Group Tracking Algorithm for Crowded Scene

Automatic  visual  monitoring  systems  gain  more  significance  as  the  enhancement  of  high speed   processors   that   are  able   to   execute   the   prolonged   algorithm   efficiently.   Video surveillance  monitoring  systems  are  typically  applied  to  study  human  behavior  in  a crowded situation. It is used to observe posture, movement, trajectories and the interaction between people. For this purpose CCD cameras are installed at many crowded places. Most researchers’  work  however  is  focused  on  the  people  classification  and  the  recognition  of activities.  Human  identification  is  important  because  of  a  need  of  surveillance  in  the crowded scenes. Group motion tracking is applied to monitor the Groups of People (GOP) as single entities in the global flow rather than monitoring each person individually. It has been  studied  on  the  basis  of  dynamic  movement  and  the  surrounding  of  crowd  density which  will  affect  the  speed  of  an  individual/group.  Large  crowd  flow  perhaps  causes deadly  accidents  if  large  numbers  of  GOP  smash  into  each  other  in  narrow  passageways, streets  or   bridges.  The   system  must   identify  multiple   GOP   within  their   global  flow according  to  their  Spatio-temporal  characteristics.  Figure  1  illustrates  the  density  of  large crowd flow. The Religious and Sport activities are the application examples. According to Crowd  Dynamics  Ltd, (Crowd  Dynamics  Ltd)  in  the  year  of  2006,  363  pilgrims  lost  their lives  while  performing  the  Hajj.  There  are  a  number  of  readily  available  wide  area surveillance  systems  but  most  of  the  systems  are  not  suitable  for  high density  crowd monitoring.  For  safety  surveillance  of  large  crowd,  there  should  be  a  system  which  can detect and track unstable GOP by careful monitoring of crowd and display results in real- time scenario. And, with the results being displayed in real-time, it will certainly assist the system’s operator to make better decision.

The literature on large crowd flow has got a less coverage from researchers. In the case of large crowd flow scenarios, such as huge flow of peoples as in religious ceremonies or in sport  activates,  where  the  flow  of  crowd  have  so  many  individuals  or  small  numbers  of groups. On this, commonly used processing techniques cannot be utilized for such uncertain conditions. Dense or huge crowded scenes have so many individuals and groups that pose considerably  constraints  on  these  current  pre-processing  techniques.  Ali  and  Shah  (2007) describes  crowd flow segmentation.The basic concept which they have used is the Lagrangian particle dynamics to uncover the spatial organization of the flow field generated by crowd flow. Their work is focussed on the crowd flow segmentation, rather than detection and tracking groups of people in a large crowd flow. Their technique is an off-line technique. They generated one mean field from sequence of images to perform the analysis.The main objective of this research work is to develop an efficient monitoring system which can detect and track GOP within a huge crowd, with accurate and computationally efficient manner.  A  high  density  crowd  flow  may  exhibits  some  basic  properties  of  fluid  flow. Techniques available in fluid mechanics can be applied to study the flow properties of GOP moving  in  a  large  crowd.  Previously,  crowd  flow  has  been  treated  as  fluid  flow  to  study crowd  behavior.  The  majority  of  research  done  in  Computational  Fluid  Dynamics  CFD  is Eulerian and Lagrangian analysis. Eulerian analyses examine fixed points in space in a fluid flow,  while  Lagrangian  analyses examine  individual  particles  paths. 

