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the role of mobility and control in the inference of representations stefano soatto ucla t. lee, a. ayvaci, j. dong, d. davis, j. balzer, j. hernandez, l. valente 1 Saturday, November 30, 13 1 what is a representation ? why do we need

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SLIDE 1

the role of mobility and control in the inference of representations

stefano soatto ucla

1

  • t. lee, a. ayvaci, j. dong, d. davis, j. balzer, j. hernandez, l. valente

1 Saturday, November 30, 13

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SLIDE 2

what is a “representation”? why do we need it? what does control have to do with it?

keywords: data processing inequality, information bottleneck, lambert-ambient model, sufficient excitation, actionable information gap, active sensing/ perception

2

2 Saturday, November 30, 13

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SLIDE 3

3

data

3 Saturday, November 30, 13

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SLIDE 4

3

data

yt . = {y0, . . . , yt}

3 Saturday, November 30, 13

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SLIDE 5

3

data

yt . = {y0, . . . , yt}

3 Saturday, November 30, 13

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SLIDE 6

3

data task

yt . = {y0, . . . , yt}

3 Saturday, November 30, 13

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SLIDE 7

3

data task

yt . = {y0, . . . , yt} ξ

3 Saturday, November 30, 13

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SLIDE 8

3

data task

yt . = {y0, . . . , yt} ξ ?

3 Saturday, November 30, 13

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SLIDE 9

3

data task “representation”?

yt . = {y0, . . . , yt} ξ ?

3 Saturday, November 30, 13

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SLIDE 10

3

data task “representation”?

yt . = {y0, . . . , yt} ξ ˆ ξ = φ(yt)

?

3 Saturday, November 30, 13

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SLIDE 11

3

data task “representation”?

yt . = {y0, . . . , yt} ξ ˆ ξ = φ(yt)

?

3 Saturday, November 30, 13

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SLIDE 12

“representation”

4

yt . = {y0, . . . , yt}

4 Saturday, November 30, 13

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SLIDE 13

“representation”

4

I(ξ; yt) ≥ I(ξ; φ(yt)) R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt}

4 Saturday, November 30, 13

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SLIDE 14

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

)

4 Saturday, November 30, 13

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SLIDE 15

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

)

sufficient statistics [r. fisher]

4 Saturday, November 30, 13

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SLIDE 16

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(ξ; yt) − I(ξ; φ(yt) | {z }

ˆ ξ

) + βH(ˆ ξ)

4 Saturday, November 30, 13

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SLIDE 17

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ)

4 Saturday, November 30, 13

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SLIDE 18

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ)

information bottleneck [n. tishby]

4 Saturday, November 30, 13

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SLIDE 19

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ)

4 Saturday, November 30, 13

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SLIDE 20

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ) min H(y∞

t |ˆ

ξ) + 1 β H(ˆ ξ)

4 Saturday, November 30, 13

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SLIDE 21

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ) min H(y∞

t |ˆ

ξ) + 1 β H(ˆ ξ)

actionable information

4 Saturday, November 30, 13

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SLIDE 22

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ) min H(y∞

t |ˆ

ξ) + 1 β H(ˆ ξ)

representation = “state”

4 Saturday, November 30, 13

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SLIDE 23

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) yt . = {y0, . . . , yt} I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ) min H(y∞

t |ˆ

ξ) + 1 β H(ˆ ξ)

function of the past that best predicts future (nuisance- invariants of the) data given available resources

4 Saturday, November 30, 13

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SLIDE 24

“representation”

4

R(ut|yt) ≤ R(ut|φ(yt)) I(ξ; yt) = I(ξ; φ(yt) | {z }

ˆ ξ

) min I(yt, ˆ ξ) − βI(ˆ ξ; ξ) min H(y∞

t |ˆ

ξ) + 1 β H(ˆ ξ)

function of the past that best predicts future (nuisance- invariants of the) data given available resources

4 Saturday, November 30, 13

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SLIDE 25

“the past”

5

φ

5 Saturday, November 30, 13

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SLIDE 26

“the past”

phylogenic data aggregation is encoded in the structure of (nuisances, invariances, policies, tradeoffs, tasks);

5

φ

5 Saturday, November 30, 13

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SLIDE 27

“the past”

phylogenic data aggregation is encoded in the structure of (nuisances, invariances, policies, tradeoffs, tasks);

  • ntogenic data aggregation is continuously

integrated into the representation

5

φ

ˆ ξ

5 Saturday, November 30, 13

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SLIDE 28

“nuisances”

account for almost all uncertainty/variability in visual data

some can be removed from the data at the outset:

lossless: canonization (e.g., contrast, planar isometries)* co-variant detection/invariant description

  • thers have to be sampled/marginalized:

e.g., scale, class-specific deformation

  • ther have to be “discovered”

e.g., occlusion “sufficient exploration”

instantiate for a specific data-formation model (LA Model)

6

6 Saturday, November 30, 13

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SLIDE 29

7

SENSING ACTION

REPRESENTATION CONTROL INFERENCE SENSORS NUISANCES CANONIZATION SCENE NUISANCES UNMODELED PHENOMENA TASK QUERIES

  • EO

IR MS IMU LIDR ...

