Object Recognition 1: Contour-based - Yonsei Universityweb.yonsei.ac.kr/hgjung/Lectures/AUE859/13. Object... · 2014-12-29 · E-mail: [email protected] Object Recognition 1:

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Object Recognition 1:Contour-based


Contour-based Object Recognition

1. Procrustes analysis

2. B-spline-based Active Contour

3. Contour tree-based pedestrian detection


Procrustes Analysis


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.



두 shape을 이루는 k개의 점들 간의 correspondence는 알고 있다고 가정한다.



각 shape을 이루는 landmark point의 무게중심 간의 차가 translation이다.



각 shape을 이루는 landmark point들의 무게중심으로부터의 평균거리 비율이 scaling이다.


Procrustes Analysis [1]Translation과 scaling이 적용된 결과

내적: 크기 곱과 cosθ

외적: 크기 곱과 sinθ


Procrustes Analysis


Procrustes Analysis


Procrustes Analysis

0 2 4 6 8 10 12 14 16 18 200

2

4

6

8

10

12

14

16

18

20


References

1. Wikipedia, “Procrustes analysis,” http://en.wikipedia.org/wiki/Procrustes_analysis


B-Spline-basedActive Contour


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.


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.


B-spline-based contour, matrix notation

• This can be expressed compactly in matrix notation as


B-spline-based contour, matrix notation


Norm and inner product for spline functions

• In the L2 case the inner product between two functions works out to be:



dsssL

x xTTL xT QBQB

0

2 1

dsssL

xTL Tx QBBQ0

1

xTLTx dsssL

QBBQ

0

1




Approximation as a spline vector, projection

xT Qssx B

xxL TL xTLQQdsss

LdsQss

Ldssxs

LβBBBBB

000

111

Lx dssxs

LQ

0

1 1 Bβ


Control vector


Norm of curves


Shape space


Euclidean similarities


The space of Euclidean similarities


Shape space


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°))


Shape vector estimation

관찰의 변량Inverse modelParameter의 변량


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


Robustness of Shape Vector Estimation

-600 -400 -200 0 200 400 600 800 1000-500

0

500

1000


Fitting spline templates: Regularized matching

데이터평균: 모델


Fitting spline templates: Regularized matching


Normal displacement in curve fitting










Recursive solution of curve-fitting problems


Recursive solution of curve-fitting problems


Curve-Fitting Example










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/


Contour tree-based Pedestrian Detection


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


DT(Distance Transform)-based Object Detection


Contour Clustering

K-medois algorithm


Hierarchical Tree of Contour Cluster


Probabilistic Matching


Bayesian Exemplar-based Hierarchical Shape Matching





생성된 계층적 보행자 윤곽선 트리의 일부분




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


• 보행자 자세의 시간적 변화 양상을 이용한 검출 및 추적



• 보행자 자세의 시간적 변화 양상을 이용한 검출 및 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














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.

Documents

Object Recognition 1: Contour-based - Yonsei Universityweb.yonsei.ac.kr/hgjung/Lectures/AUE859/13. Object... · 2014-12-29 · E-mail: [email protected] Object Recognition 1: