk
28 Triangulation Given projections of a 3D point in two or more images (with known camera matrices), find the coordinates of the point X? x 1 x 2 O 1 O 2 Triangulation We want to intersect the two visual rays corresponding to x 1 and x 2, but because of noise and numerical errors, they don t meet exactly R 2 X? R 1 x 1 x 2 O 1 O 2
29 Triangulation: Geometric approach Find shortest segment connecting the two viewing rays and let X be the midpoint of that segment X x 1 x 2 O 1 O 2 Epipolar geometry X x x Baseline line connecting the two camera centers Epipolar Plane plane containing baseline (1D family) Epipoles = intersections of baseline with image planes = projections of the other camera center = vanishing points of camera motion direction Epipolar Lines  intersections of epipolar plane with image planes (always come in corresponding pairs)
30 Epipolar constraint X x x If we observe a point x in one image, where can the corresponding point x be in the other image? Epipolar constraint X X X x x x x Potential matches for x have to lie on the corresponding epipolar line l. Potential matches for x have to lie on the corresponding epipolar line l.
31 Calibrated Camera Essential matrix Bahadir K. Gunturk Example: Converging cameras
32 Rectification! Problem: Epipolar lines not parallel to scan lines P P l P r Epipolar Plane p l Epipolar Lines p r O l e l e r Or Epipoles From Sebastian Thrun/Jana Kosecka Rectification! Problem: Epipolar lines not parallel to scan lines P Epipolar Plane P l P r Rectified Images p l Epipolar Lines p r O l Or Epipoles at infinity From Sebastian Thrun/Jana Kosecka
33 Epipolar rectification Rectified Image Pair Epipolar rectification Rectified Image Pair
34 Stereo results Scene Ground truth (from Seitz) Results with window correlation Windowbased matching (best window size) Ground truth (from Seitz)
35 Results with better method State of the art Ground truth Boykov et al., Fast Approximate Energy Minimization via Graph Cuts, International Conference on Computer Vision, September (from Seitz) How can We Improve Stereo? Spacetime stereo scanner uses unstructured light to aid in correspondence Result: Dense 3D mesh (noisy) From Sebastian Thrun/Jana Kosecka
36 Unstructured Light 3D Scanner OpenCV! cvfindchessboardcorners()! Calibrate:! cvcalibratecamera2()! cvstereocalibrate()! Rectify / Epipolar! cvinitundistortmap()! cvinitundistortrectifymap()! cvcomputecorrespondepilines()! cvfindfundamentalmatrix()! cvstereorectify()! Stereo! cvfindstereocorrespondencebm()! Depth maps! cvreprojectimageto3d()
37 Assignment #4! Download the Matlab Camera Calibration Toolbox! Read Documentation! First calibration example! Download data! Run camera calibration software! Submit results Conclusion! There s a mathematical model to describe cameras! Parameters can be estimated using a camera calibration approach! Camera calibration is key for accurate stereo reconstruction
Pin Hole Cameras & Warp Functions
Pin Hole Cameras & Warp Functions Instructor  Simon Lucey 16423  Designing Computer Vision Apps Today Pinhole Camera. Homogenous Coordinates. Planar Warp Functions. Motivation Taken from: http://img.gawkerassets.com/img/18w7i1umpzoa9jpg/original.jpg
More informationComputer Vision Projective Geometry and Calibration. Pinhole cameras
