GAN

2. Table of Contents
목차
01 G A N E X A M P L E S
02 G A N I N T R O D U C T I O N
03 G A N C O D E
04 M AT H B E H I N D G A N
05 D I F F E R E N T T Y P E S O F G A N

3. G A N EXA M PLES
LvMin Zhang*, Chengze Li*, Tien-Tsin Wong, Yi Ji, and ChunPing Liu. 2018. Two-stage Sketch Colorization.
ACM Trans. Graph. 37, 6, Article 261 (No- vember 2018), 14 pages.
https://doi.org/10.1145/3272127.3275090

4. G A N EXA M PLES
EdgeConnect: Generative Image Inpainting
with Adversarial Edge Learning

5. G A N EXA M PLES

6. G A N I N TR O D U C TI O N
Generator
(𝐺)
Discriminator
(𝐷)
FAKE
z
Discriminator
(𝐷)
REAL
real image
fake image
Generator want to fool!

7. Discr im inat or Updat e
Discriminator
(𝐷)
𝐷(𝑥)
real image(𝑥)
should be close to 1
Generator
(𝐺)
Discriminator
(𝐷)
𝐷(𝐺(𝑧))
z fake image𝐷(𝐺(𝑧))
should be close to 0

8. G e ne r a t or upda t e
Generator
(𝐺)
Discriminator
(𝐷)
𝐷(𝐺 𝑧 )
z
should be close to 1
tries to fool Discriminator
𝐷 𝐺 𝑧 1 ≈ 1
fake image(G(z))

9. G A N Los s
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Sample from real data distribution Sample from Gaussian distribution
log(𝑥) log(1 − 𝑥)

10. G A N Los s ( G e ne r a t or )
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Generator
(𝐺)
Discriminator
(𝐷)
𝐷(𝐺 𝑧 )
z
should be close to 1
tries to fool Discriminator
𝐷 𝐺 𝑧 1 ≈ 1
fake image(G(z))

11. G A N Tr a i ni ng Pr oc e s s
discriminator
Generative distribution
True data distribution

12. G A N Py t or c h Code

13. G A N Py t or c h Code

14. G A N Py t or c h Code

15. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
OUR GOAL
𝑝. 𝑥 = 𝑝OPQP(𝑥)

16. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ] = 𝐸6~8R 6 [log(1 − 𝐷 𝑥 ]

17. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Preposistion 1. 𝐹𝑜𝑟 𝐺 𝑓𝑖𝑥𝑒𝑑, 𝑡ℎ𝑒 𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑑𝑖𝑠𝑐𝑟𝑖𝑛𝑎𝑡𝑜𝑟 𝐷 𝑖𝑠
𝐷.
∗
𝑥 =
89:;: 6
89:;: 6 a8R(6)
Proof:
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
= ∫6
𝑝OPQP 𝑥 log 𝐷 𝑥 𝑑𝑥 + ∫@
𝑝@ 𝑧 log 1 − 𝐷 𝐺(𝑧 𝑑𝑧
= ∫6
𝑝OPQP 𝑥 log 𝐷 𝑥 + 𝑝. 𝑥 log 1 − 𝐷(𝑥) 𝑑𝑥
≤ ∫6
max
d
𝑝OPQP 𝑥 log(𝑦) + 𝑝. 𝑥 log 1 − 𝑦 𝑑𝑥

18. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Preposistion 1. 𝐹𝑜𝑟 𝐺 𝑓𝑖𝑥𝑒𝑑, 𝑡ℎ𝑒 𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑑𝑖𝑠𝑐𝑟𝑖𝑛𝑎𝑡𝑜𝑟 𝐷 𝑖𝑠
𝐷.
∗
𝑥 =
89:;: 6
89:;: 6 a8R(6)
Proof:
𝑓 𝑦 = max
d
[𝑝OPQP 𝑥 log 𝑦 + 𝑝. 𝑥 log 1 − 𝑦 ] = max
d
𝑎𝑙𝑜𝑔 𝑦 + 𝑏𝑙𝑜𝑔 1 − 𝑦 𝑎, 𝑏 > 0
𝑓i
𝑦 =
P
d
−
j
kld
= 0 → 𝑦 =
P
Paj

19. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Preposistion 1. 𝐹𝑜𝑟 𝐺 𝑓𝑖𝑥𝑒𝑑, 𝑡ℎ𝑒 𝑜𝑝𝑡𝑖𝑚𝑎𝑙 𝑑𝑖𝑠𝑐𝑟𝑖𝑛𝑎𝑡𝑜𝑟 𝐷 𝑖𝑠
𝐷.
∗
𝑥 =
89:;: 6
89:;: 6 a8R(6)
Proof:
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
= ∫6
𝑝OPQP 𝑥 log 𝐷 𝑥 𝑑𝑥 + ∫@
𝑝@ 𝑧 log 1 − 𝐷 𝐺(𝑧 𝑑𝑧
= ∫6
𝑝OPQP 𝑥 log 𝐷 𝑥 + 𝑝. 𝑥 log 1 − 𝐷(𝑥) 𝑑𝑥
≤ ∫6
max
d
𝑝OPQP 𝑥 log 𝑦 + 𝑝. 𝑥 log 1 − 𝑦 𝑑𝑥
∴ 𝐷.
∗
𝑥 =
𝑝OPQP 𝑥
𝑝OPQP 𝑥 + 𝑝.(𝑥)

20. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑃𝑜𝑖𝑛𝑡 𝑓𝑜𝑟 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑜𝑟
𝑝OPQP 𝑥 = 𝑝. 𝑥
𝑂𝑝𝑡𝑖𝑚𝑎𝑙 𝑃𝑜𝑖𝑛𝑡 𝑓𝑜𝑟 𝐷𝑖𝑠𝑐𝑟𝑖𝑚𝑖𝑛𝑎𝑡𝑜𝑟
𝐷.
∗
𝑥 =
𝑝OPQP 𝑥
𝑝OPQP 𝑥 + 𝑝.(𝑥)
=
1
2

21. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Theorem 1. 𝑇ℎ𝑒 𝑔𝑙𝑜𝑏𝑎𝑙 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑖𝑟𝑡𝑢𝑎𝑙 𝑡𝑟𝑎𝑖𝑛𝑖𝑛𝑔 𝑐𝑟𝑖𝑡𝑒𝑟𝑖𝑜𝑛 𝐶 𝐺 𝑖𝑠 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑑 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓
𝑝v = 𝑝OPQP. 𝐴𝑡 𝑡ℎ𝑎𝑡 𝑝𝑜𝑖𝑛𝑡, 𝐶 𝐺 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑠 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒: −𝑙𝑜𝑔4.
Proof(only if):
𝐶 𝐺 = 𝑉 𝐷∗
, 𝐺 = ∫6
𝑝OPQP 𝑥 log 𝐷∗
𝑥 𝑑𝑥 + ∫@
𝑝@ 𝑧 log 1 − 𝐷∗
𝐺(𝑧 𝑑𝑧
= ∫6
𝑝OPQP 𝑥 log
k
{
+ 𝑝. 𝑥 log 1 −
k
{
𝑑𝑥
= −𝑙𝑜𝑔2 ∫6
𝑝OPQP 𝑥 + 𝑝. 𝑥 𝑑𝑥 = −2𝑙𝑜𝑔2 = −𝑙𝑜𝑔4

22. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Theorem 1. 𝑇ℎ𝑒 𝑔𝑙𝑜𝑏𝑎𝑙 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑖𝑟𝑡𝑢𝑎𝑙 𝑡𝑟𝑎𝑖𝑛𝑖𝑛𝑔 𝑐𝑟𝑖𝑡𝑒𝑟𝑖𝑜𝑛 𝐶 𝐺 𝑖𝑠 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑑 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓
𝑝v = 𝑝OPQP. 𝐴𝑡 𝑡ℎ𝑎𝑡 𝑝𝑜𝑖𝑛𝑡, 𝐶 𝐺 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑠 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒: −𝑙𝑜𝑔4.
Proof(if):
𝐶 𝐺 = 𝑉 𝐷∗
, 𝐺 = ∫6
𝑝OPQP 𝑥 log(
89:;: 6
89:;: 6 a8R(6)
) 𝑑𝑥 + ∫@
𝑝@ 𝑧 log
8| 6
89:;: 6 a8R(6)
𝑑𝑧
= ∫6
𝑙𝑜𝑔2 − 𝑙𝑜𝑔2 𝑝OPQP(𝑥) + 𝑝OPQP 𝑥 log(
89:;: 6
89:;: 6 a8R(6)
) 𝑑𝑥
+ 𝑙𝑜𝑔2 − 𝑙𝑜𝑔2 𝑝. 𝑥 + ∫@
𝑝@ 𝑧 log
8| 6
89:;: 6 a8R(6)
𝑑𝑧
= −𝑙𝑜𝑔2 ∫6
𝑝. 𝑥 + 𝑝OPQP 𝑥 𝑑𝑥
+ ∫6
𝑝OPQP 𝑥 𝑙𝑜𝑔2 + log
89:;: 6
89:;: 6 a8R 6
+ 𝑝v 𝑥 𝑙𝑜𝑔2 + log
8| 6
89:;: 6 a8R 6
𝑑𝑥

23. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Theorem 1. 𝑇ℎ𝑒 𝑔𝑙𝑜𝑏𝑎𝑙 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑖𝑟𝑡𝑢𝑎𝑙 𝑡𝑟𝑎𝑖𝑛𝑖𝑛𝑔 𝑐𝑟𝑖𝑡𝑒𝑟𝑖𝑜𝑛 𝐶 𝐺 𝑖𝑠 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑑 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓
𝑝v = 𝑝OPQP. 𝐴𝑡 𝑡ℎ𝑎𝑡 𝑝𝑜𝑖𝑛𝑡, 𝐶 𝐺 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑠 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒: −𝑙𝑜𝑔4.
Proof(if):
∫6
𝑝OPQP 𝑥 𝑙𝑜𝑔2 + log
89:;: 6
89:;: 6 a8R 6
+ 𝑝. 𝑥 𝑙𝑜𝑔2 + log
8| 6
89:;: 6 a8R 6
𝑑𝑥
= ∫6
𝑝OPQP 𝑥 log
89:;: 6
(89:;: 6 a8| 6 )/{
+ 𝑝. 𝑥 log
8R 6
(89:;: 6 a8R 6 )/{
𝑑𝑥
= 𝐾𝐿 𝑝OPQP
89:;:a8R
{
+ 𝐾𝐿 𝑝.
89:;:a8R
{
= 2 ∗ 𝐽𝑆𝐷(𝑃OPQP|𝑝.)

24. G A N- G l oba l O pt i m a l i t y
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
Theorem 1. 𝑇ℎ𝑒 𝑔𝑙𝑜𝑏𝑎𝑙 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑜𝑓 𝑡ℎ𝑒 𝑣𝑖𝑟𝑡𝑢𝑎𝑙 𝑡𝑟𝑎𝑖𝑛𝑖𝑛𝑔 𝑐𝑟𝑖𝑡𝑒𝑟𝑖𝑜𝑛 𝐶 𝐺 𝑖𝑠 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑑 𝑖𝑓 𝑎𝑛𝑑 𝑜𝑛𝑙𝑦 𝑖𝑓
𝑝v = 𝑝OPQP. 𝐴𝑡 𝑡ℎ𝑎𝑡 𝑝𝑜𝑖𝑛𝑡, 𝐶 𝐺 𝑎𝑐ℎ𝑖𝑒𝑣𝑒𝑠 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒: −𝑙𝑜𝑔4.
Proof(if):
𝐶 𝐺 = 𝑉 𝐷∗
, 𝐺 = ∫6
𝑝OPQP 𝑥 log(
89:;: 6
89:;: 6 a8R(6)
) 𝑑𝑥 + ∫@
𝑝@ 𝑧 log
8| 6
89:;: 6 a8R(6)
𝑑𝑧
= ∫6
𝑙𝑜𝑔2 − 𝑙𝑜𝑔2 𝑝OPQP(𝑥) + 𝑝OPQP 𝑥 log(
89:;: 6
89:;: 6 a8|(6)
) 𝑑𝑥
+ 𝑙𝑜𝑔2 − 𝑙𝑜𝑔2 𝑝. 𝑥 + ∫@
𝑝@ 𝑧 log
8| 6
89:;: 6 a8R(6)
𝑑𝑧
= −𝑙𝑜𝑔2 ∫6
𝑝. 𝑥 + 𝑝OPQP 𝑥 𝑑𝑥
+ ∫6
𝑝OPQP 𝑥 𝑙𝑜𝑔2 + log
89:;: 6
89:;: 6 a8R 6
+ 𝑝. 𝑥 𝑙𝑜𝑔2 + log
8| 6
89:;: 6 a8R 6
𝑑𝑥
= −𝑙𝑜𝑔4 + 2 ∗ 𝐽𝑆𝐷 𝑝OPQP 𝑝.
≥ −𝑙𝑜𝑔4
0 𝑤ℎ𝑒𝑛 𝑝OPQP = 𝑝v