Technically,  global large  crowd  flow  has  many  similar  characteristics  as  the  fluid  flow.  When  coherent structures are studied in terms of its quantities as a consequence of crowd flow trajectories, they are named as Lagrangian Coherent Structures or LCS. The LCS separates the flow of distinct behavior by managing the boundaries  where flow field experiencing the different dynamics. This  flow boundary in unsteady flows was introduced in a series of papers by Haller  (Haller  (2001),  Haller  (2005a)  and  Haller  (2005b))  the  boundaries  are  referred  as Lagrangian   coherent   structures   (LCS).   New   method   to   evaluate   LCS   is   Finite-Time Lyapunov Exponent field (FTLE) was developed by Shadden (Shadden et al. (2005, Shadden (2006)). Davies et al. (1995) presents the image processing techniques for monitoring crowd behavior. Another idea is to treat the crowd flow as a fluid dynamic, the crowd turbulence is used to study the physics of crowd disasters (Helbing et al. 2007). The density of crowd is an important isotropic quantity that appears to determine the probability of a deadly accident. The   crowd   flow   contains   two   types   of   tragedies   that   is   trampling   and   crushing   of pedestrians  (Lee  and  Roger 2005)  Trampling  occurs  when  pedestrians  are  in  motion. Crushing usually occur when a moving crowd have a contact with a stationary crowd. The crowd motion organization phenomena such as the directional separation, lane formation, direction towards bottlenecks and stop-and-go type of flow also creates critical conditions. (Helbing et al. 2007b). In crowded scenarios, the focus is on detecting and tracking groups in a global flow rather than in studying individual motion. In this circumstance, Lagrangian Coherent Structure is the most appropriate method. Lagrangian Coherent Structure or LCS is frequently used in fluid  mechanics  applications  in  order  to  distinguish  the  fluid  flow  and  its  associated characteristics. The basic inspiration to used LCS on crowd flow is to treat a flow as a single entity globally, and to track the unstable groups inside the flow. LCS can be computed in different ways, but Finite Time Lyapunov Exponent or FTLE field is  the chosen approach (Shadden 2006) since it gives maximum stretching of the nearby particles.

Theoretical background

Lagrangian Coherent Structures LCS

The  idea  of  Lagrangian  coherent  structures  (LCS)  stems  from  dynamical  systems  which have  been  extensively  used  in  fluid  dynamics  analysis.  LCS  has  also  been  used  in  the analysis of phase space of systems on the velocity vector field. Coherent motion is defined as a  region  at  which  at  least  one  essential  flow  variable  shows  important  correlation  with another  variable  over  a  range  of  space  and  time  Shadden  (Shadden  et  al.  2005,  Shadden2006).When coherent structures are studied in terms of its quantities as a consequence of crowd flow  trajectories,  they  are  named  as  Lagrangian  Coherent  Structures  (LCS).  The  LCS  is defined as ridges in the FTLE field. Ridges are the boundaries between the flows of distinct dynamics. The boundary can be determined by tracking flow particles and searching for the material lines that are named separatrices. It has effectively been utilized to partition the flow regions for different dynamics. The technical definition of LCS states that where the gradient of the FTLE field is normal to the eigenvector with the minimum eigenvalue of the Hessian matrix,  a  scalar  field  is  formed  that  is  the  LCS  Shadden  (2006).  The  LCS  is  an  invented boundary through which the amount of two or more fluids cannot pass to each other. All the particles within the divided region have similar behavior, known as coherent behavior.In  the  case  of  time  dependent  systems,  the  crowd  flow  can  be  classified  as  stable  and unstable  manifolds  of  hyperbolic  fixed  points  as  coherent  structures.  But  typically,  one uses the notion of coherent structures in the context of more general flows. Modeling of a dynamical  system  in  a  LCS  scene  gives  boundaries  in  the  spatiotemporal  separating region.  This  organization  dynamically  separates  the  distinct  behavior  in  the  crowd  flow which  is  unseen  in  the  velocity  vector  field.  The  boundaries  of  flow  region  can  be determined  by  tracking  the  flow  particles  during  advection  which  will  indicate  the material lines. Thus, flow regions with different characteristics would be highlighted. This flow boundary in unsteady flows was introduced in a series of papers by Haller (Haller2001,  Haller  2005a  and  Haller  2005b).  These  boundaries  are  referred  to  as  Lagrangian

Coherent Structures (LCS).

