Optical Flow, KL Feature racker E-mail: hogijung@hanang.ac.kr
Motion in Computer Vision Motion Structure rom motion Detection/segmentation with direction [1] E-mail: hogijung@hanang.ac.kr
Motion Field.s.. Optical Flow [2], [3] Motion Field: an ideal representation o 3D motion as it is projected onto a camera image. Optical Flow: the approimation (or estimate) o the motion ield which can be computed rom time-aring image sequences. Under the simpliing assumptions o 1) Lambertian surace, 2) pointwise light source at ininit, and 3) no photometric distortion. E-mail: hogijung@hanang.ac.kr
Motion Field [2] An ideal representation o 3D motion as it is projected onto a camera image. he time deriatie o the image position o all image points gien that the correspond to ied 3D points. ield : position ector he motion ield is deined as where P is a point in the scene where is the distance to that scene point. V is the relatie motion between the camera and the scene, is the translational component o the motion, and ω is the angular elocit o the motion. E-mail: hogijung@hanang.ac.kr
E-mail: hogijung@hanang.ac.kr Motion Field [2] Motion Field [2] P p (1) 3D point P (,,) and 2D point p (,), ocal length Motion ield can be obtained b taking the time deriatie o (1) 2 2 V V V V (2)
E-mail: hogijung@hanang.ac.kr Motion Field [2] Motion Field [2] P V (3) he motion o 3D point P, V is deined as low B substituting (3) into (2), the basic equations o the motion ield is acquired 2 2 (4) V V V
E-mail: hogijung@hanang.ac.kr Motion Field [2] Motion Field [2] he motion ield is the sum o two components, one o which depends on translation onl, the other on rotation onl. 2 2 2 2 ranslational components Rotational components (4) (5) (6)
E-mail: hogijung@hanang.ac.kr Motion Field: Pure ranslation [2] Motion Field: Pure ranslation [2] I there is no rotational motion, the resulting motion ield has a peculiar spatial structure. I (5) is regarded as a unction o 2D point position, (5) 0 0 I ( 0, 0 ) is deined as in (6) 0 0 (6) (7)
E-mail: hogijung@hanang.ac.kr Motion Field: Pure ranslation [2] Motion Field: Pure ranslation [2] Equation (7) sa that the motion ield o a pure translation is radial. In particular, i <0, the ectors point awa rom p 0 ( 0, 0 ), which is called the ocus o epansion (FOE). I >0, the motion ield ectors point towards p 0, which is called the ocus o contraction. I =0, rom (5), all the motion ield ectors are parallel. (5) (8)
Motion Field: Motion Paralla [6] Equation (8) sa that their lengths are inersel proportional to the depth o the corresponding 3D points. (8) http://upload.wikimedia.org /wikipedia/commons/a/ab/ Paralla.gi his animation is an eample o paralla. As the iewpoint moes side to side, the objects in the distance appear to moe more slowl than the objects close to the camera [6]. E-mail: hogijung@hanang.ac.kr
E-mail: hogijung@hanang.ac.kr Motion Field: Motion Paralla [2] Motion Field: Motion Paralla [2] I two 3D points are projected into one image point, that is coincident, rotational component will be the same. Notice that the motion ector V is about camera motion. (4) 2 2
Motion Field: Motion Paralla [2] he dierence o two points motion ield will be related with translation components. And, the will be radial w.r.t FOE or FOC. 1 1 1 1 0 1 2 1 2 1 1 1 1 0 1 2 1 2 FOC E-mail: hogijung@hanang.ac.kr
Motion Field: Motion Paralla [2] Motion Paralla he relatie motion ield o two instantaneousl coincident points: 1. Does not depend on the rotational component o motion 2. Points towards (awa rom) the point p0, the anishing point o the translation direction. E-mail: hogijung@hanang.ac.kr
Motion Field: Pure Rotation w.r.t -ais [7] I there is no translation motion and rotation w.r.t - and z- ais, rom (4) 2 E-mail: hogijung@hanang.ac.kr
Motion Field: Pure Rotation w.r.t -ais [7] ranslational Motion Distance to the point,, is constant. Rotational Motion 1 2 Distance to the point,, is changing. According to, is changing, too. E-mail: hogijung@hanang.ac.kr
Estimation o the Optical Flow [4] E-mail: hogijung@hanang.ac.kr
Estimation o the Optical Flow [4] he Image Brightness Constanc Equation [2] E-mail: hogijung@hanang.ac.kr
