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Image ORB feature

G
Gavin Gao

图像处理之ORB特征,主要讲ORB特征的理论

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ORB 特征
高洪臣
cggos@outlook.com
2020 年 7 月 10 日
高洪臣 ORB 特征 2020 年 7 月 10 日 1 / 12
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Image Features
feature types
feature extraction(detection) & matching
• feature detector
• feature descriptor
高洪臣 ORB 特征 2020 年 7 月 10 日 2 / 12
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Corner / Keypoint / Interest Point
• keypoint detector
• Harris (1988)
• Shi-Tomas (1994)
• FAST1
(Features from Accelerated and Segments Test) (2006)
• AGAST (2010)
• keypoint descriptor
• BRIEF2
(Binary robust independent elementary feature) (2010)
• keypoint detector & descriptor
• SIFT (1999, 2004)
• SURF (2006)
• BRISK (Binary Robust Invariant Scalable Keypoints) (2011)
• ORB3
(2011)
• FREAK (2012)
• KAZE (2012)
1Edward Rosten and Tom Drummond. “Machine Learning for High-Speed Corner Detection.”. In: ECCV (1).
Ed. by Ales Leonardis, Horst Bischof, and Axel Pinz. Vol. 3951. Lecture Notes in Computer Science. Springer,
2006, pp. 430–443. isbn: 3-540-33832-2. url: http://dblp.uni-trier.de/db/conf/eccv/eccv2006-1.html#RostenD06.
2Michael Calonder et al. “BRIEF: Binary Robust Independent Elementary Features”. In:
Proceedings of the 11th European Conference on Computer Vision: Part IV. ECCV’10. Heraklion, Crete,
Greece: Springer-Verlag, 2010, pp. 778–792. isbn: 364215560X.
3Ethan Rublee et al. “ORB: An efficient alternative to SIFT or SURF”. In:
2011 International conference on computer vision. Ieee. 2011, pp. 2564–2571.
高洪臣 ORB 特征 2020 年 7 月 10 日 3 / 12
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ORB Overview
ORB = Oriented FAST + Rotated BRIEF
• oFAST (ORB Detector)
• keypoint position - FAST
• keypoint orientation - image patch moment
• keypoint response/score - NMS(Non-Maximal Supression)
• scale-invariant - image pyramid
• rBRIEF (ORB Descriptor)
• keypoint descriptor - BRIEF
• rotation-invariant - keypoint orientation
高洪臣 ORB 特征 2020 年 7 月 10 日 4 / 12
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Multiscale Image Pyramid
Parameters
• level: 8
• scale: 1.2
• downsample:
bilinear interpolation
produce FAST features and compute descriptors at each level in the pyramid
高洪臣 ORB 特征 2020 年 7 月 10 日 5 / 12
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FAST
fast-9
•  9 contiguous pixels in a circle (of 16 pixels) brighter than Ip + t or darker than Ip − t
• Rapid rejection by testing 1, 9, 5 then 13
NMS (Non-Maximal Suppression) 1
remove corners which have an adjacent corner with higher score
Uniform Distribution
DistributeOctTree() 2
1all called non-maximum suppression
2use Quad-Tree to iteratively segment image regions in ORB-SLAM2
高洪臣 ORB 特征 2020 年 7 月 10 日 6 / 12
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Orientation by Intensity Centroid (IC)
the moments of a patch:
mpq =
∑
x,y
xp
yq
I(x, y)
the first order moment of a patch 1
I (radius = 15):
m10 =
15∑
x=−15
15∑
y=−15
xI(x, y) =
15∑
y=0
15∑
x=−15
x [I(x, y) − I(x, −y)]
m01 =
15∑
x=−15
15∑
y=−15
yI(x, y) =
15∑
y=1
15∑
x=−15
y [I(x, y) − I(x, −y)]
the intensity centroid:
C =
(
m10
m00
,
m01
m00
)
the orientation (from the corner’s center to the centroid):
θ = atan 2 (m01, m10)
1a circular patch
高洪臣 ORB 特征 2020 年 7 月 10 日 7 / 12
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Image Gaussian Filtering/Blurring/Smoothing 1
why filtering
start by smoothing image using a Gaussian kernel at each level in the pyramid in order to
prevent the descriptor from being sensitive to high-frequency noise
Gaussian Kernel
G(u, v) =
1
2πσ2
e
− u2+v2
2σ2
Gn(u, v) =
1
s
· e
− u2+v2
2σ2 , s =
w∑
u=−w
w∑
v=−w
e
− u2+v2
2σ2
(a) (u,v) (b) kernel (σ=1.5) (c) normalized
Image Gaussian Filtering: I′(i, j) =
∑w
u=−w
∑w
v=−w
I(i + u, j + v)Gn(u, v)
1low-pass filter
高洪臣 ORB 特征 2020 年 7 月 10 日 8 / 12
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Separability of the Gaussian filter
s =
w∑
u=−w
w∑
v=−w
g(u) · g(v) =
( w∑
u=−w
g(u)
)
·
( w∑
v=−w
g(v)
)
= s′
· s′
Gn(u, v) =
1
s
· e− u2
2σ2
· e− v2
2σ2
=
1
s
· g(u) · g(v) =
g(u)
s′
·
g(v)
s′
Separable Kernel Matrix:
G(2w+1)×(2w+1) =
1
s