A vector field can be represented as a set of LCS. This LCS has sub regions in which each region contains similar behavior with respect to the crowd flow. The LCS reflects the large scale analysis of a vector field since they are based on the integration of trajectories. At each point  in  space,  the  LCS  measures  the  rate  of  separation  of  neighboring  particle  and  its trajectories. The LCS of unsteady fields usually distorts and shifts over time, but it still can be  recognized.  In  fluid dynamics,  LCS  boundaries  are  the  higher  ridges  of  Finite  Time Lyapunov Exponent Fields. This ridge refers to material surfaces that get advected with the crowd flow and move towards regions where the flow is separated in positive or negative time. The flow is separated along these boundaries surfaces.The Lyapunov exponent measures the behavior of the flow particles in a dynamical system. It  quantifies  the  exponential  rate  of  convergence  or  divergence  between  particles  of  the neighboring trajectories in a global sense. A positive exponent involves divergence, and a negative one means convergence. Therefore, a system with positive exponents has positive information in that trajectories that are initially close together move at a distance over time. The  more  positive  the  exponent,  the  faster  they  separate.  In  the  same  way  for  negative exponents, the trajectories move together with each other. A system with both positive and negative Lyapunov exponents is said to be chaotic.

Finite-Time Lyapunov Exponent field (FTLE)

A  new  method  to  evaluate  LCS  is  Finite-Time  Lyapunov  Exponent  field  (FTLE)  was developed by Shadden (Shadden et al. 2005, Shadden 2006). The LCS can be calculated in various  ways.  One  of  these  methods  is  based  on  the  FTLE  field.  It  evaluates  a  value  that corresponds to how quickly two imaginary particles would separate from each other as the flow   progresses.   It   measures   the   maximum   linearized   growth   rate   of   the  distance perturbation between the nearby flow particles over the time interval to its trajectories. In other  words,  it  measures  the  rate  at  which  two  neighboring  particles  diverge  from  each other  at  a  given  location  and  time  interval.  The  FTLE  differentiates  the  amount  of  flow particle  stretching  about  the  trajectory  over  time.  It  is  defined  by  the  local  maxima  of  the FTLE field which specifies regions with distinct dynamics in the flow Haller (2001). Let us suppose that the flow field experienced distinct dynamics in two or more different regions of the same flow. Within each sub region, FTLE contains a coherent motion in the flow that is all the particles inside each region contain a similar behavior which is indicated by  the  Eigenvalue  of  λmax  (∆)  close  to  zero.  The  boundary  of  two  flow  region  contains different dynamics in which particles at these boundaries encloses as incoherent behavior. This  condition  creates  higher  Eigenvalue  which  rises  as  boundaries  in  FTLE  field.  The maximum stretching of particles is given by the square root of the largest eigenvalue. As the stretching is produced by velocity vector field, it would increase exponentially with the time series. The logarithm of the resulting value is computed and additionally normalized by the absolute advection time |T|. This leads to the explanation of the FTLE field. The notation (formulation) of the FTLE will be defined in section 2.3.

The FTLE indicates sections in the flow with different dynamics due to flow particle pairs straddling the edges of the boundary that separate them. This is also to indicate that they are faster  than  other  arbitrary   flow  particle  pairs.  Area  of  maximum  material  stretching generates local maxima of the velocity field that may specify either local maximal stretching or  local  maximal  shear.  Trajectories  of  the  flow  particles  can  be  integrated  in  negative  or positive  time.  This  is  similar  to  the  scalar  parameters  in  a  flow  gathering  in  the  coherent structures  which  can  be  achieved  from  the  flow  vector  field.  Consequently,  FTLE  can  be calculated by integrating trajectories in backward time (T < 0). The ridges in the FTLE field indicate  attracting  material  lines  or  attracting  Lagrangian  coherent  structures  (attracting LCS)  Shadden (2006).Integrating  trajectories in  forward  time  (T  > 0)  produce  FTLE  ridges that  spot  the  location  of  distinct  flow  as  material  lines,  or  repelling  Lagrangian  coherent structures (repelling LCS).These positive-time and negative-time LCS are defined as the boundary between qualitatively different regions in the flow. The integration time can be increased or decreased depending on  the  amount  of feature  required  from  the  computation.  In  addition,  the  location  of  the ridge indicating the boundary of the dissimilar flow of crowd does not change.

