Last Lecture. Edge Detection. Filtering Pyramid
|
|
- Winifred Brooks
- 5 years ago
- Views:
Transcription
1 Last Lecture Edge Detection Filtering Pramid
2 Toda Motion Deblur Image Transformation
3 Removing Camera Shake from a Single Photograph Rob Fergus, Barun Singh, Aaron Hertzmann, Sam T. Roweis and William T. Freeman Massachusetts Institute of Technolog and Universit of Toronto
4 Overview Original Our algorithm
5 Close-up Original Naïve Sharpening Our algorithm
6 Let s take a photo Blurr result
7 Slow-motion repla
8 Slow-motion repla Motion of camera
9 Image formation process = Blurr image Sharp image Blur kernel Input to algorithm Model is approimation Desired output Convolution operator
10 Wh is this hard? Simple analog: is the product of two numbers. What are the? No unique solution: = = = etc.. Need more information!!!!
11 Multiple possible solutions Sharp image Blur kernel = Blurr image = =
12 Natural image statistics Characteristic distribution with heav tails Histogram of image gradients
13 Blur images have different statistics Histogram of image gradients
14 Parametric distribution Histogram of image gradients Use parametric model of sharp image statistics
15 Three sources of information. Reconstruction constraint: = Estimated sharp image Estimated blur kernel Input blurr image 2. Image prior: 3. Blur prior: Distribution of gradients Positive & Sparse
16 Variational Baesian method Based on work of Miskin & Macka 2 Keeps track of uncertaint in estimates of image and blur b using a distribution instead of a single estimate Helps avoid local maima and over-fitting
17 Score Variational Baesian method Objective function for a single variable Maimum a-posteriori (MAP) Variational Baes Piel intensit
18 Overview of algorithm. Pre-processing Input image 2. Kernel estimation - Multi-scale approach 3. Image reconstruction - Standard non-blind deconvolution routine
19 Preprocessing Input image Convert to grascale Remove gamma correction User selects patch from image Baesian inference too slow to run on whole image Infer kernel from this patch
20 Initialization Input image Convert to grascale Remove gamma correction User selects patch from image Initialize 33 blur kernel Blurr patch Initial image estimate Initial blur kernel
21 Inferring the kernel: multiscale method Input image Convert to grascale Remove gamma correction Loop over scales User selects patch from image Upsample estimates Variational Baes Initialize 33 blur kernel Use multi-scale approach to avoid local minima:
22 Image Reconstruction Input image Convert to grascale Remove gamma correction Loop over scales User selects patch from image Full resolution blur estimate Upsample estimates Variational Baes Initialize 33 blur kernel Non-blind deconvolution (Richardson-Luc) Deblurred image
23 Results on real images Submitted b people from their own photo collections Tpe of camera unknown Output does contain artifacts Increased noise Ringing Compares well to eisting methods
24 Original photograph
25 Blur kernel Our output
26 Original photograph Matlab s deconvblind
27 Original photograph
28 Matlab s deconvblind
29 Photoshop sharpen more
30 Our output Blur kernel
31
32 Original photograph
33 Our output Blur kernel
34 Original photograph
35 Our output Blur kernel
36 Matlab s deconvblind
37 Original photograph
38 Our output Blur kernel
39 Close-up of bird Original Our output
40 Original photograph
41 Blur kernel Our output
42 Image artifacts & estimated kernels Blur kernels Image patterns Note: blur kernels were inferred from large image patches, NOT the image patterns shown
43 Summar Method for removing camera shake from real photographs First method that can handle complicated blur kernels Uses natural image statistics Non-blind deconvolution currentl simplistic
44 Image Warping image filtering: change range of image g() = T(f()) f T f image warping: change domain of image g() = f(t()) f T f
45 Image Warping image filtering: change range of image g() = T(f()) T image warping: change domain of image g() = f(t()) T
46 Parametric (global) warping Eamples of parametric warps: translation rotation aspect affine perspective clindrical
47 Parametric (global) warping T p = (,) p = (, ) Transformation T is a coordinate-changing machine: p = T(p) What does it mean that T is global? Is the same for an point p can be described b just a few numbers (parameters) Let s represent T as a matri: p = Mp ' ' M
48 Scaling Scaling a coordinate means multipling each of its components b a scalar Uniform scaling means this scalar is the same for all components: 2