Computer Vision Projective Geometry and Calibration Professor Hager http://www.cs.jhu.edu/~hager Jason Corso http://www.cs.jhu.edu/~jcorso. Pinhole cameras Abstract camera model  box with a small hole
More information3D Geometry and Camera Calibration
3D Geometry and Camera Calibration 3D Coordinate Systems Righthanded vs. lefthanded x x y z z y 2D Coordinate Systems 3D Geometry Basics y axis up vs. y axis down Origin at center vs. corner Will often
More informationCamera Model and Calibration
Camera Model and Calibration Lecture10 Camera Calibration Determine extrinsic and intrinsic parameters of camera Extrinsic 3D location and orientation of camera Intrinsic Focal length The size of the
More informationLecture 9: Epipolar Geometry
Lecture 9: Epipolar Geometry Professor Fei Fei Li Stanford Vision Lab 1 What we will learn today? Why is stereo useful? Epipolar constraints Essential and fundamental matrix Estimating F (Problem Set 2
More informationImage Rectification (Stereo) (New book: 7.2.1, old book: 11.1)
Image Rectification (Stereo) (New book: 7.2.1, old book: 11.1) Guido Gerig CS 6320 Spring 2013 Credits: Prof. Mubarak Shah, Course notes modified from: http://www.cs.ucf.edu/courses/cap6411/cap5415/, Lecture
More informationLecture 14: Basic MultiView Geometry
Lecture 14: Basic MultiView Geometry Stereo If I needed to find out how far point is away from me, I could use triangulation and two views scene point image plane optical center (Graphic from Khurram
More informationCV: 3D to 2D mathematics. Perspective transformation; camera calibration; stereo computation; and more
CV: 3D to 2D mathematics Perspective transformation; camera calibration; stereo computation; and more Roadmap of topics n Review perspective transformation n Camera calibration n Stereo methods n Structured
More informationThere are many cues in monocular vision which suggests that vision in stereo starts very early from two similar 2D images. Lets see a few...
STEREO VISION The slides are from several sources through James Hays (Brown); Srinivasa Narasimhan (CMU); Silvio Savarese (U. of Michigan); Bill Freeman and Antonio Torralba (MIT), including their own
More informationReminder: Lecture 20: The EightPoint Algorithm. Essential/Fundamental Matrix. E/F Matrix Summary. Computing F. Computing F from Point Matches
Reminder: Lecture 20: The EightPoint Algorithm F = 0.003106950.0025646 2.965840.0280940.00771621 56.3813 13.190529.20079999.79 Readings T&V 7.3 and 7.4 Essential/Fundamental Matrix E/F Matrix Summary
More informationCamera Model and Calibration. Lecture12
Camera Model and Calibration Lecture12 Camera Calibration Determine extrinsic and intrinsic parameters of camera Extrinsic 3D location and orientation of camera Intrinsic Focal length The size of the
More informationRectification and Disparity
Rectification and Disparity Nassir Navab Slides prepared by Christian Unger What is Stereo Vision? Introduction A technique aimed at inferring dense depth measurements efficiently using two cameras. Wide
More informationCamera Models and Image Formation. Srikumar Ramalingam School of Computing University of Utah
Camera Models and Image Formation Srikumar Ramalingam School of Computing University of Utah srikumar@cs.utah.edu Reference Most slides are adapted from the following notes: Some lecture notes on geometric
More informationComputer Vision. Coordinates. Prof. Flávio Cardeal DECOM / CEFET MG.
