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Discovering activity patterns in office environment using a network of low-resolution visual sensors

  • Mohamed Eldib
  • Francis Deboeverie
  • Wilfried Philips
  • Hamid Aghajan
Original Research
  • 140 Downloads

Abstract

Understanding activity patterns in office environments is important in order to increase workers’ comfort and productivity. This paper proposes an automated system for discovering activity patterns of multiple persons in a work environment using a network of cheap low-resolution visual sensors (900 pixels). Firstly, the users’ locations are obtained from a robust people tracker based on recursive maximum likelihood principles. Secondly, based on the users’ mobility tracks, the high density positions are found using a bivariate kernel density estimation. Then, the hotspots are detected using a confidence region estimation. Thirdly, we analyze the individual’s tracks to find the starting and ending hotspots. The starting and ending hotspots form an observation sequence, where the user’s presence and absence are detected using three powerful Probabilistic Graphical Models (PGMs). We describe two approaches to identify the user’s status: a single model approach and a two-model mining approach. We evaluate both approaches on video sequences captured in a real work environment, where the persons’ daily routines are recorded over 5 months. We show how the second approach achieves a better performance than the first approach. Routines dominating the entire group’s activities are identified with a methodology based on the Latent Dirichlet Allocation topic model. We also detect routines which are characteristic of persons. More specifically, we perform various analysis to determine regions with high variations, which may correspond to specific events.

Keywords

Visual sensor network Supervised learning Probabilistic graphical models Topic models Sequence mining 

List of symbols

\(\left( x',y'\right)\)

Tracked position

\(f'\)

Probability density function of tracked positions

B

Kernel function in \(f'\)

\(\mathbf {H}\)

Bandwidth matrix in \(f'\)

\(({x'}^{(m)},{y'}^{(m)})\)

Position in cluster m

m

Cluster index

L

Number of clusters

\(K^{(m)}\)

Number of positions in cluster m

\(\mathbf {U}^{(m)}\)

Positions matrix

\(\mathbf {C}^{(m)}\)

Covariance matrix of clustered positions

\(\lambda _{1}^{(m)}\), \(\lambda _{2}^{(m)}\)

Eigenvalues of the covariance matrix \(\mathbf {C}^{(m)}\)

\(\rho\)

Correlation coefficient

\(\sigma _{{x'}^{(m)}}\)

Standard deviation of clustered \({x'}^{(m)}\) position

\(\sigma _{{y'}^{(m)}}\)

Standard deviation of clustered \({y'}^{(m)}\) position

A

Ellipse confidence level

\(\mathbf {V}^{(m)}\)

Eigenvectors matrix

\(\mathbf {D}^{(m)}\)

Diagonal matrix

\(\theta ^{(m)}\)

Rotation angel of the ellipse

S

Start of hotspot

E

End of hotspot

T

Track with start hotspot S and end hotspot E

I

Number of positions in track T

\((g_{x}^{(m)},g_{y}^{(m)})\)

Center of hotspot (cluster) m

F

Hotspot threshold

\(\mathbf {x}_t\)

Feature vector at time instant t

\(\mathbf {x}_{1:T}\)

Sequence of observations

\(\mathbf {y}_{1:T}\)

Sequence of states

T

Number of time steps

\(\hat{N}\)

Number of persons

Q

Number of states

\(p(\mathbf {x}_{1:T},y)\)

Joint distribution of \(\mathbf {x}_{1:T}\) and y

\(\gamma\), \(\delta\)

Potential functions

\(\epsilon\)

Actual potential

f

Feature function

\(p(\mathbf {y} \mid \mathbf {x})\)

Conditional probability of \(\mathbf {y}\) given \(\mathbf {x}\)

\(Z_{x}\)

Normalization function

N

Pattern length

e

Word in a document (presence status)

d

Document of words (presence status sequence)

z

Topic (activity pattern)

K

Number of topics

G

Number of constructed words

M

Number of documents

V

Vocabulary of words

\(\theta\)

Matrix of day-specific mixture weights

\(\Phi\)

Matrix of word-specific mixture weights

\(\alpha\)

Per-document activity pattern distributions hyperparameter

\(\beta\)

Per-activity word distribution hyperparameter

MAE

Mean absolute error

\(v_r\)

Estimated presence duration for hour r

\({v'}_r\)

Actual presence duration for hour r

\(\hat{H}\)

Number of hours

RAE

Relative absolute error

\(\xi\)

Training corpus model

\(G_m\)

Length of the document m

Notes

Acknowledgements

This research has been financed by the Belgian National Fund for Scientific Research (FWO Flanders) and Ghent University through the FWO project G.0.398.11.N.10. The evaluation was performed in the context of the projects “LittleSister” and the European AAL project “SONOPA,” financed by the agency for Innovation by Science and Technology (IWT), imec and the EU Ambient Assisted Living programme.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Mohamed Eldib
    • 1
  • Francis Deboeverie
    • 1
  • Wilfried Philips
    • 1
  • Hamid Aghajan
    • 1
    • 2
  1. 1.Image Processing and InterpretationTELIN, Ghent University/imecGentBelgium
  2. 2.Ambient Intelligence Research LabStanfordUSA

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