¬ hþ Ú ¿ ½ ï ¬ w h w s 8 s g oyylab/ja/wp-content/uploads/... · ô ¶ u c technical report...
TRANSCRIPT
THE INSTITUTE OF ELECTRONICS,INFORMATION AND COMMUNICATION ENGINEERS
TECHNICAL REPORT OF IEICE.
† ††
†2–12–1
††3–7–2
E-mail: †[email protected], ††[email protected]
GAT/GPT (Global Affine Transform/Global Projection Transform)GAT/GPT whole-to-part
ASIFT RANSACGAT/GPT
An initilal search method for region-based image matchingYukihiko YAMASHITA† and Toru WAKAHARA††
† Tokyo Institute of Technology2-12-1, O-okayama, Mekuro-ku, Tokyo, 152-8552
†† Hosei University3–7–2 Kajino-cho, Koganei-shi, Tokyo 184-8584
E-mail: †[email protected], ††[email protected]
Abstract GAT/GPT (Global Affine Transform/Global Projection Transform) correlation methods for imagematching that is one of the most important methods in the field of image processing can perform a precise im-age matching. When GAT/GPT correlation methods are applied to whole-to-part matching, it can be realized bysliding windows with various sizes but it needs much calculation time. In this paper we propose a fast initial searchmethod using the sliding Discrete Fourier Transformation for the region-based image matching. Furthermore, byexperiments we compare and evaluate the proposed method against the combination of ASIFT and RANSAC.Key words Image matching, region-based matching, GAT/GPT correlation, initial search
1.
2
Scale-Invariant Feature Transform (SIFT) [1], [2]SIFT Affine
ASIFT [3] RANSAC [4]
[5] Lucus-Kanade[6]
[7] GAT/GPT(Global Affine Transform/Global Projection Transform)
[8] [10]
— 1 —
Copyright ©201 by IEICE This article is a technical report without peer review, and its polished and/or extended version may be published elsewhere.
- 119 -
(a) (b) (c) (d) (e) LoG
1
GPTkNN MNIST
99.7% kNN
MNISTwhole-to-whole
Computer Vision
whole-to-part
whole-to-part
[11] [14]SIFT
ASIFT RANSAC
2.
2. 11
0 [−K, K]G[n] = e−(πn/K)2/(2σ2) σ
π −π
σK/π f [n] 12
K∑k=−K
G[k]f [n− k] (1)
K∑k=−K
kG[k]f [n− k] (2)
K∑k=−K
k2G[k]f [n− k] (3)
β = π/K
G[k] �P∑
p=0
ap cos(βpk)
kG[k] �P∑
p=1
bp sin(βpk)
k2G[k] �P∑
p=0
dp cos(βpk)
P DFTP 2 4
cp[n] =K∑
k=−K
f [n− k] cos(βpk)
sp[n] =K∑
k=−K
f [n− k] sin(βpk)
(1)-(3)
K∑k=−K
G[k]f [n− k] �P∑
p=0
apcp[n]
K∑k=−K
kG[k]f [n− k] �P∑
p=1
bpsp[n]
K∑k=−K
k2G[k]f [n− k] �P∑
p=0
dpcp[n]
1 Lenna
2. 2Kober
u[n] =n∑
k=1
f [k]eiβpk (4)
cp[n] sp[n]
— 2 —- 120 -
0
2
4
6
8
10
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Err
or
(%)
Sigma
TotalInterval
Order
0
2
4
6
8
10
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Err
or
(%)
Sigma
TotalInterval
Order
0
5
10
15
20
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Err
or
(%)
Sigma
TotalInterval
Order
(a) G[n], K = 256, P = 2 (b) nG[n], K = 256, P = 2 (c) LoG, K = 256, P = 2
0
2
4
6
8
10
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Err
or
(%)
Sigma
TotalInterval
Order
0
2
4
6
8
10
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Err
or
(%)
Sigma
TotalInterval
Order
0
2
4
6
8
10
0.6 0.8 1 1.2 1.4 1.6 1.8 2
Err
or
(%)
Sigma
TotalInterval
Order
(a) G[n], K = 256, P = 4 (b) nG[n], K = 256, P = 4 (c) LoG, K = 256, P = 4
2 Interval Order
cp[n] + isp[n] = e−iβpn(u[n + K]− u[n−K − 1]) (5)
u[n]
u[n] = u[n− 1] + f [n]eiβpn (6)
1IIR
v[n] = e−iβpv[n− 1] + f [n] (7)
cp[n] sp[n]
cp[n]+ isp[n] = (−1)p(v[n+K]−v[n−K]+x[n−K]) (8)
K p
(2017) 2
v[n+1] = 2 cos(βp)v[n]+v[n−1]+f [n+1]−eiβpf [n] (9)
cp[n] sp[n]cp[n]
2
2. 3P
σK/π K σ
σ K
2 P = 2 P = 4 G[n] nG[n] LoG2 2
P = 2 σ = 1.1 1%5% LoG 10% P = 4
σ = 0.85 0.1%0.5% LoG 1%2. 4
GPU
Lenna Barbara 1524288 (= 512× 512× 2)
3 K = 256 c1[n] 10,0002
2 IIR 12%
3.
