features digital visual effects yung-yu chuang with slides by trevor darrell cordelia schmid, david...
TRANSCRIPT
![Page 1: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/1.jpg)
Features
Digital Visual EffectsYung-Yu Chuang
with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins and Jiwon Kim
![Page 2: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/2.jpg)
Outline
• Features• Harris corner detector• SIFT• Extensions• Applications
![Page 3: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/3.jpg)
Features
![Page 4: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/4.jpg)
Features
• Also known as interesting points, salient points or keypoints. Points that you can easily point out their correspondences in multiple images using only local information.
?
![Page 5: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/5.jpg)
Desired properties for features
• Distinctive: a single feature can be correctly matched with high probability.
• Invariant: invariant to scale, rotation, affine, illumination and noise for robust matching across a substantial range of affine distortion, viewpoint change and so on. That is, it is repeatable.
![Page 6: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/6.jpg)
Applications
• Object or scene recognition• Structure from motion• Stereo• Motion tracking• …
![Page 7: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/7.jpg)
Components
• Feature detection locates where they are
• Feature description describes what they are
• Feature matching decides whether two are the same one
![Page 8: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/8.jpg)
Harris corner detector
![Page 9: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/9.jpg)
Moravec corner detector (1980)
• We should easily recognize the point by looking through a small window
• Shifting a window in any direction should give a large change in intensity
![Page 10: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/10.jpg)
Moravec corner detector
flat
![Page 11: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/11.jpg)
Moravec corner detector
flat
![Page 12: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/12.jpg)
Moravec corner detector
flat edge
![Page 13: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/13.jpg)
Moravec corner detector
flat edgecorner
isolated point
![Page 14: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/14.jpg)
yx
yxIvyuxIyxwvuE,
2),(),(),(),(
Moravec corner detector
Change of intensity for the shift [u,v]:
window functio
n
Four shifts: (u,v) = (1,0), (1,1), (0,1), (-1, 1)Look for local maxima in min{E}
intensity
shifted intensit
y
![Page 15: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/15.jpg)
Problems of Moravec detector
• Noisy response due to a binary window function• Only a set of shifts at every 45 degree is
considered• Only minimum of E is taken into account
Harris corner detector (1988) solves these problems.
![Page 16: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/16.jpg)
Harris corner detector
Noisy response due to a binary window functionUse a Gaussian function
![Page 17: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/17.jpg)
Harris corner detector
Only a set of shifts at every 45 degree is consideredConsider all small shifts by Taylor’s expansion
![Page 18: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/18.jpg)
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),(
yx
yxIvyuxIyxwvuE,
2),(),(),(),(
yx
yx vuOvIuIyxw,
222 ),(),(
![Page 19: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/19.jpg)
Harris corner detector
Equivalently, for small shifts [u,v] we have a bilinear approximation:
, where M is a 22 matrix computed from image derivatives:
v
uvuvuE ),( M
yx yyx
yxx
III
IIIyxw
,2
2
),(M
![Page 20: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/20.jpg)
Harris corner detector (matrix form)
Muu
uxx
u
ux
ux
xux 00
T
TT
T
T
II
I
II
I
II
2
2
00
2|)()(|
)(
2|)()(|)()(px
000
0
xuxxuW
IIwE
![Page 21: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/21.jpg)
Harris corner detector
Only minimum of E is taken into accountA new corner measurement by investigating the shape of the error function
represents a quadratic function; Thus, we can analyze E’s shape by looking at the property of M
MuuT
![Page 22: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/22.jpg)
Harris corner detector
High-level idea: what shape of the error function will we prefer for features?