49 Scaling Non-uniform scaling: different scalars per component: X 2, Y.5
50 Scaling Scaling operation: Or, in matri form: b a ' ' b a ' ' scaling matri S What s inverse of S?
51 2-D Rotation (, ) (, ) = cos() - sin() = sin() + cos()
52 2-D Rotation This is eas to capture in matri form: ' ' cos sin sin R cos Even though sin() and cos() are nonlinear functions of, is a linear combination of and is a linear combination of and What is the inverse transformation? Rotation b For rotation matrices T R R
53 22 Matrices What tpes of transformations can be represented with a 22 matri? 2D Identit? ' ' ' ' 2D Scale around (,)? s s * ' * ' s s ' '
54 22 Matrices What tpes of transformations can be represented with a 22 matri? 2D Rotate around (,)? * cos * sin ' * sin * cos ' cos sin sin cos ' ' 2D Shear? sh sh * ' * ' sh sh ' '
55 22 Matrices What tpes of transformations can be represented with a 22 matri? 2D Mirror about Y ais? ' ' ' ' 2D Mirror over (,)? ' ' ' '
56 22 Matrices What tpes of transformations can be represented with a 22 matri? 2D Translation? ' t ' t NO! Onl linear 2D transformations can be represented with a 22 matri
57 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 ' ' a c be d g a c b d f i h k j l
58 Homogeneous Coordinates Q: How can we represent translation as a 33 matri? ' t ' t
59 Homogeneous Coordinates Homogeneous coordinates represent coordinates in 2 dimensions with a 3-vector
60 Homogeneous Coordinates Q: How can we represent translation as a 33 matri? A: Using the rightmost column: t t Translation t t ' '
61 Translation Eample of translation ' ' t t t t t = 2 t = Homogeneous Coordinates
62 Homogeneous Coordinates Add a 3rd coordinate to ever 2D point (,, w) represents a point at location (/w, /w) (,, ) represents a point at infinit (,, ) is not allowed 2 (2,,) or (4,2,2) or (6,3,3) Convenient coordinate sstem to represent man useful transformations 2
63 Basic 2D Transformations Basic 2D transformations as 33 matrices cos sin sin cos ' ' ' ' t t ' ' sh sh Translate Rotate Shear ' ' s s Scale
64 Affine Transformations Affine transformations are combinations of Linear transformations, and Translations Properties of affine transformations: Origin does not necessaril map to origin Lines map to lines Parallel lines remain parallel Ratios are preserved Closed under composition w f e d c b a w ' '
65 Projective Transformations Projective transformations Affine transformations, and Projective warps Properties of projective transformations: Origin does not necessaril map to origin Lines map to lines Parallel lines do not necessaril remain parallel Ratios are not preserved Closed under composition w i h g f e d c b a w ' ' '
66 Matri Composition Transformations can be combined b matri multiplication w s s t t w cos sin sin cos ' ' ' p = T(t,t ) R() S(s,s ) p
67 2D image transformations These transformations are a nested set of groups Closed under composition and inverse is a member
68 Recovering Transformations? T(,) f(,) g(, ) What if we know f and g and want to recover the transform T? Using correspondences How man do we need?
69 Translation: # correspondences? How man correspondences needed for translation? How man Degrees of Freedom? What is the transformation matri? T(,)? ' ' p p p p M
70 Euclidian: # correspondences?? T(,) How man correspondences needed for translation+rotation? How man DOF?
71 Affine: # correspondences?? T(,) How man correspondences needed for affine? How man DOF?
72 Projective: # correspondences?? T(,) How man correspondences needed for projective? How man DOF?
73 Eample: warping triangles Given two triangles: ABC and A B C in 2D (2 numbers) Need to find transform T to transfer all piels from one to the other. What kind of transformation is T? How can we compute the transformation matri: T(,)? A B C A C B Source Destination ' ' f e d c b a
74 warping triangles (Barcentric Coordinaes) (,) A B Source T (,) (,) Inverse change of basis change of basis C A T 2 B Destination Don t forget to move the origin too! C Ver useful in Graphics
75 Image morphing The goal is to snthesize a fluid transformation from one image to another. Cross dissolving is a common transition between cuts, but it is not good for morphing because of the ghosting effects. image # dissolving image #2
76 Image morphing Wh ghosting? Morphing = warping + cross-dissolving shape (geometric) color (photometric)
77 Image morphing image # cross-dissolving image #2 warp morphing warp
78 Morphing sequence
79 Warp b triangulation
80 Image warping T(,) f(,) g(, ) Given a coordinate transform (, ) = T(,) and a source image f(,), how do we compute a transformed image g(, ) = f(t(,))?
81 Forward warping T(,) f(,) g(, ) Send each piel f(,) to its corresponding location (, ) = T(,) in the second image Q: what if piel lands between two piels?
82 Forward warping T(,) f(,) g(, ) Send each piel f(,) to its corresponding location (, ) = T(,) in the second image Q: what if piel lands between two piels? A: distribute color among neighboring piels (, ) Known as splatting
83 Inverse warping T - (,) f(,) g(, ) Get each piel g(, ) from its corresponding location (,) = T - (, ) in the first image Q: what if piel comes from between two piels?