FTLE field with respect to eigenvalue is first given by Shadden [2005, 2006]. The FTLE can be described as the flow region experiences distinct dynamics in two or more different areas of the same flow. Within this each region, we have a coherent motion in the flow i.e. all the particles inside each region contain similar behavior which is indicated by the eigenvalue of λmax(Δ) close  to  zero.  While  at  the  boundary  of  two  regions,  having  different  dynamics, particles at these boundaries having an incoherent behavior, creates higher eigenvalue which

are rise as boundaries in FTLE field. The absolute value |T| is used instead of T in Equation (10) for the reason that FTLE can be calculated for T > 0 and T < 0. The material line is called a repelling  LCS  when  (T>0)  over  the  time  interval  in  forward  time.  On  the  other  hand  the material line is called an attracting LCS (T < 0) over the interval in backward time. Repelling and attracting LCS reveals stable and unstable manifolds of a dynamic system.

Eigenvector parallelism method

Eigenvalues play an important role in conditions where the matrix is a transformation from one  vector  space  onto  itself.  Systems  of  linear  ordinary  differential  equations  are  the primary examples. The values can correspond to frequencies of vibration, or critical values of  stability  parameters,  or  energy  levels  of  atoms  it  has  been  discussed  in  more  detail  by Moler, C. (2008). As mentioned earlier, LCS can be defined as ridges on the flow field where particles show incoherent behavior. This phenomenon can be explained by the existence of higher  eigenvalues  at  certain  region  of  the  flow  field.  These  boundaries  separate  two regions,  and  are  known  as  separatrices.  Moreover  the  method  requires  an  approach  to extract the information from FTLE field, and identify the precise unstable GOP with respect to its surroundings.In  recent  years,  valuable  developments  have  been  made  in  image  segmentation.  Several

algorithms have been proposed in which Normalized cut algorithm, is one of the method used for image segmentation first proposed by Shi and Malik (2000). This Normalized cut algorithm is also applicable to perform segmentation on the boundaries of FTLE field. One weakness of this algorithm is that, it process at high computational time to produce results. But in this application, the prime goal is to make the algorithm efficient enough to execute in real-time in real world scenarios. This requires fast running algorithm. In order to overcome this  problem  generalized  eigenvalue  is  utilized  to  measure  vector  parallelism,  named  this phenomenon as Eigenvector Parallelism. This technique calculates eigenvalue divergence on the  FTLE  boundaries  to  identify/segment  the  exact  unstable  GOP  with  respect  to  their global flow. Consequently, it will differentiate the unstable or hazardous GOP’s boundaries from its flow boundaries with a low computational time.

Formulation of Eigenvector Parallelism Method

In Eigenvector Parallelism Method, the technique first correlates the two constitutive mean flow  fields  RMuu+T  and  holds  the  peak-mean  value  denoted  as  PMuu+T  of  the  vector  field Fuu+T. The characteristic Equation of eigenvalues and eigenvectors is given as:

Optical flow

The  input  prerequisite  for  FTLE  analysis  is  the  velocity  vector  field.  Optical  flow,  Lucas- Kanade (Lucas & Kanade 1981) technique is used. This is a two frame differential method to estimate motion in a moving object. This method aims to calculate the motion between two image frames which are taken at times t and t + 1 at every pixel location. This method is also frequently  known  as  the  differential  methods,  since  it  is  based  on  local  Taylor  series approximations of the image signal. It also uses partial derivatives with respect to the spatial and temporal coordinates.The term optic flow refers to visual phenomenon that has apparent visual motion that can be  experienced  as  an  object  move  through  the  world.  There  is  a  directly  mathematical relationship between the magnitudes of the optical flow. If the speed of motion is doubled, the optic flow will also be double. The optical flow also depends on the angle between the direction of view and the moving objects. Advantages of the optical flow algorithm include that it yields a high density of flow vectors. That is, if the flow information missing in inner parts of homogeneous objects is filled-in from the motion boundaries