02
46
810
12
0
5
10
0
20
40
60
80
100
02
46
810
12
0
5
10
0
20
40
60
80
100
02
46
810
12
0
5
10
0
20
40
60
80
100
flat edge corner
![Page 23: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/23.jpg)
Quadratic forms
• Quadratic form (homogeneous polynomial of degree two) of n variables xi
• Examples
=
![Page 24: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/24.jpg)
Symmetric matrices
• Quadratic forms can be represented by a real symmetric matrix A where
![Page 25: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/25.jpg)
Eigenvalues of symmetric matrices
Brad Osgood
![Page 26: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/26.jpg)
Eigenvectors of symmetric matrices
![Page 27: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/27.jpg)
Eigenvectors of symmetric matrices
zz
yΛyΛ
Λyy
xQΛxQ
xQΛQx
Axx
T
T
T
TTT
TT
T
21
21
11q22 q
1 xxT
1zzT
![Page 28: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/28.jpg)
Harris corner detector
Intensity change in shifting window: eigenvalue analysis
1, 2 – eigenvalues of M
direction of the slowest
change
direction of the fastest
change
(max)-1/2
(min)-1/2
Ellipse E(u,v) = const
v
uvuvuE ,),( M
![Page 29: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/29.jpg)
Visualize quadratic functions
T
10
01
10
01
10
01
10
01A
![Page 30: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/30.jpg)
Visualize quadratic functions
T
10
01
10
04
10
01
10
04A
![Page 31: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/31.jpg)
Visualize quadratic functions
T
50.087.0
87.050.0
40
01
50.087.0
87.050.0
75.130.1
30.125.3A
![Page 32: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/32.jpg)
Visualize quadratic functions
T
50.087.0
87.050.0
100
01
50.087.0
87.050.0
25.390.3
90.375.7A
![Page 33: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/33.jpg)
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:
![Page 34: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/34.jpg)
Harris corner detector
Measure of corner response:
(k – empirical constant, k = 0.04-0.06)
2
4)( 01102
11001100 aaaaaa
2tracedet MM kR
21
21
trace
det
M
M
Only for reference, you do not need them to compute R
![Page 35: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/35.jpg)
Harris corner detector
![Page 36: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/36.jpg)
Another view
![Page 37: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/37.jpg)
Another view
![Page 38: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/38.jpg)
Another view
![Page 39: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/39.jpg)
Summary of Harris detector
1. Compute x and y derivatives of image
2. Compute products of derivatives at every pixel
3. Compute the sums of the products of derivatives at each pixel
IGI xx IGI y
y
xxxIII 2 yyy
III 2 yxxy III
22 ' xxIGS 22 ' yy
IGS xyxy IGS '
![Page 40: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/40.jpg)
Summary of Harris detector
4. Define the matrix at each pixel
5. Compute the response of the detector at each pixel
6. Threshold on value of R; compute nonmax suppression.
),(),(
),(),(),(
2
2
yxSyxS
yxSyxSyxM
yxy
xyx
2tracedet MkMR
![Page 41: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/41.jpg)
Harris corner detector (input)
![Page 42: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/42.jpg)
Corner response R
![Page 43: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/43.jpg)
Threshold on R
![Page 44: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/44.jpg)
Local maximum of R
![Page 45: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/45.jpg)
Harris corner detector
![Page 46: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/46.jpg)
Harris detector: summary
• Average intensity change in direction [u,v] can be expressed 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
v
uvuvuE ,),( M
22121 kR
![Page 47: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/47.jpg)
Now we know where features are
• But, how to match them?• What is the descriptor for a feature? The
simplest solution is the intensities of its spatial neighbors. This might not be robust to brightness change or small shift/rotation.
( )
1 2 3
4 5 6
7 8 9
1 2 3 4 5 6 7 8 9
![Page 48: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/48.jpg)
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)
![Page 49: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/49.jpg)
Harris Detector: Some Properties
• Rotation invariance
Ellipse rotates but its shape (i.e. eigenvalues) remains the same
Corner response R is invariant to image rotation
![Page 50: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/50.jpg)
Harris Detector is rotation invariantRepeatability rate:
# correspondences# possible correspondences
![Page 51: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/51.jpg)
Harris Detector: Some Properties
• But: not invariant to image scale!
All points will be classified as edges
Corner !
![Page 52: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/52.jpg)
Harris detector: some properties
• Quality of Harris detector for different scale changes
Repeatability rate:# correspondences
# possible correspondences
![Page 53: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/53.jpg)
Scale invariant detection
• Consider regions (e.g. circles) of different sizes around a point
• Regions of corresponding sizes will look the same in both images
![Page 54: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/54.jpg)
Scale invariant detection
• The problem: how do we choose corresponding circles independently in each image?
