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Decentralized Human Trajectories
Tracking Using Hodge
Decomposition in Sensor
Networks
Xiaotian Yin1, Chien-Chun Ni2, Jiax...
Tracking Trajectories:
A
C
B
D
ABD
ACD
ABD
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 =...
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Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks

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Presented in SIGSPATIAL 2015
http://www3.cs.stonybrook.edu/~chni/publication/hodge/
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With the recent development of localization and tracking systems for both indoor and outdoor settings, we consider the problem of analyzing and representing the huge amount of natural trajectories from human movements that we expect to gather in the near future. In this paper we argue the topological representation, which records how a target moves around the natural obstacles in the underlying environment, can be sufficiently descriptive for many applications and efficient enough for both storing, comparing and classifying these natural human trajectories. Technically, the representation uses the homotopy type of the trajectory. By using harmonic one-forms and Hodge decomposition, we pre-process the sensor network with a purely decentralized algorithm such that the homology class of a trajectory can be obtained by a simple integration along the trajectory. This supports real-time classification of trajectories up to the homology accuracy with minimum communication cost. We test the effectiveness of our approach by showing how to classify randomly generated trajectories in a multi-level arts museum layout as well as how to distinguish real world taxi trajectories in a large city.

Published in: Science
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Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks

  1. 1. 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
  2. 2. Tracking Trajectories: A C B D ABD ACD ABD
  3. 3. Tracking Trajectories: Obstacles ?
  4. 4. • Homology : • How trajectories go around obstacles “Different” homology “Same” homology Goal: Trajectories Classification
  5. 5. 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
  6. 6. See More on Our Poster!!! 2D Flooring Plan 3D Flooring Plan

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