Post on 30-May-2020
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Object Recognition 1:Contour-based
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Contour-based Object Recognition
1. Procrustes analysis
2. B-spline-based Active Contour
3. Contour tree-based pedestrian detection
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Procrustes Analysis
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Procrustes Analysis [1]
In statistics, Procrustes analysis is a form of statistical shape analysis used to analyse the distribution of a set of shapes.
To compare the shape of two or more objects, the objects must be first optimally "superimposed".
Procrustes superimposition (PS) is performed by optimally translating, rotating and uniformly scaling the objects.
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Procrustes Analysis [1]
두 shape을 이루는 k개의 점들 간의 correspondence는 알고 있다고 가정한다.
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Procrustes Analysis [1]
각 shape을 이루는 landmark point의 무게중심 간의 차가 translation이다.
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Procrustes Analysis [1]
각 shape을 이루는 landmark point들의 무게중심으로부터의 평균거리 비율이 scaling이다.
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Procrustes Analysis [1]Translation과 scaling이 적용된 결과
내적: 크기 곱과 cosθ
외적: 크기 곱과 sinθ
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Procrustes Analysis
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Procrustes Analysis
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Procrustes Analysis
0 2 4 6 8 10 12 14 16 18 200
2
4
6
8
10
12
14
16
18
20
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
References
1. Wikipedia, “Procrustes analysis,” http://en.wikipedia.org/wiki/Procrustes_analysis
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
B-Spline-basedActive Contour
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B-spline basis function
• A spline function x(s) is constructed as a weighted sum of NB basis functions Bn(s), n=0,…, NB-1.
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B-spline basis function
• In the simplest (“regular”) case, each basis function consists of d polynomials each defined over a span of the s-axis. Let Bn,d be the nth basis function for a spline of order d.
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B-spline-based contour, matrix notation
• This can be expressed compactly in matrix notation as
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
B-spline-based contour, matrix notation
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Norm and inner product for spline functions
• In the L2 case the inner product between two functions works out to be:
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Norm and inner product for spline functions
dsssL
x xTTL xT QBQB
0
2 1
dsssL
xTL Tx QBBQ0
1
xTLTx dsssL
QBBQ
0
1
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Norm and inner product for spline functions
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Approximation as a spline vector, projection
xT Qssx B
xxL TL xTLQQdsss
LdsQss
Ldssxs
LβBBBBB
000
111
Lx dssxs
LQ
0
1 1 Bβ
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Control vector
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Norm of curves
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Shape space
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Euclidean similarities
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The space of Euclidean similarities
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Shape space
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Shape Vector Describing Transformation
-600 -400 -200 0 200 400 600 800 1000 1200-500
0
500
1000
Model Q0
X=(700, -100, 0, 0)
X=(300, 400, 3cos(30°), 3sin(30°))
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Shape vector estimation
관찰의 변량Inverse modelParameter의 변량
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Shape Vector Estimation by Pseudo-Inverse
-600 -400 -200 0 200 400 600 800 1000 1200-500
0
500
1000
Model Q0
=(700, -100, 0, 0)
=(300, 400, 3cos(30°), 3sin(30°))
X̂
X̂
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Robustness of Shape Vector Estimation
-600 -400 -200 0 200 400 600 800 1000-500
0
500
1000
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Fitting spline templates: Regularized matching
데이터평균: 모델
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Fitting spline templates: Regularized matching
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Normal displacement in curve fitting
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Normal displacement in curve fitting
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Normal displacement in curve fitting
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Normal displacement in curve fitting
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Normal displacement in curve fitting
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Recursive solution of curve-fitting problems
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Recursive solution of curve-fitting problems
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Curve-Fitting Example
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Curve-Fitting Example
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Curve-Fitting Example
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Curve-Fitting Example
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Curve-Fitting Example
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References
1. Andrew Blake and Michael Isard, “Active Contours: The Application of Techniques from Graphics, Vision, Control Theory and Statistics to Visual Tracking of Shapes in Motion,” Springer-Verlag London Limited, 1998.
http://www.robots.ox.ac.uk/~contours/
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Contour tree-based Pedestrian Detection
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
DT(Distance Transform)-based Object Detection
The dissimilarity between two pedestrian silhouettes and , , is defined by a distance transform-based template matching score, frequently called chamfer distance or modified Hausdorff distance (MHD), as
where x and y are the edge pixel coordinates of and , respectively. And, and denote the -axis and -axis translation between two silhouettes. Rotational transformation is ignored during the matching as all pedestrians in the database are assumed to be upright.
, ,
2
1, mindx dy
dxdy
yx
x y
,
dx dy
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
DT(Distance Transform)-based Object Detection
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Contour Clustering
K-medois algorithm
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Hierarchical Tree of Contour Cluster
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Probabilistic Matching
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Bayesian Exemplar-based Hierarchical Shape Matching
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Bayesian Exemplar-based Hierarchical Shape Matching
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Bayesian Exemplar-based Hierarchical Shape Matching
생성된 계층적 보행자 윤곽선 트리의 일부분
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
Bayesian Exemplar-based Hierarchical Shape Matching
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
Ho Gi Jung*, “Medoid selection from sub-tree leaf nodes for k-medoids clustering-based hierarchical template tree construction,” Electronics Letters, vol. 49, no. 2, 17 Jan. 2013, pp. 108-109.
Template Tree 구축 개선
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
• 보행자 자세의 시간적 변화 양상을 이용한 검출 및 추적
자세-윤곽선 융합을 통한 보행자 검출/추적
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
• 보행자 자세의 시간적 변화 양상을 이용한 검출 및 추적
자세-윤곽선 융합을 통한 보행자 검출/추적
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
Ho Gi Jung*, “An Internal-to-internal Transition Method for Consecutive Hierarchical Template Matching,” IET Computer Vision, accepted on 2 Aug. 2013.
Internal-to-Internal Transition Method
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
Ho Gi Jung*, “An Internal-to-internal Transition Method for Consecutive Hierarchical Template Matching,” IET Computer Vision, accepted on 2 Aug. 2013.
Internal-to-Internal Transition Method
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
Ho Gi Jung*, “An Internal-to-internal Transition Method for Consecutive Hierarchical Template Matching,” IET Computer Vision, accepted on 2 Aug. 2013.
Internal-to-Internal Transition Method
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
자세-윤곽선 융합을 통한 보행자 검출/추적
Ho Gi Jung*, “An Internal-to-internal Transition Method for Consecutive Hierarchical Template Matching,” IET Computer Vision, accepted on 2 Aug. 2013.
Internal-to-Internal Transition Method
E-mail: hogijung@hanyang.ac.krhttp://web.yonsei.ac.kr/hgjung
References
1. Dariu M. Gavrila, “A Bayesian, Exemplar-Based Approach to Hierarchical Shape Matching,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 29, No. 8, Aug. 2007, pp. 1408-1421.