84 Inverse warping T - (,) f(,) g(, ) Get each piel g(, ) from its corresponding location (,) = T - (, ) in the first image Q: what if piel comes from between two piels? A: Interpolate color value from neighbors nearest neighbor, bilinear, Gaussian, bicubic
How is project #1 going?
How is project # going? Last Lecture Edge Detection Filtering Pramid Toda Motion Deblur Image Transformation Removing Camera Shake from a Single Photograph Rob Fergus, Barun Singh, Aaron Hertzmann, Sam
More informationImage Warping CSE399b, Spring 07 Computer Vision
Image Warping CSE399b, Spring 7 Computer Vision http://maps.a9.com http://www.cs.ubc.ca/~mbrown/autostitch/autostitch.html http://www.cs.ubc.ca/~mbrown/autostitch/autostitch.html Autostiching on A9.com
More informationImage warping. image filtering: change range of image. image warping: change domain of image g(x) = f(h(x)) h(y)=0.5y+0.5. h([x,y])=[x,y/2] f h
Image warping Image warping image filtering: change range of image g() () = h(f()) h(f()) f h g h()=0.5+0.5 image warping: change domain of image g() = f(h()) f h g h([,])=[,/2] Parametric (global) warping
More informationImage Warping. Some slides from Steve Seitz
Image Warping http://www.jeffre-martin.com Some slides from Steve Seitz 5-463: Computational Photograph Aleei Efros, CMU, Spring 2 Image Transformations image filtering: change range of image g() = T(f())
More informationImage Warping. Computational Photography Derek Hoiem, University of Illinois 09/28/17. Photo by Sean Carroll
Image Warping 9/28/7 Man slides from Alosha Efros + Steve Seitz Computational Photograph Derek Hoiem, Universit of Illinois Photo b Sean Carroll Reminder: Proj 2 due monda Much more difficult than project
More informationImage Warping. Some slides from Steve Seitz
Image Warping http://www.jeffre-martin.com Some slides from Steve Seitz 5-463: Computational Photograph Aleei Efros, CMU, Fall 26 Image Warping image filtering: change range of image g() T(f()) f T f image
More informationImage Warping, mesh, and triangulation CSE399b, Spring 07 Computer Vision
http://grail.cs.washington.edu/projects/rotoscoping/ Image Warping, mesh, and triangulation CSE399b, Spring 7 Computer Vision Man of the slides from A. Efros. Parametric (global) warping Eamples of parametric
More informationImage Warping : Computational Photography Alexei Efros, CMU, Fall Some slides from Steve Seitz
Image Warping http://www.jeffre-martin.com Some slides from Steve Seitz 5-463: Computational Photograph Aleei Efros, CMU, Fall 2 Image Transformations image filtering: change range of image g() T(f())
More informationInteractive Computer Graphics. Warping and morphing. Warping and Morphing. Warping and Morphing. Lecture 14+15: Warping and Morphing. What is.
Interactive Computer Graphics Warping and morphing Lecture 14+15: Warping and Morphing Lecture 14: Warping and Morphing: Slide 1 Lecture 14: Warping and Morphing: Slide 2 Warping and Morphing What is Warping
More informationImage Warping (Szeliski Sec 2.1.2)
Image Warping (Szeliski Sec 2..2) http://www.jeffre-martin.com CS94: Image Manipulation & Computational Photograph Aleei Efros, UC Berkele, Fall 7 Some slides from Steve Seitz Image Transformations image
More informationImage Warping. Many slides from Alyosha Efros + Steve Seitz. Photo by Sean Carroll
Image Warping Man slides from Alosha Efros + Steve Seitz Photo b Sean Carroll Morphing Blend from one object to other with a series of local transformations Image Transformations image filtering: change
More informationWarping, Morphing and Mosaics
Computational Photograph and Video: Warping, Morphing and Mosaics Prof. Marc Pollefes Dr. Gabriel Brostow Toda s schedule Last week s recap Warping Morphing Mosaics Toda s schedule Last week s recap Warping
More informationProf. Feng Liu. Winter /05/2019
Prof. Feng Liu Winter 2019 http://www.cs.pd.edu/~fliu/courses/cs410/ 02/05/2019 Last Time Image alignment 2 Toda Image warping The slides for this topic are used from Prof. Yung-Yu Chuang, which use materials
More informationImage warping/morphing
Image warping/morphing Digital Visual Effects, Spring 2007 Yung-Yu Chuang 2007/3/20 with slides b Richard Szeliski, Steve Seitz, Tom Funkhouser and Aleei Efros Image warping Image formation B A Sampling
More informationCSE328 Fundamentals of Computer Graphics: Theory, Algorithms, and Applications
CSE328 Fundamentals of Computer Graphics: Theor, Algorithms, and Applications Hong in State Universit of New York at Ston Brook (Ston Brook Universit) Ston Brook, New York 794-44 Tel: (63)632-845; Fa:
More informationWarping. 12 May 2015
Warping 12 May 2015 Warping, morphing, mosaic Slides from Durand and Freeman (MIT), Efros (CMU, Berkeley), Szeliski (MSR), Seitz (UW), Lowe (UBC) http://szeliski.org/book/ 2 Image Warping Image filtering:
More informationCS4670: Computer Vision
CS467: Computer Vision Noah Snavely Lecture 8: Geometric transformations Szeliski: Chapter 3.6 Reading Announcements Project 2 out today, due Oct. 4 (demo at end of class today) Image alignment Why don
