feature matching
DESCRIPTION
Feature matching. Digital Visual Effects, Spring 2005 Yung-Yu Chuang 2005/3/16. with slides by Trevor Darrell Cordelia Schmid , David Lowe, Darya Frolova, Denis Simakov , Robert Collins and Jiwon Kim. Announcements. - PowerPoint PPT PresentationTRANSCRIPT
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Feature matching
Digital Visual Effects, Spring 2005Yung-Yu Chuang2005/3/16
with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins and Jiwon Kim
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Announcements
• Project #1 is online, you have to write a program, not just using available software.
• Send me the members of your team.• Sign up for scribe at the forum.
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Blender
http://www.blender3d.com/cms/Home.2.0.htmlBlender could be used for your project #3 matchmove.
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In the forum
• Barycentric coordinate• RBF
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Outline
• Block matching• Features• Harris corner detector• SIFT• SIFT extensions• Applications
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Correspondence by block matching• Points are individually ambiguous• More unique matches are possible with
small regions of images
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Correspondence by block matching
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Sum of squared distance
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Image blocks as a vector
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Image blocks as a vector
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Matching metrics
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Features
• Properties of features• Detector: locates feature• Descriptor and matching metrics:
describes and matches features
• In the example for block matching:– Detector: none– Descriptor: block– Matching: distance
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Desired properties for features
• Invariant: invariant to scale, rotation, affine, illumination and noise for robust matching across a substantial range of affine distortion, viewpoint change and so on.
• Distinctive: a single feature can be correctly matched with high probability
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Harris corner detector
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Moravec corner detector (1980)• We should easily recognize the point by lookin
g through a small window• Shifting a window in any direction should give
a large change in intensity
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Moravec corner detector
flat
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Moravec corner detector
flat
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Moravec corner detector
flat edge
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Moravec corner detector
flat edgecorner
isolated point
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Moravec corner detectorChange of intensity for the shift [u,v]:
2
,
( , ) ( , ) ( , ) ( , )x y
E u v w x y I x u y v I x y
IntensityShifted intensity
Window function
Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1)Look for local maxima in min{E}
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Problems of Moravec detector• Noisy response due to a binary window function• Only a set of shifts at every 45 degree is considered• Responds too strong for edges because only minim
um of E is taken into account
Harris corner detector (1988) solves these problems.
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Harris corner detector
Noisy response due to a binary window function Use a Gaussian function
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Harris corner detector
Only a set of shifts at every 45 degree is consideredConsider all small shifts by Taylor’s expansion
yxyx
yxy
yxx
yxIyxIyxwC
yxIyxwB
yxIyxwA
BvCuvAuvuE
,
,
2
,
2
22
),(),(),(
),(),(
),(),(
2),(
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Harris corner detector
( , ) ,u
E u v u v Mv
Equivalently, for small shifts [u,v] we have a bilinear approximation:
2
2,
( , ) x x y
x y x y y
I I IM w x y
I I I
, where M is a 22 matrix computed from image derivatives:
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Harris corner detector
Responds too strong for edges because only minimum of E is taken into accountA new corner measurement
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Harris corner detector
( , ) ,u
E u v u v Mv
Intensity change in shifting window: eigenvalue analysis
1, 2 – eigenvalues of M
direction of the slowest chan
ge
direction of the fastest change
(max)-1/2
(min)-1/2
Ellipse E(u,v) = const
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Harris corner detector
1
2
Corner1 and 2 are large,
1 ~ 2;
E increases in all directions
1 and 2 are small;
E is almost constant in all directions
edge 1 >> 2
edge 2 >> 1
flat
Classification of image points using eigenvalues of M:
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Harris corner detector
Measure of corner response:
2det traceR M k M
1 2
1 2
det
trace
M
M
(k – empirical constant, k = 0.04-0.06)
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Another view
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Another view
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Another view
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Summary of Harris detector
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Harris corner detector (input)
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Corner response R
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Threshold on R
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Local maximum of R
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Harris corner detector
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Harris Detector: Summary• Average intensity change in direction [u,v] can be e
xpressed as a bilinear form:
• Describe a point in terms of eigenvalues of M:measure of corner response
• A good (corner) point should have a large intensity change in all directions, i.e. R should be large positive
( , ) ,u
E u v u v Mv
2
1 2 1 2R k
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Harris Detector: Some Properties• Partial invariance to affine intensity change
Only derivatives are used => invariance to intensity shift I I + b
Intensity scale: I a I
R
x (image coordinate)
threshold
R
x (image coordinate)
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Harris Detector: Some Properties• Rotation invariance
Ellipse rotates but its shape (i.e. eigenvalues) remains the sameCorner response R is invariant to image rotation
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Harris Detector is rotation invariant
Repeatability rate:# correspondences
# possible correspondences
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Harris Detector: Some Properties
• But: non-invariant to image scale!
All points will be classified as edges
Corner !
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Harris Detector: Some Properties• Quality of Harris detector for different scale
changes
Repeatability rate:# correspondences
# possible correspondences
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SIFT (Scale Invariant Feature
Transform)
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SIFT• SIFT is an carefully designed procedure
with empirically determined parameters for the invariant and distinctive features.
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SIFT stages:
• Scale-space extrema detection• Keypoint localization• Orientation assignment• Keypoint descriptor
( )local descriptor
detector
descriptor
A 500x500 image gives about 2000 features
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1. Detection of scale-space extrema• For scale invariance, search for stable features
across all possible scales using a continuous function of scale, scale space.
• SIFT uses DoG filter for scale space because it is efficient and as stable as scale-normalized Laplacian of Gaussian.
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DoG filteringConvolution with a variable-scale Gaussian
Difference-of-Gaussian (DoG) filter
Convolution with the DoG filter
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Scale space doubles for the next octave
K=2(1/s), s+3 images for each octave
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Keypoint localization
X is selected if it is larger or smaller than all 26 neighbors
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Decide scale sampling frequency
• It is impossible to sample the whole space, tradeoff efficiency with completeness.
• Decide the best sampling frequency by experimenting on 32 real image subject to synthetic transformations.
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Decide scale sampling frequency
S=3, for larger s, too many unstable features
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Decide scale sampling frequency
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Pre-smoothing
=1.6, plus a double expansion
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Scale invariance
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2. Accurate keypoint localization• Reject points with low contrast and poorly
localized along an edge• Fit a 3D quadratic function for sub-pixel
maxima
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Accurate keypoint localization
If has offset larger than 0.5, sample point is changed.
If is less than 0.03 (low contrast), it is discarded.
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Eliminating edge responses
r=10
Let
Keep the points with
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Keypoint detector
(a) 233x189 image(b) 832 DOG extrema(c) 729 left after peak value threshold(d) 536 left after testing ratio of principle curvatures
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3. Orientation assignment
• By assigning a consistent orientation, the keypoint descriptor can be orientation invariant.
• For a keypoint, L is the image with the closest scale,
orientation histogram
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Orientation assignment
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Orientation assignment
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Orientation assignment
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Orientation assignment
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Orientation assignment
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Orientation assignment
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Orientation assignment
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Orientation assignment
0 2
36-bin orientation histogram over 360°,
weighted by m and 1.5*scale falloffPeak is the orientationLocal peak within 80% creates
multiple orientationsAbout 15% has multiple orientations
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Orientation invariance
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4. Local image descriptor
• Thresholded image gradients are sampled over 16x16 array of locations in scale space
• Create array of orientation histograms• 8 orientations x 4x4 histogram array = 128 dimensions• Normalized, clip the components larger than 0.2
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Why 4x4x8?
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Sensitivity to affine change
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SIFT demo
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Maxima in D
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Remove low contrast
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Remove edges
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SIFT descriptor
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Estimated rotation
• Computed affine transformation from rotated image to original image:
0.7060 -0.7052 128.4230 0.7057 0.7100 -128.9491 0 0 1.0000
• Actual transformation from rotated image to original image:
0.7071 -0.7071 128.6934 0.7071 0.7071 -128.6934 0 0 1.0000
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SIFT extensions
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PCA
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PCA-SIFT
• Only change step 4• Pre-compute an eigen-space for local gradient
patches of size 41x41• 2x39x39=3042 elements• Only keep 20 components• A more compact descriptor
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GLOH (Gradient location-orientation histogram)
17 location bins16 orientation binsAnalyze the 17x16=272-d eigen-space, keep 128 components
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Applications
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Recognition
SIFT Features
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3D object recognition
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3D object recognition
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Office of the past
Video of desk Images from PDF
Track & recognize
T T+1
Internal representation
Scene Graph
Desk Desk
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…> 5000images
change in viewing angle
Image retrieval
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22 correct matches
Image retrieval
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…> 5000images
change in viewing angle
+ scale change
Image retrieval
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Robot location
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Robotics: Sony AiboSIFT is used for Recognizing
charging station
Communicating with visual cards
Teaching object recognition
soccer
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Structure from Motion
• The SFM Problem– Reconstruct scene geometry and camera
motion from two or more images
Track2D Features Estimate
3D Optimize(Bundle Adjust)
Fit Surfaces
SFM Pipeline
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Structure from Motion
Poor mesh Good mesh
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Augmented reality
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Automatic image stitching
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Automatic image stitching
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Automatic image stitching
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Automatic image stitching
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Automatic image stitching
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Automatic image stitching
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Reference• Chris Harris, Mike Stephens,
A Combined Corner and Edge Detector, 4th Alvey Vision Conference, 1988, pp147-151.
• David G. Lowe, Distinctive Image Features from Scale-Invariant Keypoints, International Journal of Computer Vision, 60(2), 2004, pp91-110.
• Yan Ke, Rahul Sukthankar, PCA-SIFT: A More Distinctive Representation for Local Image Descriptors, CVPR 2004.
• Krystian Mikolajczyk, Cordelia Schmid, A performance evaluation of local descriptors, Submitted to PAMI, 2004.
• SIFT Keypoint Detector, David Lowe.• Matlab SIFT Tutorial, University of Toronto.