Smoothing of data

Data   smoothing   is   an   important   process   which   contributes   to   simplify   the   LCS implementation.  It is  based  on  Noise  Filtering  and  Mean  value.  Figure  3  shows  the  block diagram  of  data  smoothing  process.  It  is  very  useful  technique  which  exposes  the  clear picture of obtained results from optical flow. The optical flow field of crowd motion carries

scattered resulting vectors. This is shown in Figures 4 where it is observed that flow vectors of dense crowd have scattered direction and magnitude which is unable to define distinct group  behaviors.  Data  smoothing  helps  to  expose  different  groups  present  in  the  crowd flow by noise reduction and mean flow field.The task for noise reduction is performed by median filtering, which is a non-linear spatial signal enhancement technique. While mean flow field is calculated by taking mean in time series or running mean. It is commonly defined as the continuing calculation. The degree of smoothness  can  be  controlled  by  adjustment  of  the  neighborhood  range  or  the  fitting weights. Fu  denoted as optical flow field under observation and its running mean as RMu, here  u  represents  the  number  of  frame  in  real  time  video  sequence.  Running  means  is programmed in this methodology to reset after a few frames, so that FTLE field can exactly identify the true position of the unstable group.

Advection of particles

In  order  to  detect  and  track  the  movement  of  the  flow  of  crowd,  the  system  launched  a Cartesian  grid  of  particles.  This  movement  is  known  as  the  advection  of  particles.  These particles are placed on the running mean RMof flow field Fu, where particles have certain (constant) distance between them. Initially, particle position is x0, at time t. As time passes, flow  of  crowd  change  its position  therefore,  the  optical  flow  field  becomes  Fuu+T  and  its running mean RMuu+T. The final position of particle turn out to be to x(t+T;t,x0). Each particle advection is computed with a forth-order Runge-Kutta-Fehlberg algorithm.

Forth-Order Runge-Kutta-Fehlberg

The Runge–Kutta method is an important tool. It is used to perform the approximation of solutions  of ordinary  differential  equations.  There  are  different  types  of  Runge–Kutta methods,  classified  by  how  many  points  are  used  within  each  time  step.  The  method applied  in  the  FTLE  computation  is  the  4th  Order  Runge–Kutta  method.  This  is  the  most often used method of the Runge-Kutta family. It extends the idea of the mid-point method by using the information.The  fourth  order  Runge-Kutta  algorithm  requires  four  gradient  or  ‘’k’’  terms  (as  given  in equation 16), which can calculate from following equations (17), (18), (19) and (20)

the entire flow FTLE boundaries eigenvalue. This occurs because vectors at the boundaries of  FTLE  field  of  unstable  GOP  have  distinct  behaviors.  Whereas,  PMuu+T   contains  the majority  behavior  in  the  global  flow.  When  the  system  computes  the  eigenvalue  between PMuu+T  and  the  vectors  position  at  boundaries  of  FTLE  field,  as  a  result  the  stable  flow boundaries shows approximately similar characteristic as the peak-mean value. Therefore, the  eigenvalue  minimize  these  boundaries,  showing  evidence  of  the  analogous  flow.  In other  case,  unstable  GOP  boundaries  are  detected  by  the  FTLE  field  owing  to  different dynamics. Vectors at these boundaries give higher eigenvalue when they are computed with PMuu+T. Figure 10 shows the results of Eigenvector Parallelism Method where unstable GOP is detected as higher eigenvalue.

This approach has been tested by changing the direction of unstable GOP on self introduced instability  video  sequences,  and  subsequently,  observing  the  imperative  results.  As  the incoherent  or  unstable  GOP  changes  its  flow  direction  with  respect  to  the  global  flow, eigenvalue will be increased. Greater the change in direction of flow vector, higher will be the eigenvalue.  It will increase until the vectors aligned at the opposite direction as compare to  the  peak-mean  value.  In  such  case  where  vectors  are  aligned  in  opposite  directions,  a negative eigenvalues in obtained showing unstable GOP. Figure 11 elucidates the negative eigenvalue of GOP, where GOP contains opposite direction with respect to entire flow.

Identification of unstable groups

Unstable GOP has dissimilar dynamical behavior and LCS is used to track their boundaries. For  the  convergence  of  the  detected  unstable  groups,  the  technique  employed  a  simple scheme  to  study  the  neighboring  flow.  Let  the  boundary  box  of  detected  unstable  group under action denoted by Bk,l, where k, l is its dimensions. At this instance, patch of box Rk’,l’  is launched on the Bk,l, such that size of k’, l’ is determined by a ratio. It can be obtained by taking a ratio between the image frames to the detected object. The resulting ratio will be an integer  which  will  increase  the  dimension  of  k’, l’  up  to  a  certain  fold.  The  size  of  Rk’,l’   is determined  by  this  ratio  which  is  minimizing  the  computational  cost.  However  different patch size gives different computational cost. A comparison of computational cost is shown in  Table  1.  In  this  example,  similar  detected  object  is  used,  in  which  different  ratios  are tested in order to calculate the computational costs.