More informationCS 2770: Intro to Computer Vision. Multiple Views. Prof. Adriana Kovashka University of Pittsburgh March 14, 2017
CS 277: Intro to Computer Vision Multiple Views Prof. Adriana Kovashka Universit of Pittsburgh March 4, 27 Plan for toda Affine and projective image transformations Homographies and image mosaics Stereo
More informationModeling Transformations
Transformations Transformations Specif transformations for objects o Allos definitions of objects in on coordinate sstems o Allos use of object definition multiple times in a scene Adam Finkelstein Princeton
More informationModeling Transformations
Modeling Transformations Thomas Funkhouser Princeton Universit CS 426, Fall 2 Modeling Transformations Specif transformations for objects Allos definitions of objects in on coordinate sstems Allos use
More informationModeling Transformations
Modeling Transformations Michael Kazhdan (601.457/657) HB Ch. 5 FvDFH Ch. 5 Overview Ra-Tracing so far Modeling transformations Ra Tracing Image RaTrace(Camera camera, Scene scene, int width, int heigh,
More informationScene Graphs & Modeling Transformations COS 426
Scene Graphs & Modeling Transformations COS 426 3D Object Representations Points Range image Point cloud Surfaces Polgonal mesh Subdivision Parametric Implicit Solids Voels BSP tree CSG Sweep High-level
More informationDetermining the 2d transformation that brings one image into alignment (registers it) with another. And
Last two lectures: Representing an image as a weighted combination of other images. Toda: A different kind of coordinate sstem change. Solving the biggest problem in using eigenfaces? Toda Recognition
More informationModeling Transformations
שיעור 3 גרפיקה ממוחשבת תשס"ח ב ליאור שפירא Modeling Transformations Heavil based on: Thomas Funkhouser Princeton Universit CS 426, Fall 2 Modeling Transformations Specif transformations for objects Allows
More informationImage Warping and Morphing. Alexey Tikhonov
Image Warping and Morphing Alexey Tikhonov CS194: Image Manipulation & Computational Photography Alexei Efros, UC Berkeley, Fall 2016 Women in Art video http://youtube.com/watch?v=nudion-_hxs Image Warping
More informationPhoto by Carl Warner
Photo b Carl Warner Photo b Carl Warner Photo b Carl Warner Fitting and Alignment Szeliski 6. Computer Vision CS 43, Brown James Has Acknowledgment: Man slides from Derek Hoiem and Grauman&Leibe 2008 AAAI
More informationImage Warping and Morphing. Alexey Tikhonov : Computational Photography Alexei Efros, CMU, Fall 2007
Image Warping and Morphing Alexey Tikhonov 15-463: Computational Photography Alexei Efros, CMU, Fall 2007 Image Warping in Biology D'Arcy Thompson http://www-groups.dcs.st-and.ac.uk/~history/miscellaneous/darcy.html
More informationImage Warping and Morphing. Alexey Tikhonov
Image Warping and Morphing Alexey Tikhonov CS194: Image Manipulation & Computational Photography Alexei Efros, UC Berkeley, Fall 2017 Women in Art video http://youtube.com/watch?v=nudion-_hxs Image Warping
More informationModeling Transformations
Modeling Transformations Michael Kazhdan (601.457/657) HB Ch. 5 FvDFH Ch. 5 Announcement Assignment 2 has been posted: Due: 10/24 ASAP: Download the code and make sure it compiles» On windows: just build
More informationImage warping/morphing
Image warping/morphing Digital Visual Effects Yung-Yu Chuang with slides by Richard Szeliski, Steve Seitz, Tom Funkhouser and Alexei Efros Image warping Image formation B A Sampling and quantization What
More informationGeometric Image Transformations and Related Topics
Geometric Image Transformations and Related Topics 9 th Lesson on Image Processing Martina Mudrová 2004 Topics What will be the topic of the following lesson? Geometric image transformations Interpolation
More informationCS 335 Graphics and Multimedia. Geometric Warping
CS 335 Graphics and Multimedia Geometric Warping Geometric Image Operations Eample transformations Straightforward methods and their problems The affine transformation Transformation algorithms: Forward
More informationComputer Graphics. P04 Transformations. Aleksandra Pizurica Ghent University
Computer Graphics P4 Transformations Aleksandra Pizurica Ghent Universit Telecommunications and Information Processing Image Processing and Interpretation Group Transformations in computer graphics Goal:
More informationImage Metamorphosis By Affine Transformations
Image Metamorphosis B Affine Transformations Tim Mers and Peter Spiegel December 16, 2005 Abstract Among the man was to manipulate an image is a technique known as morphing. Image morphing is a special
More informationImage Transformations
Image Transformations Outline Gre-level transformations Histogram equalization Geometric transformations Affine transformations Interpolation Warping and morphing. Gre-level transformations Changes the
More informationFitting a transformation: Feature-based alignment April 30 th, Yong Jae Lee UC Davis
