scale invariant feature transform · fundamental theory 6 dog (edge) scale-space axioms. ......
TRANSCRIPT
2019-04-10
Scale Invariant Feature Transform
Han Sol Kang
ISL Lab Seminar
: SIFT
2019-04-10
Contents
2
Fundamental theory
SIFT
Introduction
Example
Summary
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Introduction
3
illumination illumination + Scale
illumination + Scale + Rotation illumination + Scale Rotation + Affine
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Introduction
4
David G Lowe
[2] Lowe, David G. "Distinctive image features from scale-invariant keypoints." International journal of computer vision 60.2 (2004): 91-110.
[1] Lowe, David G. "Object recognition from local scale-invariant features." Computer vision, 1999. The proceedings of the seventh IEEE international conference on. Vol. 2. Ieee, 1999.
A senior research scientist at Google (Seattle) in the Machine Intelligence Group.
99: Object recognition from local scale-invariant features [1]
04: Distinctive Image Features from Scale-Invariant Keypoints [2]
Autostich
: Atuomated paranoma creation
SIFT
: Matching with local invariant features
Augmented reality in natural scenes
[Overview of Research Projects]
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Introduction
5
Scale-Space Extrema Detection
Accurate KeypointLocalization
Orientation Assignment
KeypointDescription
Search over multiple scales and Image locations.
Select keypoints based on a measure of stability.
Compute best orientation(s) for each keypoint region.
Use local image gradients at selected scale and rotation to describe each keypoint region.
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Fundamental theory
6
DOG (edge)
Scale-space axioms
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Fundamental theory
7
LOG (blob)
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Fundamental theory
8
Normalized LOG
Normalization : LOG
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Fundamental theory
9
DOG & LOG
GkyxGkyxG 22)1(),,(),,(
GG 2
Heat Diffusion Equation
k
yxGkyxGG ),,(),,(
)()1()1( 22 GaussianofLaplacianNormalizedNLOGkGkDOG
1:
2:
DOG:
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Fundamental theory
10
Gaussian Pyramid
-
-
-
Difference of Gaussian(DOG)Gaussian
Convolution with
Gaussian
2
2
22
-4
-
-
-Downsample
Scale
(next
octave)
…
Scale
(1st octave)
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SIFT
11
Detection of Scale-Space Extrema
Extrema : maxima & minima
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SIFT
12
Detection of Scale-Space Extrema
Scale
),(*),,(),,( yxIyxGyxL
222 2/)(
22
1),,(
yxeyxG
),,(),,(
),(*)),,(),,((),,(
yxLkyxL
yxIyxGkyxGyxD
GkyxGkyxG 2)1(),,(),,(
sk /12:ratioscaling
s:interval
3s:ImageGaussianofnumberthe
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aerial photographs, industrial images)
SIFT
Detection of Scale-Space Extrema
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14
xx
xxx
2
2T
2
1)x(
DDDD
T
xxx
DD2
12
-ˆ
xx
x ˆ2
1)ˆ(
TDDD
))(( Tx,y,σxxxx
2
2
0)x('
DDD
T
xx
x
TDD2
2
xxx
TDD2
12
SIFT
Accurate Keypoint Localization (low contrast)
xxx
xx
ˆˆ
2
1ˆ
ˆ)ˆ(
TT
T DDDD
xx
xx
ˆˆ2
1ˆ
ˆ
TT DDD
xx
ˆˆ2
1
TDD
)5.0ˆ( xif
)03.0)ˆ(( xDif
Taylor Expansion
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SIFT
Accurate Keypoint Localization (edge)
yyxx DD)Tr(H 2)()Det( xyyyxx DDDH
r
r
r
r 2
2
222 )1()()(
)Det(
)(Tr
H
H
r
r 22 )1(
)Det(
)(Tr
H
H)10( r
yyxy
xyxx
DD
DDH Hessian Matrix
)(
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SIFT
Accurate Keypoint Localization
(a) 233x189 pixel original image
(d) 536 keypoints location
(threshold on ratio of principal curvatures)
(c) 729 keypoints location (threshold on minimum contrast)
(b) 832 keypoints location
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SIFT
Orientation Assignment
22 ))1,()1,(()),1(),1((),( yxLyxLyxLyxLyxm
))),1(),1(/())1,()1,(((tan),( 1 yxLyxLyxLyxLyx
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SIFT
Orientation Assignment
Histogram : Using 36bins
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SIFT
The Local Images Descriptor
illumination : normalization vector
(Feature vector < 0.2)
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SIFT
The Local Images Descriptor
r : the number of orientations
n : the width
The size of the resulting
descriptor vector is 2rn
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SIFT
Keypoint Matching
Object model
(train image)Test image
DB
offline online
1) Nearest-neighbor search
2) Cluster identification by Hough transform
voting
3) Model verification by linear least squares
4) Outlier detection
: Euclidean distance, K-D tree, BBF(Best-Bin-First)
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SIFT
Keypoint Matching
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Example
Recognition
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Example
Recognition
Q & A
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y
x
t
t
y
x
mm
mm
v
u
43
21
v
u
t
t
m
m
m
m
yx
yx
y
x
4
3
2
1
...
...
1000
0100
bAx
bAA][AxT1T