..

ξ ν g yt

φ∧(yt)

ˆ g(u)

ˆ ν

h(ˆ gˆ ξ, ˆ ν)

ut max

u

H(yt+1|ˆ ξt, u)

min

p(ˆ ξ|yt)

H(yt+1|ˆ ξt)

INNOVATION

n ˆ ξt

7 Saturday, November 30, 13

slide-30
SLIDE 30

7

SENSING ACTION

REPRESENTATION CONTROL INFERENCE SENSORS NUISANCES CANONIZATION SCENE NUISANCES UNMODELED PHENOMENA TASK QUERIES

  • EO

IR MS IMU LIDR ...

..

ξ ν g yt

φ∧(yt)

ˆ g(u)

ˆ ν

h(ˆ gˆ ξ, ˆ ν)

ut max

u

H(yt+1|ˆ ξt, u)

min

p(ˆ ξ|yt)

H(yt+1|ˆ ξt)

INNOVATION

n ˆ ξt

INFORMATION BOTTLENECK

7 Saturday, November 30, 13

slide-31
SLIDE 31

7

SENSING ACTION

REPRESENTATION CONTROL INFERENCE SENSORS NUISANCES CANONIZATION SCENE NUISANCES UNMODELED PHENOMENA TASK QUERIES

  • EO

IR MS IMU LIDR ...

..

ξ ν g yt

φ∧(yt)

ˆ g(u)

ˆ ν

h(ˆ gˆ ξ, ˆ ν)

ut max

u

H(yt+1|ˆ ξt, u)

min

p(ˆ ξ|yt)

H(yt+1|ˆ ξt)

INNOVATION

n ˆ ξt

INFORMATION BOTTLENECK ACTIONABLE INFORMATION INCREMENT

7 Saturday, November 30, 13

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SLIDE 32

the LA model (lambert-ambient)

8

p

S ⊂ R3

ρ : S → R+

p 7! ρ(p)

x ¯ x

D ⊂ R2

It : D → R+

gt ∈ SE(3)

( yt(x) = κt(ρ(p)) + nt(x) ∈ R+ x = π(gtp), p ∈ S ⊂ R3

8 Saturday, November 30, 13

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SLIDE 33

the LA model (lambert-ambient)

8

p

S ⊂ R3

ρ : S → R+

p 7! ρ(p)

x ¯ x

D ⊂ R2

It : D → R+

gt ∈ SE(3)

ξ = {ρ, S} ( yt(x) = κt(ρ(p)) + nt(x) ∈ R+ x = π(gtp), p ∈ S ⊂ R3

8 Saturday, November 30, 13

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SLIDE 34

the LA model (lambert-ambient)

8

p

S ⊂ R3

ρ : S → R+

p 7! ρ(p)

x ¯ x

D ⊂ R2

It : D → R+

gt ∈ SE(3)

ξ = {ρ, S} gt ∈ SE(3) ( yt(x) = κt(ρ(p)) + nt(x) ∈ R+ x = π(gtp), p ∈ S ⊂ R3

8 Saturday, November 30, 13

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SLIDE 35

the LA model (lambert-ambient)

8

p

S ⊂ R3

ρ : S → R+

p 7! ρ(p)

x ¯ x

D ⊂ R2

It : D → R+

gt ∈ SE(3)

ξ = {ρ, S} gt ∈ SE(3) ( yt(x) = κt(ρ(p)) + nt(x) ∈ R+ x = π(gtp), p ∈ S ⊂ R3 κt : R+ → R+

8 Saturday, November 30, 13

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SLIDE 36

the LA model (lambert-ambient)

8

p

S ⊂ R3

ρ : S → R+

p 7! ρ(p)

x ¯ x

D ⊂ R2

It : D → R+

gt ∈ SE(3)

ξ = {ρ, S} gt ∈ SE(3) νt = {nt, π} ( yt(x) = κt(ρ(p)) + nt(x) ∈ R+ x = π(gtp), p ∈ S ⊂ R3 κt : R+ → R+

8 Saturday, November 30, 13

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SLIDE 37

the LA model (lambert-ambient)

9

p

S ⊂ R3

ρ : S → R+

p 7! ρ(p)

x ¯ x

D ⊂ R2

It : D → R+

gt ∈ SE(3)

9 Saturday, November 30, 13

slide-38
SLIDE 38

the LA model (lambert-ambient)

9

p

S ⊂ R3

ρ : S → R+

p 7! ρ(p)

x ¯ x

D ⊂ R2

It : D → R+

gt ∈ SE(3)

yt = h(gt, ξ, νt) + nt

9 Saturday, November 30, 13

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SLIDE 39

complete representation

given one or more images, , a representation

yt

is a statistic such that

ˆ ξt ˆ ξt = φ(yt)

10

10 Saturday, November 30, 13

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SLIDE 40

complete representation

given one or more images, , a representation

yt

is a statistic such that

ˆ ξt ˆ ξt = φ(yt) φ∧(yt) = {h(e, ˆ ξt, νt), e ∈ G, νt ∈ V} . = L(ˆ ξt)

10

10 Saturday, November 30, 13

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SLIDE 41

complete representation

i.e., a statistic from which the (maximal invariant of the) images can be “hallucinated” up to an “uninformative” residual

given one or more images, , a representation

yt

is a statistic such that

ˆ ξt ˆ ξt = φ(yt) φ∧(yt) = {h(e, ˆ ξt, νt), e ∈ G, νt ∈ V} . = L(ˆ ξt)

10

10 Saturday, November 30, 13

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SLIDE 42

complete representation

i.e., a statistic from which the (maximal invariant of the) images can be “hallucinated” up to an “uninformative” residual L(ˆ ξ) = L(ξ)

given one or more images, , a representation

yt

is a statistic such that

ˆ ξt ˆ ξt = φ(yt) φ∧(yt) = {h(e, ˆ ξt, νt), e ∈ G, νt ∈ V} . = L(ˆ ξt)

10

10 Saturday, November 30, 13

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SLIDE 43

complete representation

i.e., a statistic from which the (maximal invariant of the) images can be “hallucinated” up to an “uninformative” residual

complete representation minimal complete representation

L(ˆ ξ) = L(ξ)

given one or more images, , a representation

yt

is a statistic such that

ˆ ξt ˆ ξt = φ(yt) φ∧(yt) = {h(e, ˆ ξt, νt), e ∈ G, νt ∈ V} . = L(ˆ ξt)

10

10 Saturday, November 30, 13

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SLIDE 44

complete representation

i.e., a statistic from which the (maximal invariant of the) images can be “hallucinated” up to an “uninformative” residual

complete representation minimal complete representation

L(ˆ ξ) = L(ξ) “light field”

given one or more images, , a representation

yt

is a statistic such that

ˆ ξt ˆ ξt = φ(yt) φ∧(yt) = {h(e, ˆ ξt, νt), e ∈ G, νt ∈ V} . = L(ˆ ξt)

10

10 Saturday, November 30, 13

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SLIDE 45

actionable information: uncertainty of the maximal invariant (can be computed from finite data) complete information: uncertainty of a minimal sufficient statistic of a (complete) representation actionable information gap (AIG)

information gap

11

I . = H(φ∨(ˆ ξ)) G(y) = I − H(y) H(y) . = H(φ∧(y))

11 Saturday, November 30, 13

slide-46
SLIDE 46

nuisances (aside)

“visual recognition is difficult in part because of the large variability that images of a particular object exhibit depending

  • n extrinsic factors such as vantage point, illumination

conditions, occlusions and other visibility artifacts.” theorem: for viewpoint and illumination (contrast) nuisances, the quotient (“attributed reeb tree”) is supported on a thin set

12 sundaramoorthi, petersen, varadarajan, soatto, “on the set of images modulo viewpoint and contrast changes”, cvpr 2009

12 Saturday, November 30, 13

slide-47
SLIDE 47

nuisances (aside)

“visual recognition is difficult in part because of the large variability that images of a particular object exhibit depending

  • n extrinsic factors such as vantage point, illumination

conditions, occlusions and other visibility artifacts.” theorem: for viewpoint and illumination (contrast) nuisances, the quotient (“attributed reeb tree”) is supported on a thin set

12 sundaramoorthi, petersen, varadarajan, soatto, “on the set of images modulo viewpoint and contrast changes”, cvpr 2009

{I}/W(R2 → R2) × H(R+ → R+) = ART

12 Saturday, November 30, 13

slide-48
SLIDE 48

nuisances (aside)

“visual recognition is difficult in part because of the large variability that images of a particular object exhibit depending