• Aperture problem
![Page 55: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/55.jpg)
SIFT (Scale Invariant Feature
Transform)
![Page 56: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/56.jpg)
SIFT• SIFT is an carefully designed procedure
with empirically determined parameters for the invariant and distinctive features.
![Page 57: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/57.jpg)
SIFT stages:
• Scale-space extrema detection• Keypoint localization• Orientation assignment• Keypoint descriptor
( )local descriptor
detector
descriptor
A 500x500 image gives about 2000 features
![Page 58: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/58.jpg)
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.
![Page 59: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/59.jpg)
DoG filtering
Convolution with a variable-scale Gaussian
Difference-of-Gaussian (DoG) filter
Convolution with the DoG filter
![Page 60: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/60.jpg)
Scale space doubles for the next
octave
K=2(1/
s)
Dividing into octave is for efficiency only.
![Page 61: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/61.jpg)
Detection of scale-space extrema
![Page 62: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/62.jpg)
Keypoint localization
X is selected if it is larger or smaller than all 26 neighbors
![Page 63: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/63.jpg)
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. (rotation, scaling, affine stretch, brightness and contrast change, adding noise…)
![Page 64: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/64.jpg)
Decide scale sampling frequency
![Page 65: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/65.jpg)
Decide scale sampling frequency
s=3 is the best, for larger s, too many unstable features
for detector, repeatability
for descriptor, distinctiveness
![Page 66: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/66.jpg)
Pre-smoothing
=1.6, plus a double expansion
![Page 67: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/67.jpg)
Scale invariance
![Page 68: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/68.jpg)
2. Accurate keypoint localization
• Reject points with low contrast (flat) and poorly localized along an edge (edge)
• Fit a 3D quadratic function for sub-pixel maxima
1
65
0-1 +1
![Page 69: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/69.jpg)
2. Accurate keypoint localization
• Reject points with low contrast (flat) and poorly localized along an edge (edge)
• Fit a 3D quadratic function for sub-pixel maxima
1
65
0-1 +1
2
2
)0('')0(')0()( x
fxffxf
3
1ˆ x
22 3262
626)( xxxxxf
062)(' xxf
3
16
3
13
3
126)ˆ(
2
xf
3
16
3
1
![Page 70: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/70.jpg)
2. Accurate keypoint localization
• Taylor series of several variables
• Two variables
222
22
22
1)0,0(),( y
yy
fxy
yx
fx
xx
fy
y
fx
x
ffyxf
y
x
yy
f
yx
fyx
f
xx
f
yxy
x
y
f
x
ff
y
xf 22
22
2
1
0
0
xx
xxx
0x2
2
2
1
ffff T
T
![Page 71: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/71.jpg)
Accurate keypoint localization
• Taylor expansion in a matrix form, x is a vector, f maps x to a scalar
nx
f
x
fx
f
1
1
2
2
2
2
1
2
2
2
22
2
12
21
2
21
2
21
2
nnn
n
n
x
f
xx
f
xx
f
xx
f
x
f
xx
fxx
f
xx
f
x
f
Hessian matrix(often symmetric)
gradient
![Page 72: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/72.jpg)
2D illustration
![Page 73: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/73.jpg)
2D example
-17 -1 -1
7
77
7
-9
-9
![Page 74: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/74.jpg)
Derivation of matrix form
xgx T)(h x
h
![Page 75: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/75.jpg)
Derivation of matrix form
xgx T)(h
n
n
x
x
gg 1
1
n
iii xg
1
gx
n
n
g
g
x
h
x
h
h1
1
![Page 76: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/76.jpg)
Derivation of matrix form
Axxx T)(h
x
h
![Page 77: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/77.jpg)
Derivation of matrix form
Axxx T)(h
nnnn
n
n
x
x
aa
aa
xx
1
1
111
1
n
i
n
jjiij xxa
1 1
AxxAx
T
n
i
n
jjnjiin
n
i
n
jjjii
n
xaxa
xaxa
x
h
x
h
h
1 1
1 111
1
xAAT )(
![Page 78: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/78.jpg)
Derivation of matrix form
xff
xffff
T
2
2
2
2
2
2
2
1
xxxxxx
![Page 79: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/79.jpg)
Accurate keypoint localization
• x is a 3-vector• Change sample point if offset is larger
than 0.5• Throw out low contrast (<0.03)
![Page 80: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/80.jpg)
Accurate keypoint localization
• Throw out low contrast 03.0|)ˆ(| xD
xx
xx
xx
xxxx
x
xxxxxx
x
xxxxxx
x
xx
xxx
x
ˆ2
1
)ˆ(2
1ˆ
2
1ˆ
2
1ˆ
2
1ˆ
ˆˆ2
1ˆ)ˆ(
1
2
2
1
2
2
2
2
2
2
1
2
2
2
21
2
2
2
2
T
TT
TT
