Modeling of Moving Objects in a Video Database

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Modeling of Moving Objects in a Video Database

• Presented by James Elding
• University of Alberta
• Comput 605

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Problem

• Model the Spatial and Temporal relationships of
  moving objects in a qualitative manner.
• Facilitate query processing in the domain of
  video databases.
• Integrate their moving object model into an
  object-oriented database system.
• They are attempting to solve an Information
  Retrieval problem.

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Motivation

• No research has studied the relationships between
  moving objects in a video database.
• Retrieving moving objects, which requires both
  spatial and temporal knowledge, is part of
  content-based querying.
• To model the relationships qualitatively instead
  of quantitatively.

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Spatial Representation of Salient Objects

• An object Ai is defined by an MBR (Xi,Yi,Ci)
  where Xi xsi,xfi , Yi ysi,yfi , and Ci is
  the centroid of Ai represented by a two dimension
  point Ci xi,yi.
• We can model any object at time t Ati (Xti
  ,Yti ,Cti ).
• The displacement of Ai at time interval I
  tsi,tfi is defined as DISP(Ai,I) sqrt((xits
  xitf )2 (yits yitf)2 )

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Spatial Representation of Salient Objects

• The Euclidean distance between two objects Ai and
  Aj at time tk DIST(Ai, Aj , tk) sqrt((xitk
  xitk)2 (yitk yitk)2 )
• DISP and DIST are characterized by the centroid.

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Modeling Moving Objects

• Their model uses 8 directional relations.
• Using qualitative relations to support fuzzy
  queries
• The relations can be described in terms of
  Allens temporal algebra.

Eight moving directions
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Modeling Moving Objects

• The motion of Ai over time interval Ii can be
  modeled as (Si ,di ,Ii ) where Si DISP(Ai,Ii)
  and di is one of the 8 directions.
• The above example is equivalent to
• lt ( S1,ET,I1), (S2,NT,I2),(S3,NE,I3),(S4,SE,I40)
  ,(S5,ET,I5),(S6,SE,I6)gt

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Modeling Moving Objects

• Modeling trajectories at this low a level maybe
  computationally expensive.
• It would be impossible to capture the
  relationships between moving objects using a
  quantitative model.
• The authors thus propose a qualitative model for
  describing the spatio-temporal relationships
  between moving objects.

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Modeling Moving Objects

• The relation Ai south Aj can be modeled
  accordingly
• Aix d, di, s, si, f, fi, e Ajx Aiy
  b,m Ajy

Allens 13 Temporal Interval Relations
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Modeling Moving Objects

• Let Ai and Aj be two moving objects during time
  interval Ik.
• The moving spatio-temporal relationship (mst) is
  defined as Ai( ,ß, Ik)Aj where is any
  topological relation, ß is any directional
  relation, and Ik is a time interval.
• NULL is an additional directional relation ß for
  cases where two objects have no directional
  relationship.

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Modeling Moving Objects

• The example below may represent two people
  meeting on the street, shaking hands, and moving
  away.
• The mst relation Ai Ø Aj would be
• lt(DJ,LT,I1),(DJ,LT,I2),(TC,LT,I3),(OL,NULL,I4),(T
  C,RT,I5),(DJ,RT,I6)gt

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Matching Moving Objects

• Matching trajectories and MST lists for handling
  user queries.
• Propose a systematic way to find all objects B in
  a database whose trajectory matches user
  trajectory A.
• A set of linked lists is used to represent the
  trajectory of B.
• An mst-list of two moving objects can also be
  represented with a linked list.

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Matching Moving Objects

• Figure (a) displays the is a representation of a
  single trajectory using directional relations and
  relative time positions.
• Figure (b) displays the representation of two
  moving objects using topological relations,
  directional relations, and relative time
  positions.

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Matching Moving Objects

• Exact trajectory and mst-list matches are highly
  unlikely.
• Directional and temporal measures are proposed
  for fuzzy querying.

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Matching Moving Objects

• Let M1,M2,,Mm (m 1) be the mst-list of Ai.
• Let N1,N2,,Nn (m n) be the mst-list of B.
• minDistMst(A,B)MIN distance(Mi,Nij)
  ( j 0 j n-i)
• where distance(Mi,Nij) distance(
  (Mi,Nij) ) distance( ß (Mi,Nij) )
• Recall that and ß are topological and
  directional relations respectively.
• maxDistMst(A,B) 4 m 7 m, which is used to
  normalize the final similarity score.

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Matching Moving Objects

• The final Similarity score is defined as
• MstSim(A,B) maxDistMst(A,B) - minDistMst(A,B) /
  maxDistMst(A,B)
• There exist an analogous and similar similarity
  measure for matching single trajectories to one
  another.
• It considers only the directional relations.

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Matching Moving Objects

• Modeling MST-Lists considers pairs of moving
  salient objects.
• The mst-Lists for the figure are
• abMstSet (DJ,NW,I1),(DJ,NW,I2),(DJ,WT,I3)(D
  J,NW,I4),(DJ,ET,I5),(DJ,NE,I6)
• acMstSet (DJ,NW,I1),(TC,NW,I2),(OL,NL,I3)(OL,NL
  ,I4),(OL,NL,I5),(DJ,SW,I6)
• bcMstSet (DJ,SE,I1),(DJ,SE,I2),(DJ,NE,I3)(DJ,SE
  ,I4),(DJ,SW,I5),(DJ,SW,I6)

A fictitious basketball game
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Query Processing

• They integrate their model into an ODMBS-TIGUKAT.
• Queries are facilitated through Object Query
  Language (OQL).
• Example Select x.value
• from x in c.B_SalientObjects
• where x.B_value.B_trajectory.B_simMatc
  h(myTraj) gt r
• r is a user defined threshold.

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Conclusions

• Present a way to model the trajectory of a moving
  object.
• First model to propose a model for the relative
  spatio-temporal relationships between moving
  objects.
• Support for a rich set of spatial topological and
  directional relations.
• Quantitative and qualitative properties of
  objects is preserved.

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Related Work

• Choon-Bo Shim, Jae Woo-Chang Spatio-temporal
  representation and retrieval using moving
  object's trajectories. ACM Multi Media Workshops
  2000 209-212