Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks
Presented in SIGSPATIAL 2015 http://www3.cs.stonybrook.edu/~chni/publication/hodge/ -- 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.
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Decentralized Path Homotopy Detection and Classification Using Hodge Decomposition in Sensor Networks
- 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
- 4. • Homology : • How trajectories go around obstacles “Different” homology “Same” homology Goal: Trajectories Classification
- 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
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Notes de l'éditeur
- hello everyone, my name is chienchun ni from stonybrook university, today i'm going to talk about trajectory tracking and classification.
- suppose you are a manager of a museum, you got many showrooms, and you got many visitors walk around, and you want to somehow roughtly classify the visitors's trajectory, what can you do? one way is to lable the room, and track the trajectories based on these labels.
- However, what if the show rooms become a little bit more complicated, say, there are some statues in them. Then, the visitors may ignore the statues, go around the statue or even travel pass the statues. In this kind of situation, how can we track and classify these trajectories?
- So in order to track and classify these trajectories, we use a technique call homology classification. Homology represents how trajectories go around obstacles, so if they go from different side of the obstacle, we say it's different homology, and if they go from the same side, we say it's same homology.
- So here is how we do it, suppose we have two obstacle here. First we give it a traingular mesh that each edges have some information about these two obstacles. Then when visitors go through these mesh, they accumulate two specific value corresponding to the obstacles as vectors. our core classification idea is to compare these vectors pairwisely. If these two vector have the same homology, then the result will be 0, if not, then it will be nonzero.