Download Human Motion Synthesis (II)

Synthesis of Motion from
Simple Animations
Introduction
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Produce realistic character motion
from simple animation
Non-skilled animator can quickly
produce believable animation
sequences
System is based on constraints of
input motion
Examples
Examples
Examples
Examples
Realism
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Character must satisfy laws of physics
Many possible muscle configurations
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Small subset appear realistic
Computing correct dynamics  complex
math
Tradeoff
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Level of control by animator
Artistic freedom vs. physical correctness
Process
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Animator creates rough sketch of desired
animation
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Small set of essential keyframes
System can make recommendations
System infers environmental constraints
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Focus on forces essential to realistic animation
No need to solve for all muscle forces
Model
Model
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Input to system
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Articulated character with mass
distribution
Values of joint angles at each frame
Spacetime optimization
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Solve for unknowns
Values of joint angles
Angular and linear momentums
Four Key Stages
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Constraint and stage detection
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Automatically detect environment
constraints
Separate original sequence into
constrained and unconstrained stages
Transition pose generation
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Establish poses between constrained and
unconstrained stages
Four Key Stages
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Momentum control
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Generate physical constraints
Based on Newtonian laws and
biomechanics
Objective function generation
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Construct the objective function
Smooth animation, similar to original, and
balanced
Constraints & Stage Detection
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Positional constraints
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Parameters of detection
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Minimal frames required, Tolerance of
intersections, & constrainable body parts
Constraints & Stage Detection
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Positional constraints
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Wi: Matrix that transforms point p to world
coordinates
x i = Wi p
At time i + 1, p is transformed to:
Wi+1Wi-1Wip
Define Ti+1 = Wi+1Wi-1
Constraints & Stage Detection
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Positional constraints
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Constraint on point p from time 1 to n
implies T1 through Tn all bring p to same
global position
Tixi = xi, or (Ti – I)xi = 0
Solution can be either point, line, or plane
Constraints & Stage Detection
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Sliding constraints
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Instead of fixing a point, allow it to slide
along a line (or plane)
e.g. foot of a figure skater
Point p constrained to line L:
minp,l ∑ Dist(TiWip,L)
Minimize sum of distances between xi
and the line L at each frame
Constraints & Stage Detection
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Stage Detection
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Given detected constraints, separate
original animation
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Unconstrained (flight)
Constrained (ground)
Different physics/biomechanics rules for
each
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During unconstrained, gravity is the only
external force
Transition Pose Generation
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Transition poses occur at boundaries
of stages
Store parameters about transition
poses for example motions
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Generated by animators
Motion captured data
Update database of motions
Transition Pose Generation
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Training input parameters (e.g. jump)
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Flight distance
Landing angle
Average horizontal speed, etc.
Output is three center of mass points
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Lower body
Upper body
Two arms
Transition Pose Generation
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Predict a candidate pose
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K nearest neighbor algorithm
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Select at most k similar examples
Compute candidate pose
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Three center of mass points
Interpolate poses of selected neighbors
Weighted by similarities to input sequence
Transition Pose Generation
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Construct full character pose
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Inverse kinematics problem
Minimize deviation between suggested and
original poses
Advantages to estimating small set of
parameters
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Joint angles not uniformly scaled
Same motion capture database for different
skeletal structures
Transition Pose Generation
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Transition to different skeletal structure
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CA: COM output parameter of character A
ĈA, ĈB: Corresponding COM for default pose
Intuitively, displace COM parameter by
rescaled difference between default and
suggested pose of character in database
Momentum Control
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Momentum during unconstrained
stages
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Gravity only external force
Acts on COM
Angular momentum is zero
Momentum Control
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Momentum during constrained stages
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No complex physical simulation
Based on biomechanics studies and
behavior of motion captured data
Natural dynamic motion
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First store energy (momentum
decreases)
Energy burst (small overshoot)
Momentum Control
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Enforce
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C1 continuous
at p1 and p4
p2 < p 1
d1 > d 2
p2 < p 4 < p 3
Objective Function
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Final check on realism
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Minimum mass displacement
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Compute integral of mass displacement over
body
Achieves natural joint movement
Example: bending at waist instead of knees
Minimal velocity of DOFs
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For time coherence (smoother)
Effectively minimize velocity of joint angles
Objective Function
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Static balance
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During constrained stages where character is
standing still
Analyze COM when projected onto plane
normal to gravity
Spacetime objective function is a
weighted sum of these
Conclusion
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Environment constraints
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Transition pose constraints
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Partition motion into constrained and
unconstrained stages
Defined between motion phases by pose
estimator (or user)
Momentum constraints
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Dictate behavior of linear/angular momentum
References
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C. Karen Liu, Zoran Popovic.
Synthesis of Dynamic Character
Motion from Simple Animations.
SIGGRAPH 2002.
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http://grail.cs.washington.edu/projects/
charanim/