27. DCG A N
•Replace all max pooling with convolutional stride
•Use transposed convolution for upsampling.
•Eliminate fully connected layers.
•Use Batch normalization except the output layer for the
generator and the input layer of the discriminator.
•Use ReLU in the generator except for the output which uses
tanh.
•Use LeakyReLU in the discriminator.

28. DCG A N- w a k i ng i n t he l a t e nt s pa c e

29. Condit ional GAN
Limitation of vanilla GAN: Random generation of image!
How to overcome?

30. Condit ional GAN
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥|𝑦 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧|𝑦 ]

31. Condit ional GAN
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧 ]
min
.
max
1
𝑉 𝐷, 𝐺 = 𝐸6~89:;:(6) 𝑙𝑜𝑔𝐷 𝑥|𝑦 + 𝐸@~8A(@)[log 1 − 𝐷 𝐺 𝑧|𝑦 ]

32. Pi x 2 Pi x

33. Pi x 2 Pi x ( G e ne r a t or )
L1 Loss
E D
𝐺 𝑥𝑥
Discriminator
(𝐷)
Generator
(𝐺)
𝐷(𝑥, 𝐺 𝑥 )
𝑦
Loss

34. Pi x 2 Pi x ( Di s c r i m i na t or )
𝑥
𝐷(𝑥, 𝑦)𝑦 Discriminator
(𝐷)

35. Pi x 2 Pi x - pa t c hG A N

36. CycleGAN
z h u e t a l 2 0 1 7

37. CycleGAN
z h u e t a l 2 0 1 7

38. CycleGAN
z h u e t a l 2 0 1 7

39. CycleGAN
z h u e t a l 2 0 1 7

40. CycleGAN
z h u e t a l 2 0 1 7

41. CycleGAN
z h u e t a l 2 0 1 7

42. CycleGAN
z h u e t a l 2 0 1 7

43. CycleGAN
z h u e t a l 2 0 1 7
E D
Real image from domain 𝐴
Discriminator
(𝐷)
𝐺…†
Fake image in domain 𝐵
E D
𝐺†…
Reconstructed Image
Real/Fake
Real image from domain 𝐵

44. Edge Conne c t

45. Edge Conne c t

46. Edge Conne c t
Stage1: Edge Generator

47. Edge Conne c t
Stage2: Image Completion Network

48. Edge Conne c t
Stage2: Image Completion NetworkStage1: Edge Generator

49. Edge Conne c t – Edge G e ne r a t or
Stage1: Edge Generator
𝐼vQ: 𝑔𝑟𝑜𝑢𝑛𝑑 𝑡𝑟𝑢𝑡ℎ 𝑖𝑚𝑎𝑔𝑒 𝐶vQ: 𝑔𝑟𝑜𝑢𝑛𝑑 𝑡𝑟𝑢𝑡ℎ 𝑒𝑑𝑔𝑒 𝑚𝑎𝑝 𝐼v‰Pd: 𝑔𝑟𝑎𝑦𝑠𝑐𝑎𝑙𝑒 𝑖𝑚𝑎𝑔𝑒 Ĩ v‰Pd: 𝑔𝑟𝑎𝑦𝑠𝑐𝑎𝑙𝑒 𝑖𝑚𝑎𝑔𝑒
𝑤𝑖𝑡ℎ 𝑚𝑎𝑠𝑘

50. Edge Conne c t – Edge G e ne r a t or
Stage1: Edge Generator
𝐼vQ: 𝑔𝑟𝑜𝑢𝑛𝑑 