Computer Vision Coordinates Prof. Flávio Cardeal DECOM / CEFET MG cardeal@decom.cefetmg.br Abstract This lecture discusses world coordinates and homogeneous coordinates, as well as provides an overview
More informationLecture 9 & 10: Stereo Vision
Lecture 9 & 10: Stereo Vision Professor Fei Fei Li Stanford Vision Lab 1 What we will learn today? IntroducEon to stereo vision Epipolar geometry: a gentle intro Parallel images Image receficaeon Solving
More informationRectification. Dr. Gerhard Roth
Rectification Dr. Gerhard Roth Problem Definition Given a pair of stereo images, the intrinsic parameters of each camera, and the extrinsic parameters of the system, R, and, compute the image transformation
More informationCamera Models and Image Formation. Srikumar Ramalingam School of Computing University of Utah
Camera Models and Image Formation Srikumar Ramalingam School of Computing University of Utah srikumar@cs.utah.edu VisualFunHouse.com 3D Street Art Image courtesy: Julian Beaver (VisualFunHouse.com) 3D
More informationEpipolar geometry. x x
Twoview geometry Epipolar geometry X x x Baseline line connecting the two camera centers Epipolar Plane plane containing baseline (1D family) Epipoles = intersections of baseline with image planes = projections
More informationMachine vision. Summary # 11: Stereo vision and epipolar geometry. u l = λx. v l = λy
1 Machine vision Summary # 11: Stereo vision and epipolar geometry STEREO VISION The goal of stereo vision is to use two cameras to capture 3D scenes. There are two important problems in stereo vision:
More informationRecovering structure from a single view Pinhole perspective projection
EPIPOLAR GEOMETRY The slides are from several sources through James Hays (Brown); Silvio Savarese (U. of Michigan); Svetlana Lazebnik (U. Illinois); Bill Freeman and Antonio Torralba (MIT), including their
More informationIntroduction to Homogeneous coordinates
Last class we considered smooth translations and rotations of the camera coordinate system and the resulting motions of points in the image projection plane. These two transformations were expressed mathematically
More informationLecture 6 Stereo Systems Multiview geometry
Lecture 6 Stereo Systems Multiview geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 65Feb4 Lecture 6 Stereo Systems Multiview geometry Stereo systems
More informationMidterm Exam Solutions
Midterm Exam Solutions Computer Vision (J. Košecká) October 27, 2009 HONOR SYSTEM: This examination is strictly individual. You are not allowed to talk, discuss, exchange solutions, etc., with other fellow
More informationProjective Geometry and Camera Models
/2/ Projective Geometry and Camera Models Computer Vision CS 543 / ECE 549 University of Illinois Derek Hoiem Note about HW Out before next Tues Prob: covered today, Tues Prob2: covered next Thurs Prob3:
More informationAugmented Reality II  Camera Calibration  Gudrun Klinker May 11, 2004
Augmented Reality II  Camera Calibration  Gudrun Klinker May, 24 Literature Richard Hartley and Andrew Zisserman, Multiple View Geometry in Computer Vision, Cambridge University Press, 2. (Section 5,
More informationProjective Geometry and Camera Models
Projective Geometry and Camera Models Computer Vision CS 43 Brown James Hays Slides from Derek Hoiem, Alexei Efros, Steve Seitz, and David Forsyth Administrative Stuff My Office hours, CIT 375 Monday and
More informationLaser sensors. Transmitter. Receiver. Basilio Bona ROBOTICA 03CFIOR
Mobile & Service Robotics Sensors for Robotics 3 Laser sensors Rays are transmitted and received coaxially The target is illuminated by collimated rays The receiver measures the time of flight (back and
More information3D Vision Real Objects, Real Cameras. Chapter 11 (parts of), 12 (parts of) Computerized Image Analysis MN2 Anders Brun,
3D Vision Real Objects, Real Cameras Chapter 11 (parts of), 12 (parts of) Computerized Image Analysis MN2 Anders Brun, anders@cb.uu.se 3D Vision! Philisophy! Image formation " The pinhole camera " Projective
More informationStereo vision. Many slides adapted from Steve Seitz
Stereo vision Many slides adapted from Steve Seitz What is stereo vision? Generic problem formulation: given several images of the same object or scene, compute a representation of its 3D shape What is
More informationModule 4F12: Computer Vision and Robotics Solutions to Examples Paper 2