Results and discussion

Group  motion  detection  is  a  significant  tool  to  study  the  GOP  behavior  in  a  crowded environment.   We have utilized LCS to examine GOP in a large gathering. We have tested the algorithm using a range of videos taken from Ali and Shah (2007). This consists of high density crowded scene including videos during Hajj, New York City Marathon and traffic scenes.

Group detection

In  the  sequence  entitled  ‘Inside  Makkah’,  as  shown  in  Figure  11(a),  a  dense  and  random crowd flow is observed. In this video scene, the direction of global flow is from left to right, three GOP can been seen moving against the direction of the global flow which is detected by Eigenvector Parallelism Method as shown in Figure 11(c). It is noted that two GOP are having  hazardous  motion  dynamics  with  respect  to  surrounding  crowd  because  they  are disturbing  the  global  flow.  It  can  computed  by  using  method  explain  in  Section  3.6.  The third  GOP  is  not  hazardous  despite  having  different  direction  because  they  are  moving independently without propagating inside the moving crowd. Figure 13(a) is the watershed plot  used  for  clear  visualization  of  unstable  GOP.  Similarly  Figure  13(b)  is  the  watershed plot of video sequence shown in Figure 10. Now a comparison of obtained results has been performed with well known methods i.e. K-Mean on optical flow (u,v) field. It is necessary to mention here, that numbers of segments are pre-defined to run this method. Figure 13(c) displays  result  of  K-Mean  method  which  is  unable  to  detect  unstable  GOP  present  in  the scene although, number of segments has been increased up to 12 in this case. Figure 13(d) shows resulting flow segments of the same video sequence which is under discussion, but this result is obtained from Ali and Shah (2007). Figure 13(d) shows segmentation of crowd according to flow. It is unable to track small groups present at the bottom of the video frame having distinct dynamics. Their method identified the flow (at bottom flow) as single flow and represented it as a single segment. It is because there focus is on flow segmentation not on the tracking of GOP. In contrast, our method detected the flow pattern of crowd as well as tracking small GOP having distinct dynamics with respect to surrounding flow.

The next result which is discussed here is shown in sequence Figure 1(b). The approach is tested  on  a  video  sequence  of  hurling  stones  at  Jamarat  Bridge.  This  video  represented  a highly important area where large crowd of people gather to perform a similar task. In the past, most of the deadly incidents occur at Jamarat Bridge due to collision of people in high density  crowd.  Detection  and  tracking  of  GOP  having  unstable  dynamics  are  challenging task in this video sequence, since the flow pattern is quite complex and density of crowd is very high. The proposed method is able to work and produce results in such a highly dense crowd. The direction of global flow in this scene is from right to left. Few GOP are detected and  tracked  having different  direction.  The  result  of  Eigenvector  Parallelism  Method  is displayed in Figure 14(b).Figure 14(c) is the watershed plot used for clear visualization of unstable GOP. The result was  then  compared  with  K-Mean  methods.  In  this  case  K-Mean  is  unable  to  segment  the crowd  flow  exactly,  due  to  complexity  and  density  of  the  scene.  In  Figure  14(c)  three hazardous groups are highlighted below vacuum region (at the bottom) while two GOP are present  above  vacuum  region.  While  K-Mean  method  could  only  detects  two  GOP  at  the bottom out of three while merged the upper groups with the global flow as shown in Figure 14(d). This shows the robustness of the proposed Eigenvector Parallelism Method.

Test set

The  video  sequence  of  New  York  City  Marathon  already  used  in  Figure  10,  in  which artificial  instability  was  generated  by  Ali  and  Shah  (2007).  In  this sequence  unstable  GOP had different direction with respect to the global flow but GOP was static throughout the video.   Now a moving GOP is introduced in the video sequence shown in Figure 15(a), the direction  of  mobile  GOP  is  from  left  to  right  which  is  changing  its  position  in  every incoming frame. This continuous change in position makes the GOP a challenging object to track. This is mathematically described as, Pt = (offset x + fr) + offset y. Where Pt is referred as position of patch (i.e. unstable GOP), fr is number of frame sequence which can be defined as fr= 1, 2, 3….n and offset is value where patch is initially launched.

