Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor...

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Decentralized Human Trajectories Tracking Using Hodge Decomposition in Sensor Networks Xiaotian Yin 1 , Chien-Chun Ni 2 , Jiaxin Ding 2 , Wei Han 1 , Dengpan Zhou 2 , Jie Gao 2 , Xianfeng David Gu 2 1. Havard University 2.Stony Brook University

Transcript of Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor...

Page 1: Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks

Decentralized Human Trajectories Tracking

Using Hodge Decomposition in Sensor Networks

Xiaotian Yin1, Chien-Chun Ni2, Jiaxin Ding2, Wei Han1, Dengpan Zhou2, Jie Gao2, Xianfeng David Gu2

1. Havard University 2.Stony Brook University

Page 2: Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks

Tracking Trajectories:A

C

B

D

ABD

ACDABD

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Tracking Trajectories: Obstacles

?

Page 4: Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks

• Homology : • How trajectories go around obstacles

“Different” homology “Same” homology

Goal: Trajectories Classification

Page 5: Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks

Goal: Trajectories Classification• IDEA: Hodge Decomposition & Harmonic 1-form

T1 = ( k11 , k12 )

T2 = ( k21 , k22 )

T3 = ( k31 , k32 )

T1 - T3 = ( 0 , 0 )

T2 - T3 = ( 1 , 0 )

Equivalent!

Not Equivalent

Page 6: Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks

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