TTT
TT
TT
DD
DDD
DDDDD
DDDDDDD
DDDDDDD
DDDD
![Page 81: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/81.jpg)
Eliminating edge responses
r=10
Let
Keep the points with
Hessian matrix at keypoint location
![Page 82: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/82.jpg)
Maxima in D
![Page 83: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/83.jpg)
Remove low contrast and edges
![Page 84: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/84.jpg)
Keypoint detector
233x89 832 extrema
729 after con-trast filtering
536 after cur-vature filtering
![Page 85: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/85.jpg)
3. Orientation assignment
• By assigning a consistent orientation, the keypoint descriptor can be orientation invariant.
• For a keypoint, L is the Gaussian-smoothed image with the closest scale,
orientation histogram (36 bins)
(Lx, Ly)
m
θ
![Page 86: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/86.jpg)
Orientation assignment
![Page 87: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/87.jpg)
Orientation assignment
![Page 88: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/88.jpg)
Orientation assignment
![Page 89: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/89.jpg)
Orientation assignment
σ=1.5*scale of the keypoint
![Page 90: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/90.jpg)
Orientation assignment
![Page 91: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/91.jpg)
Orientation assignment
![Page 92: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/92.jpg)
Orientation assignmentaccurate peak position is determined by fitting
![Page 93: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/93.jpg)
Orientation assignment
0 2
36-bin orientation histogram over 360°,
weighted by m and 1.5*scale falloff
Peak is the orientationLocal peak within 80% creates
multiple orientationsAbout 15% has multiple
orientations and they contribute a lot to stability
![Page 94: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/94.jpg)
SIFT descriptor
![Page 95: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/95.jpg)
4. Local image descriptor• Thresholded image gradients are sampled over
16x16 array of locations in scale space• Create array of orientation histograms (w.r.t. key
orientation)• 8 orientations x 4x4 histogram array = 128
dimensions• Normalized, clip values larger than 0.2,
renormalize
σ=0.5*width
![Page 96: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/96.jpg)
Why 4x4x8?
![Page 97: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/97.jpg)
Sensitivity to affine change
![Page 98: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/98.jpg)
Feature matching
• for a feature x, he found the closest feature x1 and the second closest feature x2. If the distance ratio of d(x, x1) and d(x, x1) is smaller than 0.8, then it is accepted as a match.
![Page 99: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/99.jpg)
SIFT flow
![Page 100: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/100.jpg)
Maxima in D
![Page 101: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/101.jpg)
Remove low contrast
![Page 102: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/102.jpg)
Remove edges
![Page 103: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/103.jpg)
SIFT descriptor
![Page 104: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/104.jpg)
![Page 105: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/105.jpg)
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
![Page 106: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/106.jpg)
SIFT extensions
![Page 107: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/107.jpg)
PCA
![Page 108: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/108.jpg)
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
![Page 109: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/109.jpg)
GLOH (Gradient location-orientation histogram)
17 location bins16 orientation binsAnalyze the 17x16=272-d eigen-space, keep 128 components
SIFT is still considered the best.
SIFT
![Page 110: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/110.jpg)
Multi-Scale Oriented Patches• Simpler than SIFT. Designed for image
matching. [Brown, Szeliski, Winder, CVPR’2005]
• Feature detector– Multi-scale Harris corners– Orientation from blurred gradient– Geometrically invariant to rotation
• Feature descriptor– Bias/gain normalized sampling of local patch
(8x8)– Photometrically invariant to affine changes in
intensity
![Page 111: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/111.jpg)
Multi-Scale Harris corner detector
• Image stitching is mostly concerned with matching images that have the same scale, so sub-octave pyramid might not be necessary.