  • n extrinsic factors such as vantage point, illumination

conditions, occlusions and other visibility artifacts.” theorem: for viewpoint and illumination (contrast) nuisances, the quotient (“attributed reeb tree”) is supported on a thin set

12 sundaramoorthi, petersen, varadarajan, soatto, “on the set of images modulo viewpoint and contrast changes”, cvpr 2009

ˆ ξt = φ(yt) {I}/W(R2 → R2) × H(R+ → R+) = ART

12 Saturday, November 30, 13

slide-49
SLIDE 49

nuisances (aside)

“visual recognition is difficult in part because of the large variability that images of a particular object exhibit depending

  • n extrinsic factors such as vantage point, illumination

conditions, occlusions and other visibility artifacts.” theorem: for viewpoint and illumination (contrast) nuisances, the quotient (“attributed reeb tree”) is supported on a thin set

12 sundaramoorthi, petersen, varadarajan, soatto, “on the set of images modulo viewpoint and contrast changes”, cvpr 2009

ˆ ξt = φ(yt) {I}/W(R2 → R2) × H(R+ → R+) = ART

from signals to symbols (canonization), without loss of information, but ... gap!

12 Saturday, November 30, 13

slide-50
SLIDE 50

(non)invertible nuisances

actionable information gap non-zero

13

13 Saturday, November 30, 13

slide-51
SLIDE 51

(non)invertible nuisances

actionable information gap non-zero invertibility depends on the sensing process: control authority

13

13 Saturday, November 30, 13

slide-52
SLIDE 52

(non)invertible nuisances

actionable information gap non-zero invertibility depends on the sensing process: control authority

  • j. j. gibson: “the occluded becomes unoccluded” in the

process of “information pickup”

13

13 Saturday, November 30, 13

slide-53
SLIDE 53

two questions:

1.how to build the best possible representation given past data

  • canonization: co-variant detection/invariant description
  • sparsity, occlusion detection, detachable objects
  • structural stability

2.how to gather future data to make the representation (as close as possible to) complete

  • mapping/exploration, navigation
  • sufficient exploration/sufficient excitation

14

14 Saturday, November 30, 13

slide-54
SLIDE 54
  • cclusion(detec,on

(1)(Lamber,an(reflec,on (2)(Constant(illumina,on (3)(Co9visibility

small dense large sparse nesterov/split9bregman( w/(weighted(isotropic(TV(for(w

15

15 Saturday, November 30, 13

slide-55
SLIDE 55

ˆ c = arg min

c

Z

D

|c(x) − c(y)|dµ(x, y)

  • s. t. c(x) < c(y), x ∈ Ω, y ∈ Ωc

Detachable(Object(Detec,on

16

(

16 Saturday, November 30, 13

slide-56
SLIDE 56

ˆ c = arg min

c

Z

D

|c(x) − c(y)|dµ(x, y)

  • s. t. c(x) < c(y), x ∈ Ω, y ∈ Ωc

dµ(x, y) = K(x, y)dxdy

Detachable(Object(Detec,on

16

(

16 Saturday, November 30, 13

slide-57
SLIDE 57

ˆ c = arg min

c

Z

D

|c(x) − c(y)|dµ(x, y)

  • s. t. c(x) < c(y), x ∈ Ω, y ∈ Ωc

dµ(x, y) = K(x, y)dxdy

Detachable(Object(Detec,on

16

(

K(x, y) = ( e(It(x)It(y))2 + ⇥ekvt(x)vt(y)k2

2

0,

  • therwise;

kx yk2 < ⇤,

16 Saturday, November 30, 13

slide-58
SLIDE 58

ˆ c = arg min

c

Z

D

|c(x) − c(y)|dµ(x, y)

  • s. t. c(x) < c(y), x ∈ Ω, y ∈ Ωc

dµ(x, y) = K(x, y)dxdy

v(x) . = w(x) − x

Detachable(Object(Detec,on

16

(

K(x, y) = ( e(It(x)It(y))2 + ⇥ekvt(x)vt(y)k2

2

0,

  • therwise;

kx yk2 < ⇤,

16 Saturday, November 30, 13

slide-59
SLIDE 59

17

17 Saturday, November 30, 13

slide-60
SLIDE 60

18

18 Saturday, November 30, 13

slide-61
SLIDE 61

19

SENSING ACTION

REPRESENTATION CONTROL INFERENCE SENSORS NUISANCES CANONIZATION SCENE NUISANCES UNMODELED PHENOMENA TASK QUERIES

  • EO

IR MS IMU LIDR ...

..

ξ ν g yt

φ∧(yt)

ˆ g(u)

ˆ ν

h(ˆ gˆ ξ, ˆ ν)

ut max

u

H(yt+1|ˆ ξt, u)

min

p(ˆ ξ|yt)

H(yt+1|ˆ ξt)

INNOVATION

n ˆ ξt

19 Saturday, November 30, 13

slide-62
SLIDE 62

information pickup

20

ˆ ut = arg max

u

min

ˆ ξt=φ(yt)

H(yt+1|ˆ ξt, u) + λH(ˆ ξt)

20 Saturday, November 30, 13

slide-63
SLIDE 63

21

21 Saturday, November 30, 13

slide-64
SLIDE 64
  • II. Exploratory path planning of

unknown environments

φ = φ(·, γ) In the rest,

22 Saturday, November 30, 13

slide-65
SLIDE 65

bounds

  • for finite complexity environment

(bounded, with finite number of simply- connected obstacles with complexity )

  • for a given exploration residual (unseen

area)

  • other technical conditions
  • “sufficient exploration” in finite steps:

23

M Q ✏ O(MQ) + O( 1 ✏2 )

23 Saturday, November 30, 13

slide-66
SLIDE 66

control/recognition bounds

  • v. karasev, nips 2012

24 Saturday, November 30, 13

slide-67
SLIDE 67

1 E x p e r i m e n t

1 . 1 R i s k a n d s e n s

  • r

p a r a m e t e r s

i t h 5 , 1 , 3 c l u t t e r

  • b

j e c t s ( l

  • w

, m e d i u m , h i g h c

  • m

p l e x i t y ) . 25 Saturday, November 30, 13

slide-68
SLIDE 68

summary

26

26 Saturday, November 30, 13

slide-69
SLIDE 69

summary

  • data processing inequality/information bottleneck: key

to representation

26

26 Saturday, November 30, 13

slide-70
SLIDE 70

summary

  • data processing inequality/information bottleneck: key

to representation

  • canonization: lossless pre-processing, constructive

procedure for maximal invariants (ART, TST/BTD) [cvpr ’09, imavis ’11]

26

26 Saturday, November 30, 13

slide-71
SLIDE 71

summary

  • data processing inequality/information bottleneck: key

to representation

  • canonization: lossless pre-processing, constructive

procedure for maximal invariants (ART, TST/BTD) [cvpr ’09, imavis ’11]

  • non-group nuisances (occlusion, scaling) cause info gap

[iccv ’09, arxiv ’11]

26

26 Saturday, November 30, 13

slide-72
SLIDE 72

summary

  • data processing inequality/information bottleneck: key

to representation

  • canonization: lossless pre-processing, constructive

procedure for maximal invariants (ART, TST/BTD) [cvpr ’09, imavis ’11]

  • non-group nuisances (occlusion, scaling) cause info gap

[iccv ’09, arxiv ’11]

  • occlusion detection [ijcv ’11], detachable object

detection [pami ’12]

26

26 Saturday, November 30, 13

slide-73
SLIDE 73

summary

  • data processing inequality/information bottleneck: key

to representation

  • canonization: lossless pre-processing, constructive

procedure for maximal invariants (ART, TST/BTD) [cvpr ’09, imavis ’11]

  • non-group nuisances (occlusion, scaling) cause info gap

[iccv ’09, arxiv ’11]

  • occlusion detection [ijcv ’11], detachable object

detection [pami ’12]

  • visual exploration [ijrr ’10, ciss ’12]

26

26 Saturday, November 30, 13

slide-74
SLIDE 74

references

  • s. soatto, “steps towards a theory of visual information”, http://arxiv.org/abs/1110.2053 and ucla-

csd100028, september 13, 2010 (also on video lecture, nips tutorial 2010; also icvss lecture notes, ‘07-’09)

  • s. soatto, “actionable information in vision”, iccv ’09, long version in “machine learning for computer

vision”, r. cipolla et al. (eds.), 2011

  • g. sundaramoorthi et al. “on the set of images modulo viewpoint and contrast changes”, cvpr ’09
  • k. wnuk and s. soatto, “multiple-instance filtering”, nips ’11
  • a. ayvaci and s. soatto, “detachable object detection”, PAMI ’12
  • t. lee and s. soatto, “video-based descriptors for object recognition”, IMAVIS ’11
  • a. ayvaci et al. “sparse occlusion detection with optical flow”, IJCV ’11
  • e. jones and s. soatto, “visual-inertial navigation, localization and mapping”, IJRR ’11
  • m. raptis and s. soatto, “tracklet descriptors for action modeling and video analysis”, ECCV ’10

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