COMPUTER VISION > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE

Size: px
Start display at page:

Download "COMPUTER VISION > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE"

Transcription

1 COMPUTER VISION > OPTICAL FLOW UTRECHT UNIVERSITY RONALD POPPE

2 OUTLINE Optical flow Lucas-Kanade Horn-Schunck Applications of optical flow Optical flow tracking Histograms of oriented flow Assignment

3 OPTICAL FLOW

4 OPTICAL FLOW The process of estimating the motion field (the trajectory of points) from time-varying image intensity (video) Or: mapping pixels from one frame to another

5 OPTICAL FLOW 2 For each pixel, we want to know its location in the next frame Can be described as a vector: Length (amount of movement) Direction of movement Can be color-coded

6 OPTICAL FLOW 3 Example: motion in video (Brox et al., PAMI 2011)

7 OPTICAL FLOW 4 Example: motion in video (Brox et al., PAMI 2011)

8 OPTICAL FLOW 5 Example: motion in video (Brox et al., PAMI 2011)

9 OPTICAL FLOW 6 Optical flow is due to: Object motion Camera motion Variations in intensity

10 APPLICATIONS Tracking Estimate depth from flow Background subtraction Object detection Image stabilization Activity recognition

11 BASIC IDEA For now, we assume two subsequent frames in a video Basic idea: For each pixel, determine where it is in the next frame We call this dense optical flow Can be done: Lucas-Kanade Horn-Schunck Both based on the same principle

12 ASSUMPTION Formally: (x, y, t) is a pixel (x, y) at time t f(x, y, t) the pixel value (intensity) When analyzing image motion, we use an important assumption based on object appearance: The intensity of the pixel under motion does not change Brightness constancy assumption (BCA) f(x + dx, y + dy, t + dt) = f(x, y, t)

13 ASSUMPTION 2 An image is a 2D projection of a 3D scene! The intensity-constant assumption is typically true for: Short-time movement Movement paralel to the image plane (in-plane or 2D motion) But less so for: Out-of-plane movement (out-of-plane rotation) At depth borders Occlusions Discontinuities at the boundaries!

14 ASSUMPTION 3 Example video: Garden sequence

15 ASSUMPTION4

16 FORMULATION Consider a pixel (x,y) at time t with intensity f(x, y, t) At t+dt, the pixel has moved with (dx,dy): (x+dx, y+dy, t+dt) We use u and v to denote dx/dt and dy/dt We are interested in finding the (u,v) for each pixel Vector (u,v) is the apparent 2D motion of the pixel (optical flow) To find the optical flow for an image, we need to find the most likely values of (u,v) for each pixel

17 FORMULATION 2 Question: what are the (u,v) vectors to go from: Frame 1 to frame 2 Answer: (2, 0) Frame 2 to frame 3 Answer: (1, 1)

18 FORMULATION 3 Example: J(x,y) = I(x + u(x, y), y + v(x, y)) I(1, 3) = 9 u(1, 3) = 3, v(1, 3) = 0 J(1, 3) = I(1 + u(1, 3), 3 + v(1, 3)) = I(4, 3) = 12

19 FORMULATION 4 Intensity-assumption: f(x, y, t) = f(x + dx, y + dy, t + dt) For a constant intensity (pixel does not change value): = (,, ) = 0 We will use Taylor series expansion: + = Same for y and t

20 FORMULATION 5 With Taylor expansion (only 1 st derivative), this becomes: +, =,, And its derivative to t: + + = 0 Substituting with u and v: =, = + + = 0

21 FORMULATION 6 Again: + + = 0 For convenience, we write: =, = and = So: + = f x and f y can be measured from the image they are the gradients in x- and y-direction! Apply derivative masks to first and second frame: x: , y: , t (1st ): , (2nd ) (Roberts)

22 ERROR FUNCTION We have to estimate (u,v) for each pixel How to know what a good estimate is? Remember the intensity-constancy assumption: Pixels are not supposed to change in intensity The cost of moving a pixel to a new location is the difference in intensity:, = + +

23 ISSUE For each pixel, we have equation + = Optical flow: u and v need to be estimated Two unknowns, one equation problem!

24 ISSUE2

25 ISSUE3

26 ISSUE4

27 ISSUE5

28 ISSUE6

29 ISSUE7

30 ISSUE8

31 ISSUE9

32 ISSUE10

33 ISSUE 11 Within the view, we cannot determine the movement

34 ISSUE12

35 ISSUE 13 Animations!

36 ISSUE 13 So we need more equations to estimate the optical flow (u,v) for each pixel Aperture problem when f x and/or f y are zero (edges and even areas) because of + = Ideally, we include a corner to be sure about the estimate Two options: Look at motion in small region: Lucas-Kanade Introduce additional constraints: Horn-Schunck

37 LUCAS-KANADE

38 LUCAS-KANADE Basic idea: Assume that neighboring pixels have same optical flow Consider a small window around a pixel More equations with the same two unknowns solvable! Formally: For each pixel i in window W, we have: + = Written in matrix form: = n: the number of pixels in the window (W=5x5 n=25)

39 LUCAS-KANADE 2 So we have a series of equations: = Over-complete system! Recall our error term:, = + + Adapted for windows:, = + + We want to find optical flow (u,v) for which the summed pixel intensity differences is smallest minimize the error

40 LUCAS-KANADE 3 We want to minimize this error:, = + + Typical solution: solve for u and v separately by setting their partial derivatives to zero Use chain rule ( = 2, = 2 ): (, ) = = 0 and (, ) = = 0 The 2 term can be dropped (it is a constant)

41 LUCAS-KANADE 4 We can write: + + = = 0 As: + = + = And in matrix form: =

42 LUCAS-KANADE 5 With the same analogy as: = = We can pre-multiply both sides of: = = with the inverse:, which gives us: =

43 LUCAS-KANADE 6 From: = Eventually, we can calculate the optical flow in both the u and v direction: = =

44 LUCAS-KANADE 7 We could also calculate this directly: = =, with = and = = ( ) ( ) is the pseudo-inverse Reworking the right-hand-side will result in the same equations

45 LUCAS-KANADE 8 Lucas-Kanade in practice uses small windows: 3x3 or 5x5 Cannot cope with larger movements (outside the window) For example: With a 5x5 window, u and v cannot be larger than 2 in any direction When the movement is larger, the results are unstable the best optical flow estimate is out of reach Solution: Use pyramids (recall SIFT lecture)

46 LUCAS-KANADE9

47 LUCAS-KANADE 10 Without pyramids: unstable results with larger motion

48 LUCAS-KANADE 11 Application of pyramids: resolution is much lower

49 LUCAS-KANADE 12 With pyramids: stable results with larger motion

50 LUCAS-KANADE 13 Some of the properties of Lucas-Kanade: Depends on image gradients (f x and f y ) For uniform colors f x =f y =0, optical flow is not defined Fast! Usually applied for each pixel: dense optical flow estimation Can also be applied only around corners (similar to SIFT) sparse result Noise has large effect on gradient, so also on optical flow estimation: Can be reduced by applying a Gaussian filter

51 QUESTIONS?

52 HORN-SCHUNCK

53 HORN-SCHUNCK Instead of using a window of pixels, Horn-Schunck optical flow estimation uses a smoothness constraint: Smaller values of u and v are favored over larger ones

54 HORN-SCHUNCK 2 Instead of using a window of pixels, Horn-Schunck optical flow estimation uses a smoothness constraint: Smaller values of u and v are favored over larger ones Original error function:, = + + Error function in Horn-Schunck:, = With the del operator: =,, (vector of partial derivatives to each variable)

55 HORN-SCHUNCK 3 Horn-Schunck error function:, = Intensity assumption Smoothness term Weighting factor Again, we want to minimize (u, v) to have the lowest error Intuitively, we are searching for (u, v) that: Follows the intensity assumption, and Minimizes the estimated motion Global estimation (hence the integrals)

56 HORN-SCHUNCK 4 Smoothness term: + = = + = 0 = = + = 0 The motion of neighboring pixels should be the same

57 HORN-SCHUNCK 5, = Using Euler-Lagrange equations, we obtain the following two equations to minimize: + + = = 0 Discrete case: = and = and are the average values of u and v

58 HORN-SCHUNCK 6 For the average intensity values, we look at the local neighborhood of a pixel: Apply a Laplacian filter Typically of limited size (3x3) or 0 0 0

59 HORN-SCHUNCK 7 Eventually, u and v become: = = With: = + + and = + +

60 HORN-SCHUNCK 8 The two equations: + + = = 0 Depend on initial values of u and v Estimated iteratively, with u = u k First set u 0 =v 0 =0 Then, set = and = Repeat algorithm until convergence (local minimum)

61 HORN-SCHUNCK 9 Properties of Horn-Schunck optical flow: Smooth flow (no jumps ) Global information, so larger motion possible Slow because of iterative nature Still: problems at the boundaries Also: might get stuck in local minimum

62 APPLICATIONS OF OPTICAL FLOW

63 OPTICAL FLOW TRACKING Given that we have an estimate of the movement of a pixel, or a small window (Lucas-Kanade), we can track this pixel Kanade-Lucas-Tomasi is a well-known tracker

64 KLT TRACKING KLT (Kanade-Lucas-Tomasi) tracking works by estimating the optical flow at certain points, from frame to frame: Typically, Harris corners are used Found on corners with strong gradient Comparable to interest points (remember from SIFT) KLT tracking is straightforward for translations of single points, more difficult for: More complex transformations (rotations, affine) Multiple points See links on website for further reading

65 KLT TRACKING Circles are tracked points

66 HISTOGRAMS OF ORIENTED FLOW We can calculate optical flow within a bounding box Often, specific movement in parts of the region is meaningful We can use the histogram of oriented gradients (HOG) concept Optical flow has a magnitude and orientation Bin flow instead of gradients

67 QUESTIONS?

68 ASSIGNMENT

69 ASSIGNMENT Assignment 3: Deadline is Tuesday March 6, 23:00 Assignment help session on Tuesday March 6, 13:15-15:00

70 NEXT LECTURE Next lecture: Training, classification, detection Tuesday March 8, 11:00-12:45, UNNIK-211

Visual Tracking (1) Feature Point Tracking and Block Matching

Visual Tracking (1) Feature Point Tracking and Block Matching Intelligent Control Systems Visual Tracking (1) Feature Point Tracking and Block Matching Shingo Kagami Graduate School of Information Sciences, Tohoku University swk(at)ic.is.tohoku.ac.jp http://www.ic.is.tohoku.ac.jp/ja/swk/

More information

Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects

Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects Intelligent Control Systems Visual Tracking (1) Tracking of Feature Points and Planar Rigid Objects Shingo Kagami Graduate School of Information Sciences, Tohoku University swk(at)ic.is.tohoku.ac.jp http://www.ic.is.tohoku.ac.jp/ja/swk/

More information

Feature Tracking and Optical Flow

Feature Tracking and Optical Flow Feature Tracking and Optical Flow Prof. D. Stricker Doz. G. Bleser Many slides adapted from James Hays, Derek Hoeim, Lana Lazebnik, Silvio Saverse, who in turn adapted slides from Steve Seitz, Rick Szeliski,

More information

Feature Tracking and Optical Flow

Feature Tracking and Optical Flow Feature Tracking and Optical Flow Prof. D. Stricker Doz. G. Bleser Many slides adapted from James Hays, Derek Hoeim, Lana Lazebnik, Silvio Saverse, who 1 in turn adapted slides from Steve Seitz, Rick Szeliski,