3. 1D(θ) θ
Q
— 3 —- 121 -
0
2
4
6
8
10
0 100000 200000 300000 400000 500000
Err
or
(%)
n
KernelKernelB
IIRIIRB
2ndIIR2ndIIRB
0
0.2
0.4
0.6
0.8
1
0 100000 200000 300000 400000 500000
Err
or
(%)
n
KernelKernelB
IIRIIRB
(a) c1[n], K = 256 (b) c1[n], K = 256 ( )
3 Kernel (6) IIR 1 IIR (7) 2ndIIR 2IIR (9) B
D(θ) =Q∑
q=−Q
dneiqθ (10)
d−q = dq dq
2Q + 1I(x, y)
IX(x, y) IY(x, y)
‖I1(x, y)‖ =√
(IX(x, y))2 + (IY(x, y))2 (11)
(x, y)δ(θ) ‖I1(x, y)‖δ(θ − θ(x, y))IX(x, y) = ‖I1(x, y)‖ cos θ(x, y) IY(x, y) =
‖I1(x, y)‖ sin θ(x, y)
dq = 12π
∫ π
−π
‖I1(x, y)‖δ(θ − θ(x, y))e−iqθdθ
= 12π‖I1(x, y)‖e−iqθ(x,y)
� (IX(x, y))− iIY(x, y))q
2π (‖I1(x, y)‖2 + ε)(q−1)/2 (12)
ε ε = 10−12
θ0
d′q
d′q = dqe−iqθ0 (13)
3. 2I (x, y)
S S
P = 4
I S/8IX IY
(12)
(a) (b)
4
2Q + 1 P = 2
S S/4 (x, y)S L
θ = 2πl/L (l = 0, 1, . . . , L− 1)
2
1 21
(x, y) 1 θ0
θ0 (x, y) M
S/4
4 M
(xm, ym) (m = 1, 2, . . . , M)
(x′m, y′m) (m = 1, 2, . . . , M)
x′m = S(xm cos θ0 − ym sin θ0) + x (14)
y′m = S(xm sin θ0 + ym cos θ0) + y (15)
S/4
(13)
— 4 —- 122 -
Algorithm 1Require: I S0 rS
SMax S TS
(xm, ym) (m = 1, 2, . . . , M)S ⇐ S0
while S ≤ SMax doI S/8IX IY
2Q + 1 S S/4for (x, y) ∈ TS do
S
for θ0 ∈ ( ) doθ0 (14) (15)
S/4(13) M(2Q + 1)
1 (x, y)1
end forend forS ⇐ rSS
end while
M(2Q + 1)1 (x, y)
(x, y) S
0.2Alogrithm 1
3. 3
(x, y) S
1
ASIFT Affine
2(rS = 2) S0
√2S0 2
√2
4.
