Faster Unsupervised Object Detection For Symbolic Representation

INOM

EXAMENSARBETE DATALOGI OCH DATATEKNIK, AVANCERAD NIVÅ, 30 HP

STOCKHOLM SVERIGE 2020,

Faster Unsupervised Object Detection For Symbolic

Representation

PEIYANG SHI

KTH

SKOLAN FÖR ELEKTROTEKNIK OCH DATAVETENSKAP

β β

z^where

β

280 × 210 × 3

H × W × C

(S, A, R, T, γ)

S s ∈ S

S

A a ∈ A

T

R γ

γ

s a

Q^∗(s, a) = R(s, a) + γ!

s^′

P (s^′|s, a)

a^′ Q^∗(s^′, a^′)

Q^∗ s

a

s^′ a^′ t + 1

V^∗ V^∗

V^∗(s) =

a Q(s, a)

p q

x z

p(x, z)

x z

p(x, z) = p(x|z)p(z)

p(z|x) = p(x|z)p(z)

p(x) = " p(x|z)p(z)

zp(x|z)p(z)dz p(z|x)

z p(z|x) q(z|x)

DKL

#q(z)||p(z|x)$

=E^q(z)[ q(z)− p(z|x)]

p(x|z)

DKL

#q(z)||p(z|x)$

=Eq(z)[ q(z)− p(x|z) − p(z)] +Eq(z)[ p(x)]

Eq(z)[ p(x)]

p(x) q(z)

p(x)−D^KL#

q(z)||p(z|x)$

=E^q(z)[ p(x|z)]−E^q(z)[ p(z)]−E^q(z)[ q(z)]

p(x)− DKL

#q(z)||p(z|x)$

=E^q(z)[ p(x|z)] − DKL

#q(z)||p(z)$

p(x) DKL

p(x)

p(x)

p

θ q φ

L(θ, φ, x) = Eq(z|x)[ pθ(x|z)] − DKL

#qφ(z|x)||pθ(z)$

E^q(z|x)[ pθ(x|z)]

Lreconst(θ, φ)

Eq(z|x)[ pθ(x|z)]

qφ(z|x) pθ(z)

q(z|x) p(x|z)

z

β β

β

L(θ, φ, x, z, β) = Eqφ(z|x)[ pθ(x|z)] − βD^KL#

qφ(z|x)||p(z)$

β β

p(z) β

[I(Z; Y )− βI(X; Z)]

I(·) β

Z X

Z Y β

z

x z

E^p(x)ˆ [DKL

#qφ(z|x)||p(z)$

] = Iqφ(x; z) + DKL

#qφ(z)||p(z)$

β

zj z

L^β−T C =L (θ, φ)+αIq_φ(z; x)+λ (qφ(z))+γ!

j

DKL

#qφ(zj)||p(z^j)$

α λ γ

z

z z ={z^attr, z^where, z^pres}

z^pres

z^where z^attr

pθ(x)

pθ(x) =

!N n=1

pN(n)

%

pθ(z|n)pθ(x|z)dz N

z z =

(z¹, z², ..., z^N) z ∼ p^zθ(·|n) x∼ p^xθ(·|z)

N

q_φ

qφ(z, z^pres|x) = q^φ(z_n+1^pres = 0|z^1:n, x)

&n i

qφ(zi, z_i^pres = 1|x, z^1:i−1)

z

n z^pres

z ={z^attr, z^where, z^pres, z^depth} z^depth

z^pres

z^pres

P (z_k^pres|ˆz_1:k−1^pres , C = 1) =

!HW c=0

P (z_k^pres|ˆz_1:k−1^pres , C = c)p(C = c|ˆz_1:k−1^pres )

C zˆ^pres_1:k−1

k−1 k

X Z

H × W Z

X

Z ∈ R^H×W ×(loc,depth,pres,M)

H× W Z

Z ={Z¹¹, Z12...ZH1, Z21...ZHW}

Z_i,j ={Zi,j^where, Z_i,j^attr, Z_i,j^depth, Z_i,j^pres}

Z_i,j^where ∈ R⁴

x, y h, w Z_i,j^attr ∈ R^M M

Z_i,j^depth ∈ R¹

Z_i,j^pres ∈ R¹

q_φ(Z|X) p_φ(X|Z)

fb(·) E^{f eat}

E^{f eat}= fb(X)