More information

Motion. 1 Introduction. 2 Optical Flow. Sohaib A Khan. 2.1 Brightness Constancy Equation

Motion. 1 Introduction. 2 Optical Flow. Sohaib A Khan. 2.1 Brightness Constancy Equation Motion Sohaib A Khan 1 Introduction So far, we have dealing with single images of a static scene taken by a fixed camera. Here we will deal with sequence of images taken at different time intervals. Motion

More information

CS 4495 Computer Vision Motion and Optic Flow

CS 4495 Computer Vision Motion and Optic Flow CS 4495 Computer Vision Aaron Bobick School of Interactive Computing Administrivia PS4 is out, due Sunday Oct 27 th. All relevant lectures posted Details about Problem Set: You may *not* use built in Harris

More information

Leow Wee Kheng CS4243 Computer Vision and Pattern Recognition. Motion Tracking. CS4243 Motion Tracking 1

Leow Wee Kheng CS4243 Computer Vision and Pattern Recognition. Motion Tracking. CS4243 Motion Tracking 1 Leow Wee Kheng CS4243 Computer Vision and Pattern Recognition Motion Tracking CS4243 Motion Tracking 1 Changes are everywhere! CS4243 Motion Tracking 2 Illumination change CS4243 Motion Tracking 3 Shape

More information

VC 11/12 T11 Optical Flow

VC 11/12 T11 Optical Flow VC 11/12 T11 Optical Flow Mestrado em Ciência de Computadores Mestrado Integrado em Engenharia de Redes e Sistemas Informáticos Miguel Tavares Coimbra Outline Optical Flow Constraint Equation Aperture

More information

CS 565 Computer Vision. Nazar Khan PUCIT Lectures 15 and 16: Optic Flow

CS 565 Computer Vision. Nazar Khan PUCIT Lectures 15 and 16: Optic Flow CS 565 Computer Vision Nazar Khan PUCIT Lectures 15 and 16: Optic Flow Introduction Basic Problem given: image sequence f(x, y, z), where (x, y) specifies the location and z denotes time wanted: displacement

More information

Lecture 16: Computer Vision

Lecture 16: Computer Vision CS4442/9542b: Artificial Intelligence II Prof. Olga Veksler Lecture 16: Computer Vision Motion Slides are from Steve Seitz (UW), David Jacobs (UMD) Outline Motion Estimation Motion Field Optical Flow Field

More information

Peripheral drift illusion

Peripheral drift illusion Peripheral drift illusion Does it work on other animals? Computer Vision Motion and Optical Flow Many slides adapted from J. Hays, S. Seitz, R. Szeliski, M. Pollefeys, K. Grauman and others Video A video

More information

CS-465 Computer Vision

CS-465 Computer Vision CS-465 Computer Vision Nazar Khan PUCIT 9. Optic Flow Optic Flow Nazar Khan Computer Vision 2 / 25 Optic Flow Nazar Khan Computer Vision 3 / 25 Optic Flow Where does pixel (x, y) in frame z move to in

More information

Visual Tracking (1) Pixel-intensity-based methods

Visual Tracking (1) Pixel-intensity-based methods Intelligent Control Systems Visual Tracking (1) Pixel-intensity-based methods Shingo Kagami Graduate School of Information Sciences, Tohoku University swk(at)ic.is.tohoku.ac.jp http://www.ic.is.tohoku.ac.jp/ja/swk/

More information

Finally: Motion and tracking. Motion 4/20/2011. CS 376 Lecture 24 Motion 1. Video. Uses of motion. Motion parallax. Motion field

Finally: Motion and tracking. Motion 4/20/2011. CS 376 Lecture 24 Motion 1. Video. Uses of motion. Motion parallax. Motion field Finally: Motion and tracking Tracking objects, video analysis, low level motion Motion Wed, April 20 Kristen Grauman UT-Austin Many slides adapted from S. Seitz, R. Szeliski, M. Pollefeys, and S. Lazebnik

More information

CS6670: Computer Vision

CS6670: Computer Vision CS6670: Computer Vision Noah Snavely Lecture 19: Optical flow http://en.wikipedia.org/wiki/barberpole_illusion Readings Szeliski, Chapter 8.4-8.5 Announcements Project 2b due Tuesday, Nov 2 Please sign

More information

Visual motion. Many slides adapted from S. Seitz, R. Szeliski, M. Pollefeys

Visual motion. Many slides adapted from S. Seitz, R. Szeliski, M. Pollefeys Visual motion Man slides adapted from S. Seitz, R. Szeliski, M. Pollefes Motion and perceptual organization Sometimes, motion is the onl cue Motion and perceptual organization Sometimes, motion is the

More information

Lecture 16: Computer Vision

Lecture 16: Computer Vision CS442/542b: Artificial ntelligence Prof. Olga Veksler Lecture 16: Computer Vision Motion Slides are from Steve Seitz (UW), David Jacobs (UMD) Outline Motion Estimation Motion Field Optical Flow Field Methods

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 14 130307 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Review Stereo Dense Motion Estimation Translational

More information

Computer Vision Lecture 20

Computer Vision Lecture 20 Computer Perceptual Vision and Sensory WS 16/17 Augmented Computing Computer Perceptual Vision and Sensory WS 16/17 Augmented Computing Computer Perceptual Vision and Sensory WS 16/17 Augmented Computing

More information

Optical flow and tracking

Optical flow and tracking EECS 442 Computer vision Optical flow and tracking Intro Optical flow and feature tracking Lucas-Kanade algorithm Motion segmentation Segments of this lectures are courtesy of Profs S. Lazebnik S. Seitz,

More information

Computer Vision Lecture 20

Computer Vision Lecture 20 Computer Perceptual Vision and Sensory WS 16/76 Augmented Computing Many slides adapted from K. Grauman, S. Seitz, R. Szeliski, M. Pollefeys, S. Lazebnik Computer Vision Lecture 20 Motion and Optical Flow

More information

Lucas-Kanade Motion Estimation. Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides.

Lucas-Kanade Motion Estimation. Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides. Lucas-Kanade Motion Estimation Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides. 1 Why estimate motion? We live in a 4-D world Wide applications Object

More information

EE795: Computer Vision and Intelligent Systems

EE795: Computer Vision and Intelligent Systems EE795: Computer Vision and Intelligent Systems Spring 2012 TTh 17:30-18:45 FDH 204 Lecture 11 140311 http://www.ee.unlv.edu/~b1morris/ecg795/ 2 Outline Motion Analysis Motivation Differential Motion Optical

More information

Matching. Compare region of image to region of image. Today, simplest kind of matching. Intensities similar.

Matching. Compare region of image to region of image. Today, simplest kind of matching. Intensities similar. Matching Compare region of image to region of image. We talked about this for stereo. Important for motion. Epipolar constraint unknown. But motion small. Recognition Find object in image. Recognize object.

More information

Lecture 19: Motion. Effect of window size 11/20/2007. Sources of error in correspondences. Review Problem set 3. Tuesday, Nov 20

Lecture 19: Motion. Effect of window size 11/20/2007. Sources of error in correspondences. Review Problem set 3. Tuesday, Nov 20 Lecture 19: Motion Review Problem set 3 Dense stereo matching Sparse stereo matching Indexing scenes Tuesda, Nov 0 Effect of window size W = 3 W = 0 Want window large enough to have sufficient intensit

More information

Motion and Optical Flow. Slides from Ce Liu, Steve Seitz, Larry Zitnick, Ali Farhadi

Motion and Optical Flow. Slides from Ce Liu, Steve Seitz, Larry Zitnick, Ali Farhadi Motion and Optical Flow Slides from Ce Liu, Steve Seitz, Larry Zitnick, Ali Farhadi We live in a moving world Perceiving, understanding and predicting motion is an important part of our daily lives Motion

More information

Dense Image-based Motion Estimation Algorithms & Optical Flow

Dense Image-based Motion Estimation Algorithms & Optical Flow Dense mage-based Motion Estimation Algorithms & Optical Flow Video A video is a sequence of frames captured at different times The video data is a function of v time (t) v space (x,y) ntroduction to motion

More information

Multi-stable Perception. Necker Cube

Multi-stable Perception. Necker Cube Multi-stable Perception Necker Cube Spinning dancer illusion, Nobuyuki Kayahara Multiple view geometry Stereo vision Epipolar geometry Lowe Hartley and Zisserman Depth map extraction Essential matrix

More information

CS664 Lecture #18: Motion

CS664 Lecture #18: Motion CS664 Lecture #18: Motion Announcements Most paper choices were fine Please be sure to email me for approval, if you haven t already This is intended to help you, especially with the final project Use

More information

CS231A Section 6: Problem Set 3

CS231A Section 6: Problem Set 3 CS231A Section 6: Problem Set 3 Kevin Wong Review 6 -! 1 11/09/2012 Announcements PS3 Due 2:15pm Tuesday, Nov 13 Extra Office Hours: Friday 6 8pm Huang Common Area, Basement Level. Review 6 -! 2 Topics

More information

Mariya Zhariy. Uttendorf Introduction to Optical Flow. Mariya Zhariy. Introduction. Determining. Optical Flow. Results. Motivation Definition

Mariya Zhariy. Uttendorf Introduction to Optical Flow. Mariya Zhariy. Introduction. Determining. Optical Flow. Results. Motivation Definition to Constraint to Uttendorf 2005 Contents to Constraint 1 Contents to Constraint 1 2 Constraint Contents to Constraint 1 2 Constraint 3 Visual cranial reflex(vcr)(?) to Constraint Rapidly changing scene

More information

Augmented Reality VU. Computer Vision 3D Registration (2) Prof. Vincent Lepetit

Augmented Reality VU. Computer Vision 3D Registration (2) Prof. Vincent Lepetit Augmented Reality VU Computer Vision 3D Registration (2) Prof. Vincent Lepetit Feature Point-Based 3D Tracking Feature Points for 3D Tracking Much less ambiguous than edges; Point-to-point reprojection

More information

Optical Flow-Based Motion Estimation. Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides.

Optical Flow-Based Motion Estimation. Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides. Optical Flow-Based Motion Estimation Thanks to Steve Seitz, Simon Baker, Takeo Kanade, and anyone else who helped develop these slides. 1 Why estimate motion? We live in a 4-D world Wide applications Object

More information

Visual Tracking. Image Processing Laboratory Dipartimento di Matematica e Informatica Università degli studi di Catania.

Visual Tracking. Image Processing Laboratory Dipartimento di Matematica e Informatica Università degli studi di Catania. Image Processing Laboratory Dipartimento di Matematica e Informatica Università degli studi di Catania 1 What is visual tracking? estimation of the target location over time 2 applications Six main areas:

More information

Comparison between Motion Analysis and Stereo

Comparison between Motion Analysis and Stereo MOTION ESTIMATION The slides are from several sources through James Hays (Brown); Silvio Savarese (U. of Michigan); Octavia Camps (Northeastern); including their own slides. Comparison between Motion Analysis

More information

Ninio, J. and Stevens, K. A. (2000) Variations on the Hermann grid: an extinction illusion. Perception, 29,

