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ON THE USE OF OPTICAL FLOW TO TEST CROWD SIMULATIONS

ON THE USE OF OPTICAL FLOW TO TEST CROWD SIMULATIONS. D. J. Kaup (a,b) , Thomas L. Clarke (a,b) , Linda Malone (c) , Rex Oleson (a,d) , Mario Rosa (a) (a) Institute for Simulation and Training, Orlando, FL 32826 (b) Mathematics Dept., University of Central Florida, Orlando, FL 32816-1364

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ON THE USE OF OPTICAL FLOW TO TEST CROWD SIMULATIONS

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  1. ON THE USE OF OPTICAL FLOW TO TEST CROWD SIMULATIONS D. J. Kaup(a,b), Thomas L. Clarke(a,b), Linda Malone(c), Rex Oleson(a,d), Mario Rosa(a) (a) Institute for Simulation and Training, Orlando, FL 32826(b) Mathematics Dept., University of Central Florida, Orlando, FL 32816-1364 (c) Dept. of Industrial Engineering and Management, Univ. of Central Florida, Orlando, FL 32816-2450 (d) SAIC, Orlando, FL

  2. Outline Purpose Background Crowd Modeling Optical Flow Current Results Case I Case II Conclusions Recent approaches

  3. Purpose How ‘good’ is a given crowd simulation? How well do the motions and actions observed, model actual crowds? Videos are good option for obtaining raw data on crowds. How to turn video data into quantitative data?

  4. Simulations Helbing-Molnar-Farkas-Vicsek (HMFV) continuous space crowd model. In HMFV model each pedestrian feels, and exerts two kinds of forces, “social" and physical. Social forces: desired direction, desired velocity, collision avoidance. Physical forces: pushing, inter-pedestrian friction, friction with obstacles.

  5. HMFV equations Symbolically, the force exerted on pedestrian i by pedestrian j has the form: Representation of Social Force(s) Representation of Physical Forces:

  6. Data for Comparison • Collect videos of crowds in different venues. • Need to quantitatively compare simulation results to actual crowd data derived from videos. • Hand counts are time intensive. • Can a quick optical flow analysis substitute for hand counts?

  7. Optical Flow I Optical Flow – given a set of points on one image (I1 at time t1) find the flow field connecting to the same points in another image (I2 at time t2). Many algorithms. Similar to PIV (Particle Image Velocimetery) used in fluid mechanics.

  8. Optical Flow II Extract Optical Flow data from videos using Lucas-Kanade algorithm. Use Intel OpenCV implementation. Find displacement (dx, dy) Minimizing ε (summing over aperture window w) solve aperture constraint problem. With uniformity assumptions, equivalent to maximizing correlation over (dx, dy) .

  9. Optical Flow III Assumptions on relationship between optical flow and actual crowd motion or flux: Any motion is due only to motion of crowd. The mapping between physical space in which people move and the image space is assumed to be a simple scaling. The reflectivity and illumination of people and other elements in the scene are taken to be uniform.

  10. Example of Video Frame Hispanic Crowd Exiting Church at Frame 200 (Manual Counting Grid is 3 x 4)

  11. Manual Counting vs. Optical Flow I Under previously given assumptions: The number of people Fy crossing a horizontal boundary in a vertical direction is proportional to the mean vertical optical flow Vy in the shaded region surrounding the boundary. A similar relation holds for Fx and Vx in the horizontal direction. Optical flow cell M. C. cell Without computer aid, it was initially only practical to count numbers of individuals crossing vertical and horizontal boundaries defined by a grid. The Geometrical Relation between Optical Flow and Boundary Crossing Rate.

  12. Optical flow count requires doubling. which results in: Final views Overlapping grids which are used to compare optical flow to manually counted fluxes.

  13. Manual counts vs. Optical Flow II Hand counts of people crossing the boundaries of a 3 by 4 grid were pre-formed on selected segments of videos. Counts were compared with optical flow calculated on a 6 by 8 grid. Limited experiments show correlation between optical flow and flux of people.

  14. Current Results Hand count information gathered for two new videos. Primarily Hispanic congregation leaving church. Primarily Anglo congregation leaving same church. Hand Counts performed on sections of 400 frames of both videos.

  15. Hispanic Case 1-400 Optical Flow Field for Hispanic Case frames 1-400 (13.3 s) Hispanic Crowd Exiting Church at Frame 200.

  16. Analysis Hispanic Case • The relation was essentially random for frames 1-400. • Examination of frames 1-400 shows crowd milling around. • time interval too long to effectively pick out any motion other than the average; in this case the average is essentially zero.

  17. Hispanic Case 701-1100 Hispanic Crowd Exiting Church at Frame 900. Optical Flow Field for Hispanic Case Frames 701-1100.

  18. Analysis Hispanic Case • Results 701-1100 showed good correlation. • Slope of best-fit-line 0.0092. • Correlation 0.329. • Correlation probably due to ‘purposeful’ movement observed during time interval.

  19. Anglo Case 1-400 Note: the minimal velocity at the position corresponding to a stationary priest Optical Flow Field for Anglo Case Frames 1-400. Anglo Crowd Exiting Church at Frame 200.

  20. Slope linear fit - 0.0036 Correlation coef. - 0.467 The relative magnitudes of the slopes in Hispanic and Anglo cases are consistent with the difference in camera distance and angle for the two cases. Analysis of Anglo Case

  21. Anglo Case 5001-5400 Optical Flow Field for Anglo Case: Frames 5001-5400. Anglo Crowd Exiting Church at Frame 5200.

  22. Analysis of Anglo Case • Crowd sparse and exhibiting random movements. • Hand count crossing rate / optical flow relation was random. • Result similar to the result observed in Hispanic case for frames 1-400.

  23. Conclusions • Correlation between hand counted crossing rates and optical flow: • High when crowd moving in definite direction. • Low when crowd moving ‘randomly’. • Optical flow does provide efficient video measurements for experimental validation of crowd simulations.

  24. Conclusions • The dependence of the proportionality constant on viewing distance has the form expected. • Comparisons at smaller time intervals may detect fluxes associated with random movements within crowds. (Current work)

  25. Ongoing Work • Manual tracker makes it possible to track all individual paths from a video. • Correlation of individuals’ motion with optical flow estimates is currently being performed. • New software (URAPIV) being tried out.

  26. Individual Hispanic Paths • Accurate paths • Density of individuals • Correlate individuals • (groups) • Expect better correlations • between M.C. and O.F. Frames 300-400

  27. PIV Algorithms • Goal of computer vision scientists is to determine camera motion as in DARPA autonomous vehicle competition. • Goal of video crowd analysis is to determine flow of crowd much like the goal of PIV in fluid dynamics. • PIV (Particle Image Velocimetery)is a topic of active research in fluid mechanics. • Algorithms such as MatPIV (MatLab PIV) are being investigated. • URAPIV is open source version.

  28. URAPIV Analysis Hispanic • Red vectors have stronger correlation.

  29. URAPIV Analysis Anglo • Red vectors have stronger correlation.

  30. Acknowledgements • P. Kincaid, B. Goldiez and R. Shumaker of the Institute for Simulation and Training for their interest and discussions throughout different stages of this work. • U.S. Army Research Development and Engineering Command, Simulation Technology Center, Contract N61339-02-C-0107. • This research has been supported in part by the National Science Foundation under Grant No. BCS-0527545.

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