ASIFT+RANSACGraffiti (800 × 640 ) Boat (850 × 680) [15]Graffiti
6 (img1∼img6)Graffiti img1 Boat img1
(430, 310) 150√
2(425, 340) 200
√2
9 Affineimg2∼img6
2 20%
ASIFT+RANSAC Graffitiimg1 490 × 368
Boat img1ASIFT+RANSAC OpenCV SIFT
RANSAC python[16] OpenCV
version 3.4.15 Graffiti 6 Boat
img1
5 (b)–(f) 6 (b)–(f)
ASIFT+RANSAC
1 CPU In-tel(R) Core(TM) i5-6400 CPU @ 2.70GHz
ASIFT+RANSAC
— 5 —- 123 -
(a) (b) img2 (c) img3 (d) img4 (e) img5 (f) img6
5 Graffiti (b)–(f)
(a) (b) img2 (c) img3 (d) img4 (e) img5 (f) img6
6 Boat (b)–(f)
ASIFT+RANSAC
GPU
5.
GAT/GPT
ASIFT+RANSAC
GAT/GPT
[1] D.G. Lowe, “Distinctive image features from scale-invariantkeypoints,” Int. J. Comput. Vision, vol.60, no.2, pp.91–110,Nov. 2004.
[2] Y. Ke and R. Sukthankar, “PCA-SIFT: A more distinc-tive representation for local image descriptors,” Proceed-ings of the 2004 IEEE Computer Society Conference onComputer Vision and Pattern Recognition, pp.506–513,CVPR’04, IEEE Computer Society, Washington, DC, USA,2004. http://dl.acm.org/citation.cfm?id=1896300.1896374
[3] J.-M. Morel and G. Yu, “ASIFT: A new framework for fullyaffine invariant image comparison,” SIAM J. Img. Sci., vol.2,no.2, pp.438–469, April 2009.
[4] M.A. Fischler and R.C. Bolles, “Random sample consen-sus: A paradigm for model fitting with applications to im-
1 (second)
Image \ Method ASIFT+RAMSAC OursGraffiti 21.881 0.699Boat 168.366 1.132
age analysis and automated cartography,” Commun. ACM,vol.24, no.6, pp.381–395, June 1981.
[5] , 1989[6] S. Baker and I. Matthews, “Lucas-kanade 20 years on: A
unifying framework,” Int. J. Comput. Vision, vol.56, no.3,pp.221–255, Feb. 2004.
[7] S. Korman, D. Reichman, G. Tsur, and S. Avidan, “FAsT-Match: Fast affine template matching,” Int. J. Comput.Vision, vol.121, no.1, pp.111–125, Jan. 2017.
[8] T. Wakahara, Y. Kimura, and A. Tomono, “Affine-invariantrecognition of gray-scale characters using global affine trans-formation correlation,” IEEE Transactions on Pattern Anal-ysis and Machine Intelligence, vol.24, no.4, pp.384–395,April 2001.
[9] Y. Yamashita and T. Wakahara, “Affine-transformation and2D-projection invariant k-NN classification of handwrittencharacters via a new matching measure,” Pattern Recogni-tion, vol.52, pp.459–470, April 2016.
[10] S. Zhang, T. Wakahara, and Y. Yamashita, “Image match-ing using GPT correlation associated with simplified HOGpatterns,” Proceedings of 2017 Seventh International Con-ference on Image Processing Theory, Tools and Applica-tions, vol.1, pp.1–6, November–December 2017.
[11] E. Elboher and M. Werman, “Cosine integral images forfast spatial and range filtering,” Proceedings of 2011 18thIEEE International Conference on Image Processing, pp.89–92, Sept. 2011.
[12] K. Sugimoto and S.-I. Kamata, “Compressive bilateral fil-tering,” IEEE Transactions on Image Processing, vol.24,no.11, pp.3357–3369, Nov. 2015.
[13] “”
vol.117 no.48, IE2017-4 pp.19–24 May 2017[14] V. Kober, “Fast algorithms for the computation of sliding
discrete sinusoidal transforms,” IEEE Transactions on Sig-nal Processing, vol.52, no.6, pp.1704–1710, June 2004.
[15] Visual Geometry Group, University of Oxford, “Affinecovariant features”. http://www.robots.ox.ac.uk/~vgg/research/affine/.
[16] A. Alekhin, “Affine invariant feature-based image match-ing sample”. https://github.com/opencv/opencv/blob/master/samples/python/asift.py.
— 6 —- 124 -