Ninio, J. and Stevens, K. A. (2000) Variations on the Hermann grid: an extinction illusion. Perception, 29, Ninio, J. and Stevens, K. A. (2000) Variations on the Hermann grid: an extinction illusion. Perception, 29, 1209-1217. CS 4495 Computer Vision A. Bobick Sparse to Dense Correspodence Building Rome in

More information

Capturing, Modeling, Rendering 3D Structures

Capturing, Modeling, Rendering 3D Structures Computer Vision Approach Capturing, Modeling, Rendering 3D Structures Calculate pixel correspondences and extract geometry Not robust Difficult to acquire illumination effects, e.g. specular highlights

More information

Visual Tracking. Antonino Furnari. Image Processing Lab Dipartimento di Matematica e Informatica Università degli Studi di Catania

Visual Tracking. Antonino Furnari. Image Processing Lab Dipartimento di Matematica e Informatica Università degli Studi di Catania Visual Tracking Antonino Furnari Image Processing Lab Dipartimento di Matematica e Informatica Università degli Studi di Catania furnari@dmi.unict.it 11 giugno 2015 What is visual tracking? estimation

More information

Optic Flow and Basics Towards Horn-Schunck 1

Optic Flow and Basics Towards Horn-Schunck 1 Optic Flow and Basics Towards Horn-Schunck 1 Lecture 7 See Section 4.1 and Beginning of 4.2 in Reinhard Klette: Concise Computer Vision Springer-Verlag, London, 2014 1 See last slide for copyright information.

More information

Autonomous Navigation for Flying Robots

Autonomous Navigation for Flying Robots Computer Vision Group Prof. Daniel Cremers Autonomous Navigation for Flying Robots Lecture 7.1: 2D Motion Estimation in Images Jürgen Sturm Technische Universität München 3D to 2D Perspective Projections

More information

EE 264: Image Processing and Reconstruction. Image Motion Estimation I. EE 264: Image Processing and Reconstruction. Outline

EE 264: Image Processing and Reconstruction. Image Motion Estimation I. EE 264: Image Processing and Reconstruction. Outline 1 Image Motion Estimation I 2 Outline 1. Introduction to Motion 2. Why Estimate Motion? 3. Global vs. Local Motion 4. Block Motion Estimation 5. Optical Flow Estimation Basics 6. Optical Flow Estimation

More information

Motion and Tracking. Andrea Torsello DAIS Università Ca Foscari via Torino 155, Mestre (VE)

Motion and Tracking. Andrea Torsello DAIS Università Ca Foscari via Torino 155, Mestre (VE) Motion and Tracking Andrea Torsello DAIS Università Ca Foscari via Torino 155, 30172 Mestre (VE) Motion Segmentation Segment the video into multiple coherently moving objects Motion and Perceptual Organization

More information

Feature Detection. Raul Queiroz Feitosa. 3/30/2017 Feature Detection 1

Feature Detection. Raul Queiroz Feitosa. 3/30/2017 Feature Detection 1 Feature Detection Raul Queiroz Feitosa 3/30/2017 Feature Detection 1 Objetive This chapter discusses the correspondence problem and presents approaches to solve it. 3/30/2017 Feature Detection 2 Outline

More information

SIFT: SCALE INVARIANT FEATURE TRANSFORM SURF: SPEEDED UP ROBUST FEATURES BASHAR ALSADIK EOS DEPT. TOPMAP M13 3D GEOINFORMATION FROM IMAGES 2014

SIFT: SCALE INVARIANT FEATURE TRANSFORM SURF: SPEEDED UP ROBUST FEATURES BASHAR ALSADIK EOS DEPT. TOPMAP M13 3D GEOINFORMATION FROM IMAGES 2014 SIFT: SCALE INVARIANT FEATURE TRANSFORM SURF: SPEEDED UP ROBUST FEATURES BASHAR ALSADIK EOS DEPT. TOPMAP M13 3D GEOINFORMATION FROM IMAGES 2014 SIFT SIFT: Scale Invariant Feature Transform; transform image

More information

Motion Estimation. There are three main types (or applications) of motion estimation:

Motion Estimation. There are three main types (or applications) of motion estimation: Members: D91922016 朱威達 R93922010 林聖凱 R93922044 謝俊瑋 Motion Estimation There are three main types (or applications) of motion estimation: Parametric motion (image alignment) The main idea of parametric motion

More information

Tracking Computer Vision Spring 2018, Lecture 24

Tracking Computer Vision Spring 2018, Lecture 24 Tracking http://www.cs.cmu.edu/~16385/ 16-385 Computer Vision Spring 2018, Lecture 24 Course announcements Homework 6 has been posted and is due on April 20 th. - Any questions about the homework? - How

More information

CPSC 425: Computer Vision

CPSC 425: Computer Vision 1 / 49 CPSC 425: Computer Vision Instructor: Fred Tung ftung@cs.ubc.ca Department of Computer Science University of British Columbia Lecture Notes 2015/2016 Term 2 2 / 49 Menu March 10, 2016 Topics: Motion

More information

EECS 556 Image Processing W 09

EECS 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 information

Comparison between Optical Flow and Cross-Correlation Methods for Extraction of Velocity Fields from Particle Images

Comparison between Optical Flow and Cross-Correlation Methods for Extraction of Velocity Fields from Particle Images Comparison between Optical Flow and Cross-Correlation Methods for Extraction of Velocity Fields from Particle Images (Optical Flow vs Cross-Correlation) Tianshu Liu, Ali Merat, M. H. M. Makhmalbaf Claudia

More information

Computer Vision Lecture 20

Computer 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 information

SUMMARY: DISTINCTIVE IMAGE FEATURES FROM SCALE- INVARIANT KEYPOINTS

SUMMARY: DISTINCTIVE IMAGE FEATURES FROM SCALE- INVARIANT KEYPOINTS SUMMARY: DISTINCTIVE IMAGE FEATURES FROM SCALE- INVARIANT KEYPOINTS Cognitive Robotics Original: David G. Lowe, 004 Summary: Coen van Leeuwen, s1460919 Abstract: This article presents a method to extract