2s
![Page 112: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/112.jpg)
Multi-Scale Harris corner detector
smoother version of gradients
Corner detection function:
Pick local maxima of 3x3 and larger than 10
![Page 113: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/113.jpg)
Keypoint detection function
Experiments show roughly the same performance.
![Page 114: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/114.jpg)
Non-maximal suppression
• Restrict the maximal number of interest points, but also want them spatially well distributed
• Only retain maximums in a neighborhood of radius r.
• Sort them by strength, decreasing r from infinity until the number of keypoints (500) is satisfied.
![Page 115: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/115.jpg)
Non-maximal suppression
![Page 116: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/116.jpg)
Sub-pixel refinement
![Page 117: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/117.jpg)
Orientation assignment
• Orientation = blurred gradient
![Page 118: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/118.jpg)
Descriptor Vector• Rotation Invariant Frame
– Scale-space position (x, y, s) + orientation ()
![Page 119: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/119.jpg)
MSOP descriptor vector• 8x8 oriented patch sampled at 5 x scale.
See TR for details. • Sampled from with
spacing=5
8 pixels40 pixels
![Page 120: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/120.jpg)
MSOP descriptor vector• 8x8 oriented patch sampled at 5 x scale.
See TR for details. • Bias/gain normalisation: I’ = (I – )/• Wavelet transform
8 pixels40 pixels
![Page 121: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/121.jpg)
Detections at multiple scales
![Page 122: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/122.jpg)
Summary
• Multi-scale Harris corner detector• Sub-pixel refinement• Orientation assignment by gradients• Blurred intensity patch as descriptor
![Page 123: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/123.jpg)
Feature matching• Exhaustive search
– for each feature in one image, look at all the other features in the other image(s)
• Hashing– compute a short descriptor from each feature
vector, or hash longer descriptors (randomly)
• Nearest neighbor techniques– k-trees and their variants (Best Bin First)
![Page 124: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/124.jpg)
Wavelet-based hashing• Compute a short (3-vector) descriptor
from an 8x8 patch using a Haar “wavelet”
• Quantize each value into 10 (overlapping) bins (103 total entries)
• [Brown, Szeliski, Winder, CVPR’2005]
![Page 125: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/125.jpg)
Nearest neighbor techniques• k-D tree
and
• Best BinFirst(BBF)
Indexing Without Invariants in 3D Object Recognition, Beis and Lowe, PAMI’99
![Page 126: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/126.jpg)
Applications
![Page 127: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/127.jpg)
Recognition
SIFT Features
![Page 128: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/128.jpg)
3D object recognition
![Page 129: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/129.jpg)
3D object recognition
![Page 130: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/130.jpg)
Office of the past
Video of desk Images from PDF
Track & recognize
T T+1
Internal representation
Scene Graph
Desk Desk
![Page 131: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/131.jpg)
…> 5000images
change in viewing angle
Image retrieval
![Page 132: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/132.jpg)
22 correct matches
Image retrieval
![Page 133: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/133.jpg)
…> 5000images
change in viewing angle
+ scale change
Image retrieval
![Page 134: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/134.jpg)
Robot location
![Page 135: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/135.jpg)
Robotics: Sony Aibo
SIFT is used for Recognizing
charging station
Communicating with visual cards
Teaching object recognition
soccer
![Page 136: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/136.jpg)
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
![Page 137: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/137.jpg)
Structure from Motion
Poor mesh Good mesh
![Page 138: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/138.jpg)
Augmented reality
![Page 139: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/139.jpg)
Automatic image stitching
![Page 140: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/140.jpg)
Automatic image stitching
![Page 141: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/141.jpg)
Automatic image stitching
![Page 142: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/142.jpg)
Automatic image stitching
![Page 143: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/143.jpg)
Automatic image stitching
![Page 144: Features Digital Visual Effects Yung-Yu Chuang with slides by Trevor Darrell Cordelia Schmid, David Lowe, Darya Frolova, Denis Simakov, Robert Collins](https://reader036.vdocuments.net/reader036/viewer/2022062308/56649d345503460f94a0b07f/html5/thumbnails/144.jpg)
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.