g(−w)g(−w) . . . g(−w)g(0) . . . g(−w)g(w)
...
...
...
g(0)g(−w) . . . g(0)g(0) . . . g(0)g(w)
...
...
...
g(w)g(−w) . . . g(w)g(0) . . . g(w)g(w)








=
1
s′








g(−w)
...
g(0)
...
g(w)








·
1
s′
[
g(−w) . . . g(0) . . . g(w)
]
高洪臣 ORB 特征 2020 年 7 月 10 日 9 / 12
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Separability of the Gaussian filter
Image Gaussian Filtering:
I′
(i, j) =
w∑
u=−w
w∑
v=−w
I(i + u, j + v)Gn(u, v)
=
w∑
u=−w
w∑
v=−w
I(i + u, j + v)
1
s
g(u)g(v)
=
w∑
u=−w
w∑
v=−w
I(i + u, j + v)
1
s′
g(u)
1
s′
g(v)
=
w∑
u=−w
[ w∑
v=−w
I(i + u, j + v)
g(v)
s′
]
g(u)
s′
=
w∑
u=−w
S(i + u)
g(u)
s′
• kernel size: (2w + 1) × (2w + 1), w = 3
1 int gaussKernel[4] = { 224, 192, 136, 72 };
高洪臣 ORB 特征 2020 年 7 月 10 日 10 / 12
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BRIEF
• vector dim: 256 bits (32 bytes)
• each vector ←→ each keypoint
for each bit, select a pair of points in a patch I which centered a corner p and compare
their intensity
S =
( p1, . . . , pn
q1, . . . , qn
)
∈ R(2×2)×256
τ(I; pi, qi) :=
{
1 : I(pi)  I(qi)
0 : I(pi) ≥ I(qi)
the descriptor (each bit ←→ each pair of points (pi, qi)):
f(n) =
n
∑
i=1
2i−1
τ(I; pi, qi), (n = 256)
高洪臣 ORB 特征 2020 年 7 月 10 日 11 / 12
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rBRIEF
• construct a lookup table of precomputed BRIEF patterns
1 static int ORB_pattern[256*4] = {
2 8, -3, 9, 5,
3 4, 2, 7,-12,
4 -11, 9, -8, 2,
5 7,-12, 12,-13, // ...
6 }
• steered BRIEF, for each bit of the descriptor
p′
i = p + Rθ(pi − p)
q′
i = p + Rθ(qi − p)
, Rθ =
[
cos θ − sin θ
sin θ cos θ
]
τ(I; p′
i, q′
i) :=
{
1 : I(p′
i)  I(q′
i)
0 : I(p′
i) ≥ I(q′
i)
1 float angle = (float)kpt.angle*factorPI;
2 float a = (float)cos(angle), b = (float)sin(angle);
3 #define GET_VALUE(idx) 
4 center[cvRound(pattern[idx].x*b + pattern[idx].y*a)*step + 
5 cvRound(pattern[idx].x*a - pattern[idx].y*b)]
高洪臣 ORB 特征 2020 年 7 月 10 日 12 / 12