Fitting a transformation: Feature-based alignment April 3 th, 25 Yong Jae Lee UC Davis Announcements PS2 out toda; due 5/5 Frida at :59 pm Color quantization with k-means Circle detection with the Hough
More informationMulti-stable Perception. Necker Cube
Multi-stable Perception Necker Cube Spinning dancer illusion, Nobuuki Kaahara Fitting and Alignment Computer Vision Szeliski 6.1 James Has Acknowledgment: Man slides from Derek Hoiem, Lana Lazebnik, and
More informationComputer Graphics. Geometric Transformations
Contents coordinate sstems scalar values, points, vectors, matrices right-handed and left-handed coordinate sstems mathematical foundations transformations mathematical descriptions of geometric changes,
More informationComputer Graphics. Geometric Transformations
Computer Graphics Geometric Transformations Contents coordinate sstems scalar values, points, vectors, matrices right-handed and left-handed coordinate sstems mathematical foundations transformations mathematical
More information3D Geometry and Camera Calibration
3D Geometr and Camera Calibration 3D Coordinate Sstems Right-handed vs. left-handed 2D Coordinate Sstems ais up vs. ais down Origin at center vs. corner Will often write (u, v) for image coordinates v
More information3-Dimensional Viewing
CHAPTER 6 3-Dimensional Vieing Vieing and projection Objects in orld coordinates are projected on to the vie plane, hich is defined perpendicular to the vieing direction along the v -ais. The to main tpes
More informationLimitations of Thresholding
Limitations of Thresholding Wh can we segment images much better b ee than through thresholding processes? We might improve results b considering image contet: Surface Coherence Gradient.illusion.arp.jpg
More informationEditing and Transformation
Lecture 5 Editing and Transformation Modeling Model can be produced b the combination of entities that have been edited. D: circle, arc, line, ellipse 3D: primitive bodies, etrusion and revolved of a profile
More informationCS4670: Computer Vision
CS4670: Computer Vision Noah Snavely Lecture 9: Image alignment http://www.wired.com/gadgetlab/2010/07/camera-software-lets-you-see-into-the-past/ Szeliski: Chapter 6.1 Reading All 2D Linear Transformations
More informationBroad field that includes low-level operations as well as complex high-level algorithms
Image processing About Broad field that includes low-level operations as well as complex high-level algorithms Low-level image processing Computer vision Computational photography Several procedures and
More informationImage warping , , Computational Photography Fall 2017, Lecture 10
Image warping http://graphics.cs.cmu.edu/courses/15-463 15-463, 15-663, 15-862 Computational Photography Fall 2017, Lecture 10 Course announcements Second make-up lecture on Friday, October 6 th, noon-1:30
More informationMAN-522: COMPUTER VISION SET-2 Projections and Camera Calibration
MAN-522: COMPUTER VISION SET-2 Projections and Camera Calibration Image formation How are objects in the world captured in an image? Phsical parameters of image formation Geometric Tpe of projection Camera
More informationAffine and Projective Transformations
CS 674: Intro to Computer Vision Affine and Projective Transformations Prof. Adriana Kovaska Universit of Pittsburg October 3, 26 Alignment problem We previousl discussed ow to matc features across images,
More informationTransformations II. Week 2, Wed Jan 17
Universit of British Columbia CPSC 34 Computer Graphics Jan-Apr 27 Tamara Munzner Transformations II Week 2, Wed Jan 7 http://www.ugrad.cs.ubc.ca/~cs34/vjan27 Readings for Jan 5-22 FCG Chap 6 Transformation
More informationEECS 556 Image Processing W 09. Interpolation. Interpolation techniques B splines
EECS 556 Image Processing W 09 Interpolation Interpolation techniques B splines What is image processing? Image processing is the application of 2D signal processing methods to images Image representation
More informationComputer Vision Lecture 20
Computer Vision Lecture 2 Motion and Optical Flow Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de 28.1.216 Man slides adapted from K. Grauman, S. Seitz, R. Szeliski,
More informationPerspective Projection Transformation
Perspective Projection Transformation Where does a point of a scene appear in an image?? p p Transformation in 3 steps:. scene coordinates => camera coordinates. projection of camera coordinates into image
More informationThe 3-D Graphics Rendering Pipeline
The 3-D Graphics Rendering Pipeline Modeling Trival Rejection Illumination Viewing Clipping Projection Almost ever discussion of 3-D graphics begins here Seldom are an two versions drawn the same wa Seldom
More informationScale Invariant Feature Transform (SIFT) CS 763 Ajit Rajwade
Scale Invariant Feature Transform (SIFT) CS 763 Ajit Rajwade What is SIFT? It is a technique for detecting salient stable feature points in an image. For ever such point it also provides a set of features
More informationIntroduction to Computer Vision
