networked robotsken goldberg, uc berkeley

goldberg@berkeley.eduhttp://goldberg.berkeley.edu

berkeley automation sciences labieor and eecs depts

Telegarden (1995- 2004)

networked robot:

tele-actor:

Networked robot cameras:

Frame Selection Problem:

Given n requests, find optimal frame

One Optimal Frame

Related Work

• Facility Location Problems– Megiddo and Supowit [84]– Eppstein [97]– Halperin et al. [02]

• Rectangle Fitting, Range Search, Range Sum, and Dominance Sum– Friesen and Chan [93] – Kapelio et al [95]– Mount et al [96]– Grossi and Italiano [99,00]– Agarwal and Erickson [99]– Zhang [02]

Related Work• Similarity Measures

– Kavraki [98]– Broder et al [98, 00]– Veltkamp and Hagedoorn [00]

• CSCW, Multimedia – Baecker [92], Meyers [96]– Kuzuoka et al [00]– Gasser [00], Hayes et al [01]– Shipman [99], Kerne [03], Li [01]

Problem Definition• Assumptions

– Camera has fixed aspect ratio: 4 x 3– Candidate frame = [x, y, z] t

– (x, y) R2 (continuous set)– z Z (discrete set)

(x, y)3z

4z

Problem Definition

Requested frames: i=[xi, yi, zi], i=1,…,n

Problem Definition• “Satisfaction” for user i: 0 Si 1

Si = 0 Si = 1

= i = i

•Symmetric Difference

•Intersection-Over-Union

SDArea

AreaIOU

i

i

1)(

)(

)(

)()(

i

ii

Area

AreaAreaSD

Similarity Metrics

Nonlinear functions of (x,y)…

Intersection over Maximum:

),(

)(

),max(

)1,)/min(()/(),(

i

i

i

i

biiii

Max

Area

aa

p

zzaps

Requested frame i , Area= ai

Candidate frame

Area = api

),(),( yxpyxs iii

)1,)/min(()/(),( biiiii zzaps

(for fixed z)

4z x

3z

4(zi-z)

Satisfaction Function

– si(x,y) is a plateau •One top plane•Four side planes•Quadratic surfaces at corners•Critical boundaries: 4 horizontal, 4

vertical

• Global Satisfaction:

n

iii

n

i

biii

yxpyxS

zzapS

1

1

),(),(

)1,)/min(()/()(

for fixed z

Find * = arg max S()

“Plateau” Vertices• Intersection between boundaries

– Self intersection:– Plateau intersection:

y

x

Line Sweeping

• Sweep horizontally: solve at each vertical boundary– Sort critical points along y axis: O(n

log n)– 1D problem at each vertical boundary

O(n) – O(n) 1D problems– O(n2) total runtime

x

Continuous Resolution Version• Lemma: At least one optimal frame has its

corner at a virtual corner.– Align origin with each virtual corner, expand frame– O(n2) Virtual corners– 3D problem→ O(n2) 1D sub problems

r6

r2

r5

r3

x

y

r4

r1

O0.00

0.40

0.80

1.20

1.60

0 20 40 60 80 100 120 140 160z

S(z)

Candidate frame Piecewise polynomial with n segments

Processing Zoom Type Complexity

Centralized Discrete Exact O(n2)

Centralized Discrete Approx O(nk log(nk)), k=(log(1/ε)/ε)2

Centralized Contin Exact O(n3)

Centralized Contin Approx O((n + 1/3) log2 n)

Distributed Discrete Exact O(n), Client: O(n)

Distributed Contin Approx O(n), Client O(1/3)

Frame Selection Algorithms

robotic video cameras

Collaborative Observatories for Natural Environments (CONE)

Dez Song (Texas A&M), Ken Goldberg (UC Berkeley)

motion sensors

timed checks

sensor networks

humans: amateurs and profs.

2005-2008

Ivory Billed Woodpecker

Alpha Lab (UC Berkeley)Tiffany ShlainDez Song (CS, Texas A&M)Jane McGonigal, Irene Chien, Kris Paulsen (UCB)Dana Plautz (Intel Research Lab, Oregon)Eric Paulos (Intel Research Lab, Berkeley)Judith Donath (Media Lab, MIT) Frank van der Stappen (CS, Utrecht)Vladlen Koltun (EECS, UC Stanford)George Bekey (CS, USC)Karl Bohringer (CS, UW)Anatoly Pashkevich (Informatics, Belarus)

Thank you