Engineering Tripos Part IIB FOURTH YEAR Module 4F2: Computer Vision and Robotics Solutions to Examples Paper 2. Perspective projection and vanishing points (a) Consider a line in 3D space, defined in cameracentered
More informationModels and The Viewing Pipeline. Jian Huang CS456
Models and The Viewing Pipeline Jian Huang CS456 Vertex coordinates list, polygon table and (maybe) edge table Auxiliary: Per vertex normal Neighborhood information, arranged with regard to vertices and
More information3D FACE RECONSTRUCTION BASED ON EPIPOLAR GEOMETRY
IJDW Volume 4 Number JanuaryJune 202 pp. 4550 3D FACE RECONSRUCION BASED ON EPIPOLAR GEOMERY aher Khadhraoui, Faouzi Benzarti 2 and Hamid Amiri 3,2,3 Signal, Image Processing and Patterns Recognition
More informationPerspective Projection [2 pts]
Instructions: CSE252a Computer Vision Assignment 1 Instructor: Ben Ochoa Due: Thursday, October 23, 11:59 PM Submit your assignment electronically by email to iskwak+252a@cs.ucsd.edu with the subject line
More informationMultiview geometry problems
Multiview geometry Multiview geometry problems Structure: Given projections o the same 3D point in two or more images, compute the 3D coordinates o that point? Camera 1 Camera 2 R 1,t 1 R 2,t 2 Camera
More information3D Viewing. CS 4620 Lecture 8
3D Viewing CS 46 Lecture 8 13 Steve Marschner 1 Viewing, backward and forward So far have used the backward approach to viewing start from pixel ask what part of scene projects to pixel explicitly construct
More informationCS 231A: Computer Vision (Winter 2018) Problem Set 2
CS 231A: Computer Vision (Winter 2018) Problem Set 2 Due Date: Feb 09 2018, 11:59pm Note: In this PS, using python2 is recommended, as the data files are dumped with python2. Using python3 might cause
More informationLecture 3: Camera Calibration, DLT, SVD
Computer Vision Lecture 3 2328 Lecture 3: Camera Calibration, DL, SVD he Inner Parameters In this section we will introduce the inner parameters of the cameras Recall from the camera equations λx = P
More informationImage Formation I Chapter 2 (R. Szelisky)
Image Formation I Chapter 2 (R. Selisky) Guido Gerig CS 632 Spring 22 cknowledgements: Slides used from Prof. Trevor Darrell, (http://www.eecs.berkeley.edu/~trevor/cs28.html) Some slides modified from
More informationVisual Recognition: Image Formation
Visual Recognition: Image Formation Raquel Urtasun TTI Chicago Jan 5, 2012 Raquel Urtasun (TTIC) Visual Recognition Jan 5, 2012 1 / 61 Today s lecture... Fundamentals of image formation You should know
More informationCHAPTER 3 DISPARITY AND DEPTH MAP COMPUTATION
CHAPTER 3 DISPARITY AND DEPTH MAP COMPUTATION In this chapter we will discuss the process of disparity computation. It plays an important role in our caricature system because all 3D coordinates of nodes
More informationFundamentals of Stereo Vision Michael Bleyer LVA Stereo Vision
Fundamentals of Stereo Vision Michael Bleyer LVA Stereo Vision What Happened Last Time? Human 3D perception (3D cinema) Computational stereo Intuitive explanation of what is meant by disparity Stereo matching
More informationColorado School of Mines. Computer Vision. Professor William Hoff Dept of Electrical Engineering &Computer Science.
Professor Willia Hoff Dept of Electrical Engineering &Coputer Science http://inside.ines.edu/~whoff/ 1 Caera Calibration 2 Caera Calibration Needed for ost achine vision and photograetry tasks (object
More informationLecture 7 Measurement Using a Single Camera. Lin ZHANG, PhD School of Software Engineering Tongji University Fall 2016
Lecture 7 Measurement Using a Single Camera Lin ZHANG, PhD School of Software Engineering Tongji University Fall 2016 If I have an image containing a coin, can you tell me the diameter of that coin? Contents
More informationCompositing a bird's eye view mosaic
Compositing a bird's eye view mosaic Robert Laganiere School of Information Technology and Engineering University of Ottawa Ottawa, Ont KN 6N Abstract This paper describes a method that allows the composition
More informationCS 4495 Computer Vision A. Bobick. Motion and Optic Flow. Stereo Matching
Stereo Matching Fundamental matrix Let p be a point in left image, p in right image l l Epipolar relation p maps to epipolar line l p maps to epipolar line l p p Epipolar mapping described by a 3x3 matrix
More informationRecap: Features and filters. Recap: Grouping & fitting. Now: Multiple views 10/29/2008. Epipolar geometry & stereo vision. Why multiple views?
