Motion estimation Parametric motion (image alignment) Tracking Optical flow.
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Transcript of Motion estimation Parametric motion (image alignment) Tracking Optical flow.
![Page 1: Motion estimation Parametric motion (image alignment) Tracking Optical flow.](https://reader035.fdocuments.us/reader035/viewer/2022062408/56649f1d5503460f94c348e8/html5/thumbnails/1.jpg)
Motion estimation
• Parametric motion (image alignment)• Tracking• Optical flow
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Tracking
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Three assumptions
• Brightness consistency• Spatial coherence• Temporal persistence
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Brightness consistency
Image measurement (e.g. brightness) in a small region remain the same although their location may change.
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Spatial coherence
• Neighboring points in the scene typically belong to the same surface and hence typically have similar motions.
• Since they also project to nearby pixels in the image, we expect spatial coherence in image flow.
![Page 6: Motion estimation Parametric motion (image alignment) Tracking Optical flow.](https://reader035.fdocuments.us/reader035/viewer/2022062408/56649f1d5503460f94c348e8/html5/thumbnails/6.jpg)
Temporal persistence
The image motion of a surface patch changes gradually over time.
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Image registration
Goal: register a template image T(x) and an input image I(x), where x=(x,y)T. (warp I so that it matches T)
Image alignment: I(x) and T(x) are two images
Tracking: T(x) is a small patch around a point p in the image at t. I(x) is the image at time t+1.
Optical flow: T(x) and I(x) are patches of images at t and t+1.T
fixed
I
warp
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Simple approach (for translation)
• Minimize brightness difference
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Simple SSD algorithm
For each offset (u, v)
compute E(u,v);
Choose (u, v) which minimizes E(u,v);
Problems:• Not efficient• No sub-pixel accuracy
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Lucas-Kanade algorithm
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Linear image registration in medical images
rigid (rotation + translation)
3+3 DOF
Linear registration = similarity (rotation + translation+scale)
3+3+3 DOF
affine (rotation+translation+scale+shear)
3+3+3+3 DOF Used when regsitering images of a same patient
Theoretically a similarity transform should be enough bt in practice an affine transformation is use to account for other
image/scan artefacts.
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x
p)W(x;xp
WHΔp )()(1 ITI
T
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x
p)W(x;xp
WHΔp )()(1 ITI
T
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x
p)W(x;xp
WHΔp )()(1 ITI
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x
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WHΔp )()(1 ITI
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x
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WHΔp )()(1 ITI
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x
p)W(x;xp
WHΔp )()(1 ITI
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x
p)W(x;xp
WHΔp )()(1 ITI
T
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x
p)W(x;xp
WHΔp )()(1 ITI
T
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x
p)W(x;xp
WHΔp )()(1 ITI
T
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x
p)W(x;xp
WHΔp )()(1 ITI
T
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x
p)W(x;xp
WHΔp )()(1 ITI
T
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Lucas-Kanade algorithm
iterate1) warp I with W(x;p)2) compute error image T(x,y)-I(W(x,p))3) compute gradient image with W(x,p)4) evaluate Jacobian at (x;p)5) compute 6) compute Hessian7) compute 8) solve 9) update p by p+until converge
p
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Coarse-to-fine strategy
J Jw Iwarp refine
ina
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+
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pyramid construction
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Application of image alignment
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Direct vs feature-based
• Direct methods use all information and can be very accurate, but they depend on the fragile “brightness constancy” assumption.
• Iterative approaches require initialization.• Not robust to illumination change and
noise images.• In early days, direct method is better.
• Feature based methods are now more robust and potentially faster.
• Even better, it can recognize panorama without initialization.