Estimation o the Optical Flow [4] I V I t V I t I Assumption he image brightness is continuous and dierentiable as man times as needed in both the spatial and temporal domain. he image brightness can be regarded as a plane in a small area. E-mail: hogijung@hanang.ac.kr
Optical Field: Aperture Problem [2], [4], [9] he component o the motion ield in the direction orthogonal to the spatial image gradient is not constrained b the image brightness constanc equation. Gien local inormation can determine component o optical low ector onl in direction o brightness gradient. E-mail: hogijung@hanang.ac.kr
Optical Field: Aperture Problem [2], [9] he aperture problem. he grating appears to be moing down and to the right, perpendicular to the orientation o the bars. But it could be moing in man other directions, such as onl down, or onl to the right. It is impossible to determine unless the ends o the bars become isible in the aperture. http://upload.wikimedia.org/wikipedia/commons//0/aperture_pr oblem_animated.gi E-mail: hogijung@hanang.ac.kr
Optical Field: Methods or Determining Optical Flow [4] E-mail: hogijung@hanang.ac.kr
Optical Field: Phase Correlation Method [10] E-mail: hogijung@hanang.ac.kr
Optical Field: Phase Correlation Method [10] E-mail: hogijung@hanang.ac.kr
Optical Field: Phase Correlation Method [10] E-mail: hogijung@hanang.ac.kr
Optical Field: Lucas-Kanade Method [8] Assuming that the optical low (V, ) is constant in a small window o size mm with m>1, which is center at (, ) and numbering the piels within as 1 n, n=m 2, a set o equations can be ound: I V I t E-mail: hogijung@hanang.ac.kr
Optical Field: Lucas-Kanade Method [8] c.) Harris corner detector E-mail: hogijung@hanang.ac.kr
KL Feature racker [11] E-mail: hogijung@hanang.ac.kr
KL Feature racker [11] F () 로 weighting E-mail: hogijung@hanang.ac.kr
KL Feature racker [11] I V I t KL: An Implementation o the Kanade-Lucas-omasi Feature racker http://www.ces.clemson.edu/~stb/klt/ E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] Since the Lucas-Kanade algorithm was proposed in 1981 image alignment has become one o the most widel used techniques in computer ision. Besides optical low, some o its other applications include - tracking (Black and Jepson, 1998; Hager and Belhumeur, 1998), - parametric and laered motion estimation (Bergen et al., 1992), - mosaic construction (Shum and Szeliski, 2000), - medical image registration (Christensen and Johnson, 2001), - ace coding (Baker and Matthews, 2001; Cootes et al., 1998). E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] Minimizing the epression in Equation (1) is a non-linear optimization task een i W(; p) is linear in p because the piel alues I() are, in general, non-linear in. E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] Setting this epression to equal zero and soling gies the closed orm solution or the minimum o the epression in Equation (6) as: SD E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] E-mail: hogijung@hanang.ac.kr
Lucas-Kanade Method: A Uniing Framework [12] E-mail: hogijung@hanang.ac.kr
Reerences 1. Richard Szeliski, Dense motion estimation, Computer Vision: Algorithms and Applications, 19 June 2009 (drat), pp. 383-426. 2. Emanuele rucco, Alessandro Verri, 8. Motion, Introductor echniques or 3-D Computer Vision, Prentice Hall, New Jerse 1998, pp.177-218. 3. Wikipedia, Motion ield, aailable on www.wikipedia.org. 4. Wikipedia, Optical low, aailable on www.wikipedia.org. 5. Alessandro Verri, Emanuele rucco, Finding the Epipole rom Uncalibrated Optical Flow, BMVC 1997, aailable on http://www.bma.ac.uk/bmc/1997/papers/052/bmc.html. 6. Wikipedia, Paralle, aailable on www.wikipedia.org. 7. Jae Ku Suhr, Ho Gi Jung, Kwanghuk Bae, Jaihie Kim, Outlier rejection or cameras on intelligent ehicles, Pattern Recognition Letters 29 (2008) 828-840. 8. Wikipedia, Lucas-Kanade Optical Flow Method, aailable on www.wikipedia.org. 9. Wikipedia, Aperture Problem, aailable on www.wikipedia.org. 10. Wikipedia, Phase correlation, aailable on http://en.wikipedia.org/wiki/phase_correlation 11. Wikipedia, Kanade-Lucas-omasi eature tracker, aailable on http://en.wikipedia.org/wiki/kanade%e2%80%93lucas%e2%80%93omasi_eature_track er 12. Simon Baker, Iain Matthews, Lucas-Kanade 20 ears: A Uniing Framework, International Journal o Computer Vision, 56(3), 221-255, 2004. E-mail: hogijung@hanang.ac.kr