More information

Outline 7/2/201011/6/

Outline 7/2/201011/6/ Outline Pattern recognition in computer vision Background on the development of SIFT SIFT algorithm and some of its variations Computational considerations (SURF) Potential improvement Summary 01 2 Pattern

More information

ECE Digital Image Processing and Introduction to Computer Vision

ECE Digital Image Processing and Introduction to Computer Vision ECE592-064 Digital Image Processing and Introduction to Computer Vision Depart. of ECE, NC State University Instructor: Tianfu (Matt) Wu Spring 2017 Recap, SIFT Motion Tracking Change Detection Feature

More information

Lecture 20: Tracking. Tuesday, Nov 27

Lecture 20: Tracking. Tuesday, Nov 27 Lecture 20: Tracking Tuesday, Nov 27 Paper reviews Thorough summary in your own words Main contribution Strengths? Weaknesses? How convincing are the experiments? Suggestions to improve them? Extensions?

More information

CAP 5415 Computer Vision Fall 2012

CAP 5415 Computer Vision Fall 2012 CAP 5415 Computer Vision Fall 01 Dr. Mubarak Shah Univ. of Central Florida Office 47-F HEC Lecture-5 SIFT: David Lowe, UBC SIFT - Key Point Extraction Stands for scale invariant feature transform Patented

More information

Ruch (Motion) Rozpoznawanie Obrazów Krzysztof Krawiec Instytut Informatyki, Politechnika Poznańska. Krzysztof Krawiec IDSS

Ruch (Motion) Rozpoznawanie Obrazów Krzysztof Krawiec Instytut Informatyki, Politechnika Poznańska. Krzysztof Krawiec IDSS Ruch (Motion) Rozpoznawanie Obrazów Krzysztof Krawiec Instytut Informatyki, Politechnika Poznańska 1 Krzysztof Krawiec IDSS 2 The importance of visual motion Adds entirely new (temporal) dimension to visual

More information

Notes 9: Optical Flow

Notes 9: Optical Flow Course 049064: Variational Methods in Image Processing Notes 9: Optical Flow Guy Gilboa 1 Basic Model 1.1 Background Optical flow is a fundamental problem in computer vision. The general goal is to find

More information

Image processing and features

Image processing and features Image processing and features Gabriele Bleser gabriele.bleser@dfki.de Thanks to Harald Wuest, Folker Wientapper and Marc Pollefeys Introduction Previous lectures: geometry Pose estimation Epipolar geometry

More information

Coarse-to-fine image registration

Coarse-to-fine image registration Today we will look at a few important topics in scale space in computer vision, in particular, coarseto-fine approaches, and the SIFT feature descriptor. I will present only the main ideas here to give

More information

Horn-Schunck and Lucas Kanade 1

Horn-Schunck and Lucas Kanade 1 Horn-Schunck and Lucas Kanade 1 Lecture 8 See Sections 4.2 and 4.3 in Reinhard Klette: Concise Computer Vision Springer-Verlag, London, 2014 1 See last slide for copyright information. 1 / 40 Where We

More information

Computational Optical Imaging - Optique Numerique. -- Single and Multiple View Geometry, Stereo matching --

Computational Optical Imaging - Optique Numerique. -- Single and Multiple View Geometry, Stereo matching -- Computational Optical Imaging - Optique Numerique -- Single and Multiple View Geometry, Stereo matching -- Autumn 2015 Ivo Ihrke with slides by Thorsten Thormaehlen Reminder: Feature Detection and Matching

More information

SURVEY OF LOCAL AND GLOBAL OPTICAL FLOW WITH COARSE TO FINE METHOD

SURVEY OF LOCAL AND GLOBAL OPTICAL FLOW WITH COARSE TO FINE METHOD SURVEY OF LOCAL AND GLOBAL OPTICAL FLOW WITH COARSE TO FINE METHOD M.E-II, Department of Computer Engineering, PICT, Pune ABSTRACT: Optical flow as an image processing technique finds its applications

More information

Fundamental matrix. Let p be a point in left image, p in right image. Epipolar relation. Epipolar mapping described by a 3x3 matrix F

Fundamental matrix. Let p be a point in left image, p in right image. Epipolar relation. Epipolar mapping described by a 3x3 matrix F 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 F Fundamental

More information

Motion Analysis. Motion analysis. Now we will talk about. Differential Motion Analysis. Motion analysis. Difference Pictures

Motion Analysis. Motion analysis. Now we will talk about. Differential Motion Analysis. Motion analysis. Difference Pictures Now we will talk about Motion Analysis Motion analysis Motion analysis is dealing with three main groups of motionrelated problems: Motion detection Moving object detection and location. Derivation of

More information

Computer Vision II Lecture 4

Computer Vision II Lecture 4 Computer Vision II Lecture 4 Color based Tracking 29.04.2014 Bastian Leibe RWTH Aachen http://www.vision.rwth-aachen.de leibe@vision.rwth-aachen.de Course Outline Single-Object Tracking Background modeling

More information

Automatic Image Alignment (direct) with a lot of slides stolen from Steve Seitz and Rick Szeliski

Automatic Image Alignment (direct) with a lot of slides stolen from Steve Seitz and Rick Szeliski Automatic Image Alignment (direct) with a lot of slides stolen from Steve Seitz and Rick Szeliski 15-463: Computational Photography Alexei Efros, CMU, Fall 2005 Today Go over Midterm Go over Project #3