E^{f eat} ∈ R^{Cf×W ×H} Z

H, W Cf

Z^loc Z^where, Z^depth, Z^pres

q_φ^loc Z_i,j^loc= Z_i,j^where, Z_i,j^pres, Z_i,j^depth

q(Z^loc|X) = qφ(Z^where, Z^depth, Z^pres|fb(X))

= qφ(Z^where, Z^depth, Z^pres|E^{f eat}) Zi,j

z z

z = Zi,j

z ={z^where, z^depth, z^pres, z^attr}

z

[i, j]

p(Z) = 'HW

i p(zi|zi−1, z_i−2...)

z E^{f eat}

E^{f eat}

q_φ^loc(Z^loc|E^{f eat}) =

H,W&

i,j

q_φ^loc(Z_i,j^loc|Ei,j^context)

E_i,j^context={E_N−i,N−j^{f eat} , ..., E_N,N^{f eat}, ...E_{N +i,N +j}^{f eat} }

z^where [i, j] E^{f eat}

z^where z_x^where

z_y^where z_h^where

z_w^where

H× W

z^where

z^where={zx^where, z_y^where, z_w^where, z_h^where} z_x^where, z^where_y

z_w^where, z^where_h

z^where

b

bx =#

(σz_x^where)(B x− B ^x) + B x+ i$ cw

b_y =#

(σz_y^where)(B _y− B y) + B _y+ i$ c_h

σ B _∗

B _∗

(i, j) c_∗

A

bw =#

σ(z_w^where)(A w− A ^w) + A w

$Aw

bh =#

σ(z_h^where)(A h− A ^h) + A h

$Ah

A w A h

A

h_obj× wobj

q_φ^attr

x^′ = ST N (X, T )

x^′ X

T

T (z^where) =

⎡

⎣

bw 0 bx

0 bh by

0 0 1

⎤

⎦

wobj× hobj

H_img, W_img, C_img

X^′ ={X, C}, X^′ ∈ R^{Himg×Wimg×(Cimg+2)} C ∈ R^{Himg×Wimg×2}

Ci,j ={i, j}

z^attr

q_φ^attr(z^attr|x^′) p^attr_θ (x^′|z^attr) x^′

x^′ β

z^where H× W

HW

z^pres z^depth z^pres ∈ {0, 1}

z^pres = 1

z^depth

z^depth ∈ [0, ∞) σ(z^depth)∈ [0, 1]

ˆ

xi,j z^depth

blend( ˆXi,j) = ˆXi,j ∗ z^depth ,HW

k,t Z_k,t^depth ∗ pθ(z^pres|X)

N (0, 1)

z^attr∼ N (µ^attr, σ^attr) z^where∼ N (µ^where, σ^where)

z^depth∼ N (µ^depth, σ^depth)

z^pres

pθ(z^pres) = 1 HW

qφ(z^pres|X)

Decoder(z)

z^attr H× W xˆ_ij

z^where

T⁻¹(z^where) =

⎡

⎣

bw 0 bx

0 bh by

0 0 1

⎤

⎦

−1

HW

T⁻¹ blend(·)

z^pres Xˆ^′ =

H,W!

i,j

ST N (blend(x^′_i,j), T⁻¹(z^where))∗ pθ(z^pres|X)

Z^where, Z^pres, Z^attr

z^depth

z^attr z^pres

Sˆ

S = Zˆ ^pres⊙ Z^attr

⊙

z^where

E^{f eat} Z X p(z^pres)

1e⁻⁴ 28× 28 48× 48 z^attr

z_h^where z_w^where N (5.013100487582577, 0.5) N (0, 1)

z^where, z^pres, z^depth z^attr

z^where, z^pres, z^depth

ACE =|Ngroundtruth− Npredicted|

z^pres

z^attr z^attr

z^where, z^pres z^depth

z_h^where z_w^where

z^where

z^where z^where

z

z_h^where z_w^where

z_h^where z_w^where

β

β

β

β β

β

β

TRITA -EECS-EX:194

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