Recap: Features and filters Epipolar geometry & stereo vision Tuesday, Oct 21 Kristen Grauman UTAustin Transforming and describing images; textures, colors, edges Recap: Grouping & fitting Now: Multiple
More informationFinal Exam Study Guide CSE/EE 486 Fall 2007
Final Exam Study Guide CSE/EE 486 Fall 2007 Lecture 2 Intensity Sufaces and Gradients Image visualized as surface. Terrain concepts. Gradient of functions in 1D and 2D Numerical derivatives. Taylor series.
More informationStructure from Motion. Prof. Marco Marcon
Structure from Motion Prof. Marco Marcon Summingup 2 Stereo is the most powerful clue for determining the structure of a scene Another important clue is the relative motion between the scene and (mono)
More informationAgenda. Perspective projection. Rotations. Camera models
Image formation Agenda Perspective projection Rotations Camera models Light as a wave + particle Light as a wave (ignore for now) Refraction Diffraction Image formation Digital Image Film Human eye Pixel
More informationThreeDimensional Sensors Lecture 2: ProjectedLight Depth Cameras
ThreeDimensional Sensors Lecture 2: ProjectedLight Depth Cameras Radu Horaud INRIA Grenoble RhoneAlpes, France Radu.Horaud@inria.fr http://perception.inrialpes.fr/ Outline The geometry of active stereo.
More informationScalable geometric calibration for multiview camera arrays
Scalable geometric calibration for multiview camera arrays Bernhard Blaschitz, Doris Antensteiner, Svorad Štolc Bernhard.Blaschitz@ait.ac.at AIT Austrian Institute of Technology GmbH Intelligent Vision
More informationBasilio Bona DAUIN Politecnico di Torino
ROBOTICA 03CFIOR DAUIN Politecnico di Torino Mobile & Service Robotics Sensors for Robotics 3 Laser sensors Rays are transmitted and received coaxially The target is illuminated by collimated rays The
More informationSingle View Geometry. Camera model & Orientation + Position estimation. What am I?
Single View Geometry Camera model & Orientation + Position estimation What am I? Vanishing points & line http://www.wetcanvas.com/ http://pennpaint.blogspot.com/ http://www.joshuanava.biz/perspective/inotherwordstheobserversimplypointsinthesamedirectionasthelinesinordertofindtheirvanishingpoint.html
More informationLecture 6 Stereo Systems Multi view geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 624Jan15
Lecture 6 Stereo Systems Multi view geometry Professor Silvio Savarese Computational Vision and Geometry Lab Silvio Savarese Lecture 624Jan15 Lecture 6 Stereo Systems Multi view geometry Stereo systems
More informationGeometry of image formation
eometry of image formation Tomáš Svoboda, svoboda@cmp.felk.cvut.cz Czech Technical University in Prague, Center for Machine Perception http://cmp.felk.cvut.cz Last update: November 3, 2008 Talk Outline
More informationCS 4495 Computer Vision A. Bobick. Motion and Optic Flow. Stereo Matching
Stereo Matching Fundamental matrix Let p be a point in left image, p in right image l l Epipolar relation p maps to epipolar line l p maps to epipolar line l p p Epipolar mapping described by a 3x3 matrix
More informationProjector Calibration for Pattern Projection Systems
Projector Calibration for Pattern Projection Systems I. Din *1, H. Anwar 2, I. Syed 1, H. Zafar 3, L. Hasan 3 1 Department of Electronics Engineering, Incheon National University, Incheon, South Korea.