More information

BSB663 Image Processing Pinar Duygulu. Slides are adapted from Selim Aksoy

BSB663 Image Processing Pinar Duygulu. Slides are adapted from Selim Aksoy BSB663 Image Processing Pinar Duygulu Slides are adapted from Selim Aksoy Image matching Image matching is a fundamental aspect of many problems in computer vision. Object or scene recognition Solving

More information

SE 263 R. Venkatesh Babu. Object Tracking. R. Venkatesh Babu

SE 263 R. Venkatesh Babu. Object Tracking. R. Venkatesh Babu Object Tracking R. Venkatesh Babu Primitive tracking Appearance based - Template Matching Assumptions: Object description derived from first frame No change in object appearance Movement only 2D translation

More information

Face Tracking : An implementation of the Kanade-Lucas-Tomasi Tracking algorithm

Face Tracking : An implementation of the Kanade-Lucas-Tomasi Tracking algorithm Face Tracking : An implementation of the Kanade-Lucas-Tomasi Tracking algorithm Dirk W. Wagener, Ben Herbst Department of Applied Mathematics, University of Stellenbosch, Private Bag X1, Matieland 762,

More information

Motion Estimation (II) Ce Liu Microsoft Research New England

Motion Estimation (II) Ce Liu Microsoft Research New England Motion Estimation (II) Ce Liu celiu@microsoft.com Microsoft Research New England Last time Motion perception Motion representation Parametric motion: Lucas-Kanade T I x du dv = I x I T x I y I x T I y

More information

Final Review CMSC 733 Fall 2014

Final Review CMSC 733 Fall 2014 Final Review CMSC 733 Fall 2014 We have covered a lot of material in this course. One way to organize this material is around a set of key equations and algorithms. You should be familiar with all of these,

More information

Computer Vision 2. SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung. Computer Vision 2 Dr. Benjamin Guthier

Computer Vision 2. SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung. Computer Vision 2 Dr. Benjamin Guthier Computer Vision 2 SS 18 Dr. Benjamin Guthier Professur für Bildverarbeitung Computer Vision 2 Dr. Benjamin Guthier 1. IMAGE PROCESSING Computer Vision 2 Dr. Benjamin Guthier Content of this Chapter Non-linear

More information

Local Features: Detection, Description & Matching

Local Features: Detection, Description & Matching Local Features: Detection, Description & Matching Lecture 08 Computer Vision Material Citations Dr George Stockman Professor Emeritus, Michigan State University Dr David Lowe Professor, University of British

More information

Edge and corner detection

Edge and corner detection Edge and corner detection Prof. Stricker Doz. G. Bleser Computer Vision: Object and People Tracking Goals Where is the information in an image? How is an object characterized? How can I find measurements

More information

Final Exam Study Guide

Final Exam Study Guide Final Exam Study Guide Exam Window: 28th April, 12:00am EST to 30th April, 11:59pm EST Description As indicated in class the goal of the exam is to encourage you to review the material from the course.

More information

The Lucas & Kanade Algorithm

The Lucas & Kanade Algorithm The Lucas & Kanade Algorithm Instructor - Simon Lucey 16-423 - Designing Computer Vision Apps Today Registration, Registration, Registration. Linearizing Registration. Lucas & Kanade Algorithm. 3 Biggest

More information

Digital Image Processing (CS/ECE 545) Lecture 5: Edge Detection (Part 2) & Corner Detection

Digital Image Processing (CS/ECE 545) Lecture 5: Edge Detection (Part 2) & Corner Detection Digital Image Processing (CS/ECE 545) Lecture 5: Edge Detection (Part 2) & Corner Detection Prof Emmanuel Agu Computer Science Dept. Worcester Polytechnic Institute (WPI) Recall: Edge Detection Image processing

More information

The SIFT (Scale Invariant Feature

The SIFT (Scale Invariant Feature The SIFT (Scale Invariant Feature Transform) Detector and Descriptor developed by David Lowe University of British Columbia Initial paper ICCV 1999 Newer journal paper IJCV 2004 Review: Matt Brown s Canonical

More information

Image features. Image Features

Image features. Image Features Image features Image features, such as edges and interest points, provide rich information on the image content. They correspond to local regions in the image and are fundamental in many applications in

More information

16720 Computer Vision: Homework 3 Template Tracking and Layered Motion.

16720 Computer Vision: Homework 3 Template Tracking and Layered Motion. 16720 Computer Vision: Homework 3 Template Tracking and Layered Motion. Instructor: Martial Hebert TAs: Varun Ramakrishna and Tomas Simon Due Date: October 24 th, 2011. 1 Instructions You should submit

More information

CS 4495 Computer Vision A. Bobick. CS 4495 Computer Vision. Features 2 SIFT descriptor. Aaron Bobick School of Interactive Computing

CS 4495 Computer Vision A. Bobick. CS 4495 Computer Vision. Features 2 SIFT descriptor. Aaron Bobick School of Interactive Computing CS 4495 Computer Vision Features 2 SIFT descriptor Aaron Bobick School of Interactive Computing Administrivia PS 3: Out due Oct 6 th. Features recap: Goal is to find corresponding locations in two images.