Introduction to Computer Vision Michael J. Black Oct 2009 Motion estimation Goals Motion estimation Affine flow Optimization Large motions Why affine? Monday dense, smooth motion and regularization. Robust
More informationLast Time. Correct Transparent Shadow. Does Ray Tracing Simulate Physics? Does Ray Tracing Simulate Physics? Refraction and the Lifeguard Problem
Graphics Pipeline: Projective Last Time Shadows cast ra to light stop after first intersection Reflection & Refraction compute direction of recursive ra Recursive Ra Tracing maimum number of bounces OR
More informationGeometric Model of Camera
Geometric Model of Camera Dr. Gerhard Roth COMP 42A Winter 25 Version 2 Similar Triangles 2 Geometric Model of Camera Perspective projection P(X,Y,Z) p(,) f X Z f Y Z 3 Parallel lines aren t 4 Figure b
More informationM y. Image Warping. Targil 7 : Image Warping. Image Warping. 2D Geometric Transformations. image filtering: change range of image g(x) = T(f(x))
Hebrew Universi Image Processing - 6 Image Warping Hebrew Universi Image Processing - 6 argil 7 : Image Warping D Geomeric ransormaions hp://www.jere-marin.com Man slides rom Seve Seiz and Aleei Eros Image
More informationCS4670: Computer Vision
CS4670: Computer Vision Noah Snavely Lecture 34: Segmentation From Sandlot Science Announcements In-class exam this Friday, December 3 Review session in class on Wednesday Final projects: Slides due: Sunday,
More informationEpipolar Constraint. Epipolar Lines. Epipolar Geometry. Another look (with math).
Epipolar Constraint Epipolar Lines Potential 3d points Red point - fied => Blue point lies on a line There are 3 degrees of freedom in the position of a point in space; there are four DOF for image points
More informationMotion estimation. Lihi Zelnik-Manor
Motion estimation Lihi Zelnik-Manor Optical Flow Where did each piel in image 1 go to in image 2 Optical Flow Pierre Kornprobst's Demo ntroduction Given a video sequence with camera/objects moving we can
More informationAnnouncements. Equation of Perspective Projection. Image Formation and Cameras
Announcements Image ormation and Cameras Introduction to Computer Vision CSE 52 Lecture 4 Read Trucco & Verri: pp. 22-4 Irfanview: http://www.irfanview.com/ is a good Windows utilit for manipulating images.
More informationOptical flow. Cordelia Schmid
Optical flow Cordelia Schmid Motion field The motion field is the projection of the 3D scene motion into the image Optical flow Definition: optical flow is the apparent motion of brightness patterns in
More information2D Image Transforms Computer Vision (Kris Kitani) Carnegie Mellon University
2D Image Transforms 16-385 Computer Vision (Kris Kitani) Carnegie Mellon University Extract features from an image what do we do next? Feature matching (object recognition, 3D reconstruction, augmented
More informationModeling Transformations Revisited
Modeling Transformations Revisited Basic 3D Transformations Translation Scale Shear Rotation 3D Transformations Same idea as 2D transformations o Homogeneous coordinates: (,,z,w) o 44 transformation matrices
More informationEE795: Computer Vision and Intelligent Systems
EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 10 130221 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Canny Edge Detector Hough Transform Feature-Based
More informationComputer Graphics. Si Lu. Fall er_graphics.htm 10/11/2017
Computer Graphics Si Lu Fall 27 http://www.cs.pd.edu/~lusi/cs447/cs447_547_comput er_graphics.htm //27 Last time Filtering Resampling 2 Toda Compositing NPR 3D Graphics Toolkits Transformations 3 Demo
More informationGeneral Purpose Computation (CAD/CAM/CAE) on the GPU (a.k.a. Topics in Manufacturing)
ME 29-R: General Purpose Computation (CAD/CAM/CAE) on the GPU (a.k.a. Topics in Manufacturing) Sara McMains Spring 29 lecture 2 Toda s GPU eample: moldabilit feedback Two-part mold [The Complete Sculptor
More informationCSE528 Computer Graphics: Theory, Algorithms, and Applications
CSE528 Computer Graphics: Theor, Algorithms, and Applications Hong Qin State Universit of New York at Ston Brook (Ston Brook Universit) Ston Brook, New York 794--44 Tel: (63)632-845; Fa: (63)632-8334 qin@cs.sunsb.edu
More informationImage Alignment AJIT RAJWADE
Image Alignment AJIT RAJWADE Basics A digital image a discrete/sampled version of a visual stimulus Can be regarded as a function I = f(,) where (,) are spatial (integer) coordinates in a domain W = [0,-]
More informationCamera Calibration. Schedule. Jesus J Caban. Note: You have until next Monday to let me know. ! Today:! Camera calibration
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
More informationHomogeneous Coordinates
COMS W4172 3D Math 2 Steven Feiner Department of Computer Science Columbia Universit New York, NY 127 www.cs.columbia.edu/graphics/courses/csw4172 Februar 1, 218 1 Homogeneous Coordinates w X W Y X W Y
More informationLinear Algebra and Image Processing: Additional Theory regarding Computer Graphics and Image Processing not covered by David C.
Linear Algebra and Image Processing: Additional Theor regarding Computer Graphics and Image Processing not covered b David C. La Dr. D.P. Huijsmans LIACS, Leiden Universit Februar 202 Differences in conventions
More informationIMAGE DENOISING TO ESTIMATE THE GRADIENT HISTOGRAM PRESERVATION USING VARIOUS ALGORITHMS
IMAGE DENOISING TO ESTIMATE THE GRADIENT HISTOGRAM PRESERVATION USING VARIOUS ALGORITHMS P.Mahalakshmi 1, J.Muthulakshmi 2, S.Kannadhasan 3 1,2 U.G Student, 3 Assistant Professor, Department of Electronics
More informationWhat and Why Transformations?
2D transformations What and Wh Transformations? What? : The geometrical changes of an object from a current state to modified state. Changing an object s position (translation), orientation (rotation)
More informationImage Warping and Mosacing
Image Warping and Mosacing 15-463: 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 informationProf. Feng Liu. Fall /25/2018
Prof. Feng Liu Fall 08 http://www.cs.pd.edu/~fliu/courses/cs7/ 0/5/08 Last time Clipping Toda Rasterization In-class Mid-term November Close-book eam Notes on page of A or Letter size paper Where We Stand
More informationMore on Transformations. COS 426, Spring 2019 Princeton University
More on Transformations COS 426, Spring 2019 Princeton Universit Agenda Grab-bag of topics related to transformations: General rotations! Euler angles! Rodrigues s rotation formula Maintaining camera transformations!
More informationComputer Graphics. 2D transformations. Transforma3ons in computer graphics. Overview. Basic classes of geometric transforma3ons
Transforma3ons in computer graphics omputer Graphics Transforma3ons leksandra Piurica Goal: introduce methodolog to hange coordinate sstem Move and deform objects Principle: transforma3ons are applied
More informationComputing F class 13. Multiple View Geometry. Comp Marc Pollefeys
Computing F class 3 Multiple View Geometr Comp 90-089 Marc Pollefes Multiple View Geometr course schedule (subject to change) Jan. 7, 9 Intro & motivation Projective D Geometr Jan. 4, 6 (no class) Projective
More informationProjections. Brian Curless CSE 457 Spring Reading. Shrinking the pinhole. The pinhole camera. Required:
Reading Required: Projections Brian Curless CSE 457 Spring 2013 Angel, 5.1-5.6 Further reading: Fole, et al, Chapter 5.6 and Chapter 6 David F. Rogers and J. Alan Adams, Mathematical Elements for Computer
More informationStereo Matching! Christian Unger 1,2, Nassir Navab 1!! Computer Aided Medical Procedures (CAMP), Technische Universität München, Germany!!