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Image ORB feature

  • 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Image Features feature types feature extraction(detection) & matching • feature detector • feature descriptor 高洪臣 ORB 特征 2020 年 7 月 10 日 2 / 12
  • 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corner / Keypoint / Interest Point • keypoint detector • Harris (1988) • Shi-Tomas (1994) • FAST1 (Features from Accelerated and Segments Test) (2006) • AGAST (2010) • keypoint descriptor • BRIEF2 (Binary robust independent elementary feature) (2010) • keypoint detector & descriptor • SIFT (1999, 2004) • SURF (2006) • BRISK (Binary Robust Invariant Scalable Keypoints) (2011) • ORB3 (2011) • FREAK (2012) • KAZE (2012) 1Edward Rosten and Tom Drummond. “Machine Learning for High-Speed Corner Detection.”. In: ECCV (1). Ed. by Ales Leonardis, Horst Bischof, and Axel Pinz. Vol. 3951. Lecture Notes in Computer Science. Springer, 2006, pp. 430–443. isbn: 3-540-33832-2. url: http://dblp.uni-trier.de/db/conf/eccv/eccv2006-1.html#RostenD06. 2Michael Calonder et al. “BRIEF: Binary Robust Independent Elementary Features”. In: Proceedings of the 11th European Conference on Computer Vision: Part IV. ECCV’10. Heraklion, Crete, Greece: Springer-Verlag, 2010, pp. 778–792. isbn: 364215560X. 3Ethan Rublee et al. “ORB: An efficient alternative to SIFT or SURF”. In: 2011 International conference on computer vision. Ieee. 2011, pp. 2564–2571. 高洪臣 ORB 特征 2020 年 7 月 10 日 3 / 12
  • 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ORB Overview ORB = Oriented FAST + Rotated BRIEF • oFAST (ORB Detector) • keypoint position - FAST • keypoint orientation - image patch moment • keypoint response/score - NMS(Non-Maximal Supression) • scale-invariant - image pyramid • rBRIEF (ORB Descriptor) • keypoint descriptor - BRIEF • rotation-invariant - keypoint orientation 高洪臣 ORB 特征 2020 年 7 月 10 日 4 / 12
  • 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiscale Image Pyramid Parameters • level: 8 • scale: 1.2 • downsample: bilinear interpolation produce FAST features and compute descriptors at each level in the pyramid 高洪臣 ORB 特征 2020 年 7 月 10 日 5 / 12
  • 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . FAST fast-9 • 9 contiguous pixels in a circle (of 16 pixels) brighter than Ip + t or darker than Ip − t • Rapid rejection by testing 1, 9, 5 then 13 NMS (Non-Maximal Suppression) 1 remove corners which have an adjacent corner with higher score Uniform Distribution DistributeOctTree() 2 1all called non-maximum suppression 2use Quad-Tree to iteratively segment image regions in ORB-SLAM2 高洪臣 ORB 特征 2020 年 7 月 10 日 6 / 12
  • 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orientation by Intensity Centroid (IC) the moments of a patch: mpq = ∑ x,y xp yq I(x, y) the first order moment of a patch 1 I (radius = 15): m10 = 15∑ x=−15 15∑ y=−15 xI(x, y) = 15∑ y=0 15∑ x=−15 x [I(x, y) − I(x, −y)] m01 = 15∑ x=−15 15∑ y=−15 yI(x, y) = 15∑ y=1 15∑ x=−15 y [I(x, y) − I(x, −y)] the intensity centroid: C = ( m10 m00 , m01 m00 ) the orientation (from the corner’s center to the centroid): θ = atan 2 (m01, m10) 1a circular patch 高洪臣 ORB 特征 2020 年 7 月 10 日 7 / 12
