Drawing a Skeleton Fast FromMotion Capture Data

Jonathan Kipling Knight

Nov 7, 2006

7 Nov 2006 JKK 2

Introduction

• Purpose

• Motion Capture

• Data Files

• Skeleton Formation

• Closed Form Solution

• Conclusion

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Purpose

• Draw an articulated framework of solid segments connected by joints.

• Use live data capture to draw figure.

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Motion Capture

• Magnetic Trackers• Position and Orientation Transmitted

• Light Dots• 3D Position if in view

• Figure Tracking• Computer vision and image analysis

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Motion Capture Session

05_05

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

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Data Files

• No international standard• Proprietary, semi-open formats

• C3D oldest from Dr. Andrew Dainis• Bad Data

• Users partially fill fields• Units incorrect• Frame rate incorrect• Signed/unsigned mismatches

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Producing a Skeleton

• Single Time Frame• Produce position, size and orientation of

each segment• Markers are fixed 3D positions on segment• Orientation is included with magnetic

trackers• Rotation Points are fixed on TWO

segments but are not in data

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Producing a Skeleton

• How to Move Between Frames• Inverse Kinematics popular• Forward and Inverse Kinetics• Closed Form Solutions

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Inverse Kinematics

• What joint angles are needed to get to next position and orientation?

• Good for filling in large frame gaps

• Sometimes more than one answer

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Inverse Kinematics Example

QuickTime™ and aCinepak decompressor

are needed to see this picture.

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Closed Form Solution

• Requires 1-3 positions on each segment

• Each frame independently drawn

• Quickest O(26N)

• As accurate as data O(/N)

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Segment Tree

• Root segment usually hips

• Leaf segments hands, head and feet

• No loops

Root

Leaves

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Solve Sphere at Each Joint

• One marker on child produces sphere around joint relative to parent

• Must know orientation of parent• 1-3 markers needed or• Magnetic trackers

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Three Point Orientation

• Three Orthogonal Axes

€

rx =

r p 2 −

r p 1

€

rz =

r x ×

r p 3 −

r p 1( )

€

ry =

r z ×

r x

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Two Point Orientation

• Three Orthogonal Axes

€

rx =

r p 2 −

r p 1

€

rz =

r x ×

r c −

r p 1( )

€

ry =

r z ×

r x

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One Point Orientation

• Three Orthogonal Axes

€

rx =

r c −

r p 1

€

rz =

r x ×

r n

€

ry =

r z ×

r x

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Center of Sphere

• Asymptotically Unbiased Generalized Delogne-Kåsa Method

€

rc =

r m + 1

2 C− ˆ σ 2( )−1r

s

€

rm = 1

N

r ′ p i

i=1

N

∑

€

C = 1N −1

r ′ p i −

r m ( )

r ′ p i −

r m ( )

T

i=1

N

∑

€

rs = 1

N −1

r ′ p i −

r m ( )

r ′ p i −

r m ( )

T r ′ p i −

r m ( )

i=1

N

∑

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UGDK

• Asymptotically unbiased if measurement error estimate is correct

• Fastest known O(26N)

• Cholesky inverse of 3x3 matrix

€

limN→∞

Er c ( ) =

r c 0

€

Covr ′ p i( ) = ˆ σ 2I

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100 Point Comparison

MLE

GDKE

UGDK

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Marker Requirements

• 3 Markers on root segment of tree

• 1-3 Markers on all other segments

• Segments with 1 Marker should have one degree of freedom (e.g.knee,elbow)

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Break Dance

QuickTime™ and aMotion JPEG B decompressor

are needed to see this picture.

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Salsa Dance

QuickTime™ and aMotion JPEG B decompressor

are needed to see this picture.

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Conclusion

• UGDK is fastest available sphere solution O(26N)

• Asymptotically unbiased answer

• As accurate as data O(/N)

• 1-3 Marker requirements per segment

• Provides skeleton to attach solid shape