Stereo Matching Christian Unger 12 Nassir Navab 1 1 Computer Aided Medical Procedures CAMP) Technische Universität München German 2 BMW Group München German Hardware Architectures. Microprocessors Pros:
More informationCS770/870 Spring 2017 Transformations
CS770/870 Spring 2017 Transformations Coordinate sstems 2D Transformations Homogeneous coordinates Matrices, vectors, points Coordinate Sstems Coordinate sstems used in graphics Screen coordinates: the
More information(x, y) (ρ, θ) ρ θ. Polar Coordinates. Cartesian Coordinates
Coordinate Sstems Point Representation in two dimensions Cartesian Coordinates: (; ) Polar Coordinates: (; ) (, ) ρ θ (ρ, θ) Cartesian Coordinates Polar Coordinates p = CPS1, 9: Computer Graphics D Geometric
More informationCS559: Computer Graphics
CS559: Computer Graphics Lecture 8: 3D Transforms Li Zhang Spring 28 Most Slides from Stephen Chenne Finish Color space Toda 3D Transforms and Coordinate sstem Reading: Shirle ch 6 RGB and HSV Green(,,)
More informationAnnouncements. Recognition I. Optical Flow: Where do pixels move to? dy dt. I + y. I = x. di dt. dx dt. = t
Announcements I Introduction to Computer Vision CSE 152 Lecture 18 Assignment 4: Due Toda Assignment 5: Posted toda Read: Trucco & Verri, Chapter 10 on recognition Final Eam: Wed, 6/9/04, 11:30-2:30, WLH
More informationEECS 556 Image Processing W 09
EECS 556 Image Processing W 09 Motion estimation Global vs. Local Motion Block Motion Estimation Optical Flow Estimation (normal equation) Man slides of this lecture are courtes of prof Milanfar (UCSC)
More informationLecture 7: Image Morphing. Idea #2: Align, then cross-disolve. Dog Averaging. Averaging vectors. Idea #1: Cross-Dissolving / Cross-fading
Lecture 7: Image Morphing Averaging vectors v = p + α (q p) = (1 - α) p + α q where α = q - v p α v (1-α) q p and q can be anything: points on a plane (2D) or in space (3D) Colors in RGB or HSV (3D) Whole
More informationUses of Transformations. 2D transformations Homogeneous coordinates. Transformations. Transformations. Transformations. Transformations and matrices
Uses of Transformations 2D transformations Homogeneous coordinates odeling: position and resie parts of a comple model; Viewing: define and position the virtual camera Animation: define how objects move/change
More informationGLOBAL EDITION. Interactive Computer Graphics. A Top-Down Approach with WebGL SEVENTH EDITION. Edward Angel Dave Shreiner
GLOBAL EDITION Interactive Computer Graphics A Top-Down Approach with WebGL SEVENTH EDITION Edward Angel Dave Shreiner This page is intentionall left blank. 4.10 Concatenation of Transformations 219 in
More informationTransformations. Examples of transformations: shear. scaling
Transformations Eamples of transformations: translation rotation scaling shear Transformations More eamples: reflection with respect to the y-ais reflection with respect to the origin Transformations Linear
More informationCS 558: Computer Vision 3 rd Set of Notes
1 CS 558: Computer Vision 3 rd Set of Notes Instructor: Philippos Mordohai Webpage: www.cs.stevens.edu/~mordohai E-mail: Philippos.Mordohai@stevens.edu Office: Lieb 215 Overview Denoising Based on slides
More information3D Computer Vision II. Reminder Projective Geometry, Transformations. Nassir Navab. October 27, 2009
3D Computer Vision II Reminder Projective Geometr, Transformations Nassir Navab based on a course given at UNC b Marc Pollefes & the book Multiple View Geometr b Hartle & Zisserman October 27, 29 2D Transformations
More informationCS231M Mobile Computer Vision Structure from motion
CS231M Mobile Computer Vision Structure from motion - Cameras - Epipolar geometry - Structure from motion Pinhole camera Pinhole perspective projection f o f = focal length o = center of the camera z y
More informationMidterm Wed. Local features: detection and description. Today. Last time. Local features: main components. Goal: interest operator repeatability
Midterm Wed. Local features: detection and description Monday March 7 Prof. UT Austin Covers material up until 3/1 Solutions to practice eam handed out today Bring a 8.5 11 sheet of notes if you want Review
More information1. We ll look at: Types of geometrical transformation. Vector and matrix representations
Tob Howard COMP272 Computer Graphics and Image Processing 3: Transformations Tob.Howard@manchester.ac.uk Introduction We ll look at: Tpes of geometrical transformation Vector and matri representations
More informationMotivation. What we ve seen so far. Demo (Projection Tutorial) Outline. Projections. Foundations of Computer Graphics
Foundations of Computer Graphics Online Lecture 5: Viewing Orthographic Projection Ravi Ramamoorthi Motivation We have seen transforms (between coord sstems) But all that is in 3D We still need to make
More informationCAP5415-Computer Vision Lecture 8-Mo8on Models, Feature Tracking, and Alignment. Ulas Bagci
CAP545-Computer Vision Lecture 8-Mo8on Models, Feature Tracking, and Alignment Ulas Bagci bagci@ucf.edu Readings Szeliski, R. Ch. 7 Bergen et al. ECCV 92, pp. 237-252. Shi, J. and Tomasi, C. CVPR 94, pp.593-6.
More informationWarps, Filters, and Morph Interpolation
Warps, Filters, and Morph Interpolation Material in this presentation is largely based on/derived from slides originally by Szeliski, Seitz and Efros Brent M. Dingle, Ph.D. 2015 Game Design and Development
More informationComputer Vision Lecture 18
Course Outline Computer Vision Lecture 8 Motion and Optical Flow.0.009 Bastian Leibe RWTH Aachen http://www.umic.rwth-aachen.de/multimedia leibe@umic.rwth-aachen.de Man slides adapted from K. Grauman,
More information