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Tracking
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Tracking
I(x,y,t) I(x+u,y+v,t+1)(u, v)
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Tracking
0),,()1,,( tyxItvyuxI
0),,(),,(),,(),,(),,( tyxItyxItyxvItyxuItyxI tyx
0),,(),,(),,( tyxItyxvItyxuI tyx
0 tyx IvIuI optical flow constraint equation
brightness constancy
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Optical flow constraint equation
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Multiple constraints
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Area-based method• Assume spatial smoothness
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Area-based method
• Assume spatial smoothness
yx
tyx IvIuIvuE,
2),(
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Area-based method
must be invertible
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Area-based method• The eigenvalues tell us about the local
image structure.• They also tell us how well we can estimate
the flow in both directions.• Link to Harris corner detector.
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Textured area
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Edge
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Homogenous area
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KLT tracking
• Select features by • Monitor features by measuring
dissimilarity
),( 21min
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Aperture problem
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Aperture problem
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Aperture problem
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Demo for aperture problem
• http://www.sandlotscience.com/Distortions/Breathing_Square.htm
• http://www.sandlotscience.com/Ambiguous/Barberpole_Illusion.htm
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Aperture problem
• Larger window reduces ambiguity, but easily violates spatial smoothness assumption
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KLT tracking
http://www.ces.clemson.edu/~stb/klt/
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KLT tracking
http://www.ces.clemson.edu/~stb/klt/
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SIFT tracking (matching actually)
Frame 0 Frame 10
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SIFT tracking
Frame 0 Frame 100
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SIFT tracking
Frame 0 Frame 200
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KLT vs SIFT tracking
• KLT has larger accumulating error; partly because our KLT implementation doesn’t have affine transformation?
• SIFT is surprisingly robust• Combination of SIFT and KLT (example)
http://www.frc.ri.cmu.edu/projects/buzzard/smalls/
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Rotoscoping (Max Fleischer 1914)
1937
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Tracking for rotoscoping
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Tracking for rotoscoping
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Waking life (2001)
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A Scanner Darkly (2006)
• Rotoshop, a proprietary software. Each minute of animation required 500 hours of work.
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Optical flow
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Single-motion assumption
Violated by• Motion discontinuity• Shadows• Transparency• Specular reflection• …
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Multiple motion
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Multiple motion
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Simple problem: fit a line
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Least-square fit
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Least-square fit
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Robust statistics
• Recover the best fit for the majority of the data
• Detect and reject outliers
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Approach
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Robust weighting
Truncated quadratic
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Robust weighting
Geman & McClure
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Robust estimation
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Fragmented occlusion
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Regularization and dense optical flow
• Neighboring points in the scene typically belong to the same surface and hence typically have similar motions.
• Since they also project to nearby pixels in the image, we expect spatial coherence in image flow.
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Input image Horizontal motion
Vertical motion
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Application of optical flow
videomatching
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Input for the NPR algorithm
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Brushes
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Edge clipping
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Gradient
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Smooth gradient
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Edge clipping
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Temporal artifacts
Frame-by-frame application of the NPR algorithm
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Temporal coherence
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References• B.D. Lucas and T. Kanade, An Iterative Image Registration Technique
with an Application to Stereo Vision, Proceedings of the 1981 DARPA Image Understanding Workshop, 1981, pp121-130.
• Bergen, J. R. and Anandan, P. and Hanna, K. J. and Hingorani, R., Hierarchical Model-Based Motion Estimation, ECCV 1992, pp237-252.
• J. Shi and C. Tomasi, Good Features to Track, CVPR 1994, pp593-600. • Michael Black and P. Anandan, The Robust Estimation of Multiple
Motions: Parametric and Piecewise-Smooth Flow Fields, Computer Vision and Image Understanding 1996, pp75-104.
• S. Baker and I. Matthews, Lucas-Kanade 20 Years On: A Unifying Framework, International Journal of Computer Vision, 56(3), 2004, pp221 - 255.
• Peter Litwinowicz, Processing Images and Video for An Impressionist
Effects, SIGGRAPH 1997. • Aseem Agarwala, Aaron Hertzman, David Salesin and Steven Seitz,
Keyframe-Based Tracking for Rotoscoping and Animation, SIGGRAPH 2004, pp584-591.