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 Yin1, Chien-Chun Ni2, Jiaxin Ding2, Wei Han1, Dengpan Zhou2, Jie Gao2, Xianfeng David Gu2
1. Havard University 2.Stony Brook University
Tracking Trajectories:A
C
B
D
ABD
ACDABD
Tracking Trajectories: Obstacles
?
• Homology : • How trajectories go around obstacles
“Different” homology “Same” homology
Goal: Trajectories Classification
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
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