More informationDepth from two cameras: stereopsis
Depth from two cameras: stereopsis Epipolar Geometry Canonical Configuration Correspondence Matching School of Computer Science & Statistics Trinity College Dublin Dublin 2 Ireland www.scss.tcd.ie Lecture
More informationStereo Vision Based Mapping and Immediate Virtual Walkthroughs
Stereo Vision Based Mapping and Immediate Virtual Walkthroughs Heiko Hirschmüller M.Sc., Dipl.Inform. (FH) Submitted in partial fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY June
More informationCamera Calibration using Vanishing Points
Camera Calibration using Vanishing Points Paul Beardsley and David Murray * Department of Engineering Science, University of Oxford, Oxford 0X1 3PJ, UK Abstract This paper describes a methodformeasuringthe
More informationCamera Calibration and 3D Reconstruction from Single Images Using Parallelepipeds
Camera Calibration and 3D Reconstruction from Single Images Using Parallelepipeds Marta Wilczkowiak Edmond Boyer Peter Sturm Movi Gravir Inria RhôneAlpes, 655 Avenue de l Europe, 3833 Montbonnot, France
More informationImage warping and stitching
Image warping and stitching May 4 th, 2017 Yong Jae Lee UC Davis Last time Interactive segmentation Featurebased alignment 2D transformations Affine fit RANSAC 2 Alignment problem In alignment, we will
More informationThreeDimensional Viewing Hearn & Baker Chapter 7
ThreeDimensional Viewing Hearn & Baker Chapter 7 Overview 3D viewing involves some tasks that are not present in 2D viewing: Projection, Visibility checks, Lighting effects, etc. Overview First, set up
More informationImage Warping and Mosacing
Image Warping and Mosacing 15463: Rendering and Image Processing Alexei Efros with a lot of slides stolen from Steve Seitz and Rick Szeliski Today Mosacs Image Warping Homographies Programming Assignment
More informationMiniature faking. In closeup photo, the depth of field is limited.
Miniature faking In closeup photo, the depth of field is limited. http://en.wikipedia.org/wiki/file:jodhpur_tilt_shift.jpg Miniature faking Miniature faking http://en.wikipedia.org/wiki/file:oregon_state_beavers_tiltshift_miniature_greg_keene.jpg
More informationBinocular stereo. Given a calibrated binocular stereo pair, fuse it to produce a depth image. Where does the depth information come from?
Binocular Stereo Binocular stereo Given a calibrated binocular stereo pair, fuse it to produce a depth image Where does the depth information come from? Binocular stereo Given a calibrated binocular stereo
More informationCamera Projection Models We will introduce different camera projection models that relate the location of an image point to the coordinates of the
Camera Projection Models We will introduce different camera projection models that relate the location of an image point to the coordinates of the corresponding 3D points. The projection models include:
More information1 CSE 252A Computer Vision I Fall 2017
Assignment 1 CSE A Computer Vision I Fall 01 1.1 Assignment This assignment contains theoretical and programming exercises. If you plan to submit hand written answers for theoretical exercises, please
More informationCSE 167: Introduction to Computer Graphics Lecture #3: Coordinate Systems
CSE 167: Introduction to Computer Graphics Lecture #3: Coordinate Systems Jürgen P. Schulze, Ph.D. University of California, San Diego Spring Quarter 2015 Announcements Project 2 due Friday at 1pm Homework
More informationIntroduction to Computer Vision. Introduction CMPSCI 591A/691A CMPSCI 570/670. Image Formation
Introduction CMPSCI 591A/691A CMPSCI 570/670 Image Formation Lecture Outline Light and Optics Pinhole camera model Perspective projection Thin lens model Fundamental equation Distortion: spherical & chromatic
More informationJump Stitch Metadata & Depth Maps Version 1.1
Jump Stitch Metadata & Depth Maps Version 1.1 jumphelp@google.com Contents 1. Introduction 1 2. Stitch Metadata File Format 2 3. Coverage Near the Poles 4 4. Coordinate Systems 6 5. Camera Model 6 6.
More informationImage warping and stitching
Image warping and stitching May 5 th, 2015 Yong Jae Lee UC Davis PS2 due next Friday Announcements 2 Last time Interactive segmentation Featurebased alignment 2D transformations Affine fit RANSAC 3 Alignment
More informationElements of Computer Vision: Multiple View Geometry. 1 Introduction. 2 Elements of Geometry. Andrea Fusiello
Elements of Computer Vision: Multiple View Geometry. Andrea Fusiello http://www.sci.univr.it/~fusiello July 11, 2005 c Copyright by Andrea Fusiello. This work is licensed under the Creative Commons AttributionNonCommercialShareAlike
More informationTransforms. COMP 575/770 Spring 2013
Transforms COMP 575/770 Spring 2013 Transforming Geometry Given any set of points S Could be a 2D shape, a 3D object A transform is a function T that modifies all points in S: T S S T v v S Different transforms
More informationSingleview metrology
Singleview metrology Magritte, Personal Values, 952 Many slides from S. Seitz, D. Hoiem Camera calibration revisited What if world coordinates of reference 3D points are not known? We can use scene features
More informationOverview. Augmented reality and applications Markerbased augmented reality. Camera model. Binary markers Textured planar markers
Augmented reality Overview Augmented reality and applications Markerbased augmented reality Binary markers Textured planar markers Camera model Homography Direct Linear Transformation What is augmented
More informationA Stratified Approach for Camera Calibration Using Spheres
IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. XX, NO. Y, MONTH YEAR 1 A Stratified Approach for Camera Calibration Using Spheres KwanYee K. Wong, Member, IEEE, Guoqiang Zhang, StudentMember, IEEE and Zhihu
More informationColorado School of Mines. Computer Vision. Professor William Hoff Dept of Electrical Engineering &Computer Science.
Professor William Hoff Dept of Electrical Engineering &Computer Science http://inside.mines.edu/~whoff/ 1 Stereo Vision 2 Inferring 3D from 2D Model based pose estimation single (calibrated) camera Stereo
More informationVision 3D articielle Multiple view geometry
Vision 3D articielle Multiple view geometry Pascal Monasse monasse@imagine.enpc.fr IMAGINE, École des Ponts ParisTech Contents Multiview constraints Multiview calibration Incremental calibration Global
More informationRectification for Any Epipolar Geometry
Rectification for Any Epipolar Geometry Daniel Oram Advanced Interfaces Group Department of Computer Science University of Manchester Mancester, M13, UK oramd@cs.man.ac.uk Abstract This paper proposes
More informationAUTORECTIFICATION OF USER PHOTOS. Krishnendu Chaudhury, Stephen DiVerdi, Sergey Ioffe.
AUTORECTIFICATION OF USER PHOTOS Krishnendu Chaudhury, Stephen DiVerdi, Sergey Ioffe krish@google.com, diverdi@google.com, sioffe@google.com ABSTRACT The image auto rectification project at Google aims
More informationAccurate and Dense WideBaseline Stereo Matching Using SWPOC
Accurate and Dense WideBaseline Stereo Matching Using SWPOC Shuji Sakai, Koichi Ito, Takafumi Aoki Graduate School of Information Sciences, Tohoku University, Sendai, 980 8579, Japan Email: sakai@aoki.ecei.tohoku.ac.jp
More informationPart I: Single and Two View Geometry Internal camera parameters
!! 43 1!???? Imaging eometry Multiple View eometry Perspective projection Richard Hartley Andrew isserman O p y VPR June 1999 where image plane This can be written as a linear mapping between homogeneous
More information3D Computer Vision. Depth Cameras. Prof. Didier Stricker. Oliver Wasenmüller
3D Computer Vision Depth Cameras Prof. Didier Stricker Oliver Wasenmüller Kaiserlautern University http://ags.cs.unikl.de/ DFKI Deutsches Forschungszentrum für Künstliche Intelligenz http://av.dfki.de
More informationLecture 10 Multiview Stereo (3D Dense Reconstruction) Davide Scaramuzza
Lecture 10 Multiview Stereo (3D Dense Reconstruction) Davide Scaramuzza REMODE: Probabilistic, Monocular Dense Reconstruction in Real Time, ICRA 14, by Pizzoli, Forster, Scaramuzza [M. Pizzoli, C. Forster,
More informationComputer Vision. Geometric Camera Calibration. Samer M Abdallah, PhD
Computer Vision Samer M Abdallah, PhD Faculty of Engineering and Architecture American University of Beirut Beirut, Lebanon Geometric Camera Calibration September 2, 2004 1 Computer Vision Geometric Camera
More informationImage warping and stitching
Image warping and stitching Thurs Oct 15 Last time Featurebased alignment 2D transformations Affine fit RANSAC 1 Robust featurebased alignment Extract features Compute putative matches Loop: Hypothesize
More informationCEE598  Visual Sensing for Civil Infrastructure Eng. & Mgmt.