  • 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Image Gaussian Filtering/Blurring/Smoothing 1 why filtering start by smoothing image using a Gaussian kernel at each level in the pyramid in order to prevent the descriptor from being sensitive to high-frequency noise Gaussian Kernel G(u, v) = 1 2πσ2 e − u2+v2 2σ2 Gn(u, v) = 1 s · e − u2+v2 2σ2 , s = w∑ u=−w w∑ v=−w e − u2+v2 2σ2 (a) (u,v) (b) kernel (σ=1.5) (c) normalized Image Gaussian Filtering: I′(i, j) = ∑w u=−w ∑w v=−w I(i + u, j + v)Gn(u, v) 1low-pass filter 高洪臣 ORB 特征 2020 年 7 月 10 日 8 / 12
  • 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Separability of the Gaussian filter s = w∑ u=−w w∑ v=−w g(u) · g(v) = ( w∑ u=−w g(u) ) · ( w∑ v=−w g(v) ) = s′ · s′ Gn(u, v) = 1 s · e− u2 2σ2 · e− v2 2σ2 = 1 s · g(u) · g(v) = g(u) s′ · g(v) s′ Separable Kernel Matrix: G(2w+1)×(2w+1) = 1 s         g(−w)g(−w) . . . g(−w)g(0) . . . g(−w)g(w) ... ... ... g(0)g(−w) . . . g(0)g(0) . . . g(0)g(w) ... ... ... g(w)g(−w) . . . g(w)g(0) . . . g(w)g(w)         = 1 s′         g(−w) ... g(0) ... g(w)         · 1 s′ [ g(−w) . . . g(0) . . . g(w) ] 高洪臣 ORB 特征 2020 年 7 月 10 日 9 / 12
  • 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Separability of the Gaussian filter Image Gaussian Filtering: I′ (i, j) = w∑ u=−w w∑ v=−w I(i + u, j + v)Gn(u, v) = w∑ u=−w w∑ v=−w I(i + u, j + v) 1 s g(u)g(v) = w∑ u=−w w∑ v=−w I(i + u, j + v) 1 s′ g(u) 1 s′ g(v) = w∑ u=−w [ w∑ v=−w I(i + u, j + v) g(v) s′ ] g(u) s′ = w∑ u=−w S(i + u) g(u) s′ • kernel size: (2w + 1) × (2w + 1), w = 3 1 int gaussKernel[4] = { 224, 192, 136, 72 }; 高洪臣 ORB 特征 2020 年 7 月 10 日 10 / 12
  • 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BRIEF • vector dim: 256 bits (32 bytes) • each vector ←→ each keypoint for each bit, select a pair of points in a patch I which centered a corner p and compare their intensity S = ( p1, . . . , pn q1, . . . , qn ) ∈ R(2×2)×256 τ(I; pi, qi) := { 1 : I(pi) I(qi) 0 : I(pi) ≥ I(qi) the descriptor (each bit ←→ each pair of points (pi, qi)): f(n) = n ∑ i=1 2i−1 τ(I; pi, qi), (n = 256) 高洪臣 ORB 特征 2020 年 7 月 10 日 11 / 12
  • 12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . rBRIEF • construct a lookup table of precomputed BRIEF patterns 1 static int ORB_pattern[256*4] = { 2 8, -3, 9, 5, 3 4, 2, 7,-12, 4 -11, 9, -8, 2, 5 7,-12, 12,-13, // ... 6 } • steered BRIEF, for each bit of the descriptor p′ i = p + Rθ(pi − p) q′ i = p + Rθ(qi − p) , Rθ = [ cos θ − sin θ sin θ cos θ ] τ(I; p′ i, q′ i) := { 1 : I(p′ i) I(q′ i) 0 : I(p′ i) ≥ I(q′ i) 1 float angle = (float)kpt.angle*factorPI; 2 float a = (float)cos(angle), b = (float)sin(angle); 3 #define GET_VALUE(idx) 4 center[cvRound(pattern[idx].x*b + pattern[idx].y*a)*step + 5 cvRound(pattern[idx].x*a - pattern[idx].y*b)] 高洪臣 ORB 特征 2020 年 7 月 10 日 12 / 12