Planning Tracking Motions for an Intelligent Virtual Camera

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Planning Tracking Motions for an Intelligent
Virtual Camera

• Tsai-Yen Li Tzong-Hann Yu
• Presented by Chris Varma
• May 22, 2002

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Presentation Outline

• Problem considered
• Definition
• Related work
• Similar problems
• Problem space
• General formulation
• Specific formulation
• Actual formulation
• Search criteria
• Planning efficiency
• Tracking direction
• View distance
• Overall movement
• View angle

• Approach
• Best-first planning (BFP)
• Cost Function
• Post-processing steps
• Implementation
• Experiments
• Improvements
• QA

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Problem Definition

• How to automatically generate viewpoint motions
  for a virtual camera according to the pre-planned
  trajectory of an interactive tour guide
  application
• Different from active vision problems requires
  maintaining constant visibility with the target
  while optimizing certain camera-specific criteria
• Different from traditional path planning
• Consider visibility constraints
• Obstructions to cameras view and its geometry
  not the same

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Related Work

• Similar visibility related problems in robotics
• Installing minimal of sensors (or cameras)
  statically is art gallery problem
• Allowing sensors (or cameras) to move actively is
  pursuit evasion problem

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Similar Problems

• Similar problems about object tracking solved by
  Gleicher and Witkin (1992)
• Used dynamic programming approach to generate
  motion for observer (or camera) to track moving
  target
• But, targets trajectory was partially known
• If motion of target is predictable, then can find
  optimal solution off-line
• Otherwise, must use on-line solution
• Planner tested for off-line use took about 20
  sec.
• But, dont use because
• Tour guide app is interactive 20 sec. is too
  slow
• Our targets motion is predictable so better
  solutions possible off-line

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General Formulation

• Target t and viewpoint v (or camera)
• Parameterization qt (xt, yt, ?t) and qv (xv,
  yv, ?v)
• Free C-space of t and v Ctfree and Cvfree
• Composite free C-space of t and v
• Xfree Ctfree x Cvfree, is a 6D space where
  solution path should reside
• Suppose targets trajectory given as function of
  time (t) and all qt collision-free
• CT(xv, yv, ?v, t) (xt(t), yt(t), ?t(t), xv,
  yv, ?v), is configuration-time space
• But, not all configurations in CT legal b/c must
  also satisfy the visibility and velocity
  constraints of camera!

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Specific Formulation

• Specify vs configuration with respect to ts
  coordinate system
• qv (ø, l, f),
• so CT Cv x T
• Tracking direction Ø orientation of vector
  connecting t and v
• Preferred view distance l
• View Angle f between direction that camera is
  pointing to and vector connecting v and t
• S fixed width of view cone

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Actual Formulation

• Technical issue 4-dimensional space, as CT, is
  too large to search for interactive app
• Solution simplify further by decoupling f b/c
• v can be modeled as an enclosed circle so any
  orientation of circle wont violate configuration
  constraint
• Assume can rotate v as fast as moving target,
  then can adjust view angle passively to maintain
  visibility of t
• Account for f after other parameters set
• So, first search 3D configuration-time space,
• CT (t, ø, l), t time

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Search Criteria planning efficiency

• Since this is an interactive app, efficiency is
  the most important criteria
• The planner returns the first feasible trajectory
  satisfying
• Configuration constraints
• Visibility constraints
• Corresponds to the time dimension in CT and CT

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Search Criteria tracking direction

• Since simulating motion of camera following tour
  guide, want camera behind guide
• So force tracking direction Ø to say within range
  of orientations centered at orientation directly
  behind target

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Search Criteria view distance

• To maintain clear image of tour guide, near and
  far clipping distances need to be applied to
  further constrain viewpoint motion
• So maintain view distance l as closely as
  possible

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Search Criteria overall movement

• Want to minimize overall movement of viewpoint
  b/c
• Frequent movement causes scene discrepancy and
  motion sickness
• Frequent movement provides less opportunity for
  3D rendering speedup
• Thus reduce movement, denoted d, in each step of
  tracking trajectory
• d is function of current and previous Ø and l

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Search Criteria view angle

• Technical issue moving target may move out of
  sight if view angle f outside range
• Solution keep target clearly at center of view
  whenever possible without introducing frequent
  scene changes
• This is a tradeoff
• User defined

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Approach Best-first Planning

• Search starts from qi(ts, fi, li) and tries to
  find path to legal goal qg(te, , ) in last time
  slice.
• First feasible path returned if one exists
• A configuration considered legal iff
• Parameters in legal bounds
• Viewpoint doesnt collide with obstacle
• View cone not obstructed

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Approach Cost Function (1)

• f4 normalized cost function for the Euclidean
  distance
• moved from the parent configuration
• p returns the previous position of the viewpoint
  for the given approaching direction
• dist returns the distance between two positions
• dir an integer indicating the direction where
  the current configuration was created

• f1 cost function for the distance between the
  current and the ending time slices. te is the
  ending time
• f2 normalized cost function for the tracking
  direction
• f0 is a preferred neutral tracking direction
• f3 normalized cost function for the view
  distance. L0 is a preferred neutral view distance

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Approach Cost Function (2)

• Cost function is linear combination of individual
  cost functions
• Weights are user specified
• For tour guide app, large w1 to make f1 dominant
  b/c planning time is most important

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Approach Post-processing

• BFP returns path consisting of sequence of
  configurations indexed by time
• Post-processing
• Path is smoothed to replace portions with
  straight-line segments of same lengths in
  CT-space s.t. accumulated costs for new segments
  are smaller
• Unlock view angle f and allow to change s.t. it
  minimizes viewpoints rotational movement
• i.e. dont rotate viewpoint unless target going
  to exit view cone

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Implementation

• Written in Java
• Planner has 2 parts
• Path planning computes sequences of holonomic
  motions for target
• Motion tracking computes tracking motion for
  viewpoint
• Running time is linear in of time steps
• Actual run time depends on volume of regions
  visited during search process
• Worst case no feasible pathall nodes in CT
  visited in a few seconds
• Average case run time is fractions of second to
  few seconds

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Experiments
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Improvements

• In current planner, configuration collisions and
  visibility occlusion are computed on the fly
• But, if we have complex environment, would be
  better to preprocess this since we are off-line
  anyway
• So could systematically compute forbidden regions
  in CT-space as preprocessing and use hash table
  to check for collision

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QA