CEE598  Visual Sensing for Civil Infrastructure Eng. & Mgmt. Session 4 Affine Structure from Motion Mani GolparvarFard Department of Civil and Environmental Engineering 329D, Newmark Civil Engineering
More informationExterior Orientation Parameters
Exterior Orientation Parameters PERS 12/2001 pp 13211332 Karsten Jacobsen, Institute for Photogrammetry and GeoInformation, University of Hannover, Germany The georeference of any photogrammetric product
More informationSRI Small Vision System
Small Vision System Calibration 1 SRI Small Vision System Calibration Supplement to the User s Manual Software version 2.2b July 2001 Kurt Konolige and David Beymer SRI International konolige@ai.sri.com
More informationStereo. Outline. Multiple views 3/29/2017. Thurs Mar 30 Kristen Grauman UT Austin. Multiview geometry, matching, invariant features, stereo vision
Stereo Thurs Mar 30 Kristen Grauman UT Austin Outline Last time: Human stereopsis Epipolar geometry and the epipolar constraint Case example with parallel optical axes General case with calibrated cameras
More informationOmni Stereo Vision of Cooperative Mobile Robots
Omni Stereo Vision of Cooperative Mobile Robots Zhigang Zhu*, Jizhong Xiao** *Department of Computer Science **Department of Electrical Engineering The City College of the City University of New York (CUNY)
More informationLecture 5.3 Camera calibration. Thomas Opsahl
Lecture 5.3 Camera calibration Thomas Opsahl Introduction The image u u x X W v C z C World frame x C y C z C = 1 For finite projective cameras, the correspondence between points in the world and points
More informationMapping NonDestructive Testing Data on the 3D Geometry of Objects with Complex Shapes
More Info at Open Access Database www.ndt.net/?id=17670 Mapping NonDestructive Testing Data on the 3D Geometry of Objects with Complex Shapes Abstract by S. Soldan*, D. Ouellet**, P.Hedayati**, A. Bendada**,
More informationPerspective Correction Methods for CameraBased Document Analysis
Perspective Correction Methods for CameraBased Document Analysis L. Jagannathan and C. V. Jawahar Center for Visual Information Technology International Institute of Information Technology Gachibowli,
More informationRobust Geometry Estimation from two Images
Robust Geometry Estimation from two Images Carsten Rother 09/12/2016 Computer Vision I: Image Formation Process Roadmap for next four lectures Computer Vision I: Image Formation Process 09/12/2016 2 Appearancebased
More informationCSE 252B: Computer Vision II
CSE 252B: Computer Vision II Lecturer: Serge Belongie Scribes: Jeremy Pollock and Neil Alldrin LECTURE 14 Robust Feature Matching 14.1. Introduction Last lecture we learned how to find interest points
More informationDTU M.SC.  COURSE EXAM Revised Edition
Written test, 16 th of December 1999. Course name : 04250  Digital Image Analysis Aids allowed : All usual aids Weighting : All questions are equally weighed. Name :...................................................
More informationCS4670/5760: Computer Vision Kavita Bala Scott Wehrwein. Lecture 23: Photometric Stereo
CS4670/5760: Computer Vision Kavita Bala Scott Wehrwein Lecture 23: Photometric Stereo Announcements PA3 Artifact due tonight PA3 Demos Thursday Signups close at 4:30 today No lecture on Friday Last Time:
More information