Algorithm computational time

The robustness of the work depends on the fast running algorithm that will run efficiently, in order to do real-time analysis. To apply the Lagrangian technique on the image sequences requires few numbers of frames in reading memory. These frames become the integration length  |T|  for  the  algorithm.  This  requirement  indicates  that  Lagrangian  methodology  is only applicable for off-line analysis. The solution of off-line analysis problem is solved by MatLab™   M-file   and   pre-system   Simulink™   interface,   both   simultaneously   worked together.  Simulink  model  worked  as  pre-system,  consist  of  reading  frames  from  data acquisition box and data smoothing. While the M-file worked as post-system, contains of all the methodology of Lagrangian technique.  This project is applicable for frame wise analysis rather than estimate one mean field from the integration length |T|. In this formulation, the integration  length  |T|  represents  the  next  frame  in  real-time  videos.  The  algorithm  was implemented,  and  all  analyses  have  been  conducted  on  a  3  GHz  core2duo  Pentium  IV computer, executing Windows XP. The processing time for a single frame, size of 400×400 RGB  image,  is  approximately  0.5  second  that  is  2  frames  per  second.  This  technique  has assumed that the group motion is a slow performing motion because people moving in a large  crowded  scene.  However,  the  execution  time  can  be  increased  up  to  5  frames  per second  by  reducing  the  image  size.  Nevertheless,  this  will  cause  a  loss  of  spatial  image information.

In   general   Lagrangian   sense,   taking   a   denser   particle   grid   will   give   higher   spatial resolutions, which will lead to a higher computation time. If longer time integration is used, more of the boundaries will be exposed. Since flow particles were observed for longer time period consequently more boundaries will be exposed. This methodology cannot make use of  longer  time  integration  due  to  the  computational  cost  restriction.  Table  2  shows  the computational  cost  of  sub-systems  for  different  sub-methods.  Table  2  is  computed  on  the sequence title “Inside Makkah”.


This chapter provides a general framework for group motion detection and tracking in real- time  crowded  scenarios  by  using  Lagrangian  based  approach.  The  main  objective  of  this research is to detect and track Groups of People (GOP) that may create a calamity due to

their  unstable  motion.  This  objective  has  been  achieved  by  employing  a  Lagrangian Coherent structure (LCS). The motivation for using LCS method came from the field of fluid mechanics which is able to reveal the spatial organization of the flow field created by the crowd   flow.   The   Finite   Time   Lyapunov   Exponent   (FTLE)   Field   is   one   of   the   most appropriate approaches to obtain the LCS.   It measures the maximum divergence between two particles as the flow progresses. At first the optical flow was used to give the flow field on  which  the  system  launched  a  particle  grid  for  tracking  the  advection  of  crowd  flow. These  advected  of  particles  are  mapped  by  flow  mapping  on  which  spatial  gradient  is computed.   Finally   Finite-time   Lyapunov   Exponent   (FTLE)   field   is   computed   on   this gradient  of  flow  map.  The  FTLE  field  restores  the  boundaries  where  the  crowd  flow experiences the dynamic change. On these boundaries, the system employed a new method of   eigenvector   parallelism   in   order   to   identify   the   precise   unstable   groups   that   are propagating in the global flow. One of the common requirements of the motion detection algorithms in computer vision is the perspective views of camera. In this approach for detection of GOP in a crowded scene, the  flow  of  crowd  must  be  visualized  from  certain  height  for  the  visibility  of  the  spatial organization of the flow. The variability of the image captured will also produce significant noise source to the overall analysis. In this case, stationary camera is used to minimize the capture  noise  factor.  The  developed  monitoring system  successfully  tracks  a  range  of objects, which can easily be used for actual monitoring requirements. The method suggested is very robust and can be adapted to various crowded scenarios such as traffic flow and fish schooling, where thousands of objects are involved.

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