More information

Corner Detection. Harvey Rhody Chester F. Carlson Center for Imaging Science Rochester Institute of Technology

Corner Detection. Harvey Rhody Chester F. Carlson Center for Imaging Science Rochester Institute of Technology Corner Detection Harvey Rhody Chester F. Carlson Center for Imaging Science Rochester Institute of Technology rhody@cis.rit.edu April 11, 2006 Abstract Corners and edges are two of the most important geometrical

More information

CS 378: Autonomous Intelligent Robotics. Instructor: Jivko Sinapov

CS 378: Autonomous Intelligent Robotics. Instructor: Jivko Sinapov CS 378: Autonomous Intelligent Robotics Instructor: Jivko Sinapov http://www.cs.utexas.edu/~jsinapov/teaching/cs378/ Visual Registration and Recognition Announcements Homework 6 is out, due 4/5 4/7 Installing

More information

Feature Descriptors. CS 510 Lecture #21 April 29 th, 2013

Feature Descriptors. CS 510 Lecture #21 April 29 th, 2013 Feature Descriptors CS 510 Lecture #21 April 29 th, 2013 Programming Assignment #4 Due two weeks from today Any questions? How is it going? Where are we? We have two umbrella schemes for object recognition

More information

CS201: Computer Vision Introduction to Tracking

CS201: Computer Vision Introduction to Tracking CS201: Computer Vision Introduction to Tracking John Magee 18 November 2014 Slides courtesy of: Diane H. Theriault Question of the Day How can we represent and use motion in images? 1 What is Motion? Change

More information

EECS150 - Digital Design Lecture 14 FIFO 2 and SIFT. Recap and Outline

EECS150 - Digital Design Lecture 14 FIFO 2 and SIFT. Recap and Outline EECS150 - Digital Design Lecture 14 FIFO 2 and SIFT Oct. 15, 2013 Prof. Ronald Fearing Electrical Engineering and Computer Sciences University of California, Berkeley (slides courtesy of Prof. John Wawrzynek)

More information

CSE 252A Computer Vision Homework 3 Instructor: Ben Ochoa Due : Monday, November 21, 2016, 11:59 PM

CSE 252A Computer Vision Homework 3 Instructor: Ben Ochoa Due : Monday, November 21, 2016, 11:59 PM CSE 252A Computer Vision Homework 3 Instructor: Ben Ochoa Due : Monday, November 21, 2016, 11:59 PM Instructions: Homework 3 has to be submitted in groups of 3. Review the academic integrity and collaboration

More information

Line, edge, blob and corner detection

Line, edge, blob and corner detection Line, edge, blob and corner detection Dmitri Melnikov MTAT.03.260 Pattern Recognition and Image Analysis April 5, 2011 1 / 33 Outline 1 Introduction 2 Line detection 3 Edge detection 4 Blob detection 5

More information

C18 Computer vision. C18 Computer Vision. This time... Introduction. Outline.

C18 Computer vision. C18 Computer Vision. This time... Introduction. Outline. C18 Computer Vision. This time... 1. Introduction; imaging geometry; camera calibration. 2. Salient feature detection edges, line and corners. 3. Recovering 3D from two images I: epipolar geometry. C18

More information

Motion Estimation and Optical Flow Tracking

Motion Estimation and Optical Flow Tracking Image Matching Image Retrieval Object Recognition Motion Estimation and Optical Flow Tracking Example: Mosiacing (Panorama) M. Brown and D. G. Lowe. Recognising Panoramas. ICCV 2003 Example 3D Reconstruction

More information

Detection of Moving Objects in Colour based and Graph s axis Change method

Detection of Moving Objects in Colour based and Graph s axis Change method Detection of Moving Objects in Colour based and Graph s axis Change method Gagandeep Kaur1 Student of Master of Technology, Department of Computer Engineering, YCOE, GuruKashi Campus, Punjabi university,

More information

Lecture 6: Edge Detection

Lecture 6: Edge Detection #1 Lecture 6: Edge Detection Saad J Bedros sbedros@umn.edu Review From Last Lecture Options for Image Representation Introduced the concept of different representation or transformation Fourier Transform

More information

Local Feature Detectors

Local Feature Detectors Local Feature Detectors Selim Aksoy Department of Computer Engineering Bilkent University saksoy@cs.bilkent.edu.tr Slides adapted from Cordelia Schmid and David Lowe, CVPR 2003 Tutorial, Matthew Brown,

More information

The 2D/3D Differential Optical Flow

The 2D/3D Differential Optical Flow The 2D/3D Differential Optical Flow Prof. John Barron Dept. of Computer Science University of Western Ontario London, Ontario, Canada, N6A 5B7 Email: barron@csd.uwo.ca Phone: 519-661-2111 x86896 Canadian

More information

Spatial track: motion modeling

Spatial track: motion modeling Spatial track: motion modeling Virginio Cantoni Computer Vision and Multimedia Lab Università di Pavia Via A. Ferrata 1, 27100 Pavia virginio.cantoni@unipv.it http://vision.unipv.it/va 1 Comparison between

More information

Optic Flow and Motion Detection

Optic Flow and Motion Detection Optic Flow and Motion Detection Computer Vision and Imaging Martin Jagersand Readings: Szeliski Ch 8 Ma, Kosecka, Sastry Ch 4 Image motion Somehow quantify the frame-to to-frame differences in image sequences.

More information

Spatial track: motion modeling

Spatial track: motion modeling Spatial track: motion modeling Virginio Cantoni Computer Vision and Multimedia Lab Università di Pavia Via A. Ferrata 1, 27100 Pavia virginio.cantoni@unipv.it http://vision.unipv.it/va 1 Comparison between

More information

Optical flow. Cordelia Schmid

Optical 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 information

Announcements. Motion. Structure-from-Motion (SFM) Motion. Discrete Motion: Some Counting

Announcements. Motion. Structure-from-Motion (SFM) Motion. Discrete Motion: Some Counting Announcements Motion Introduction to Computer Vision CSE 152 Lecture 20 HW 4 due Friday at Midnight Final Exam: Tuesday, 6/12 at 8:00AM-11:00AM, regular classroom Extra Office Hours: Monday 6/11 9:00AM-10:00AM

More information

Optical Flow Estimation with CUDA. Mikhail Smirnov

Optical Flow Estimation with CUDA. Mikhail Smirnov Optical Flow Estimation with CUDA Mikhail Smirnov msmirnov@nvidia.com Document Change History Version Date Responsible Reason for Change Mikhail Smirnov Initial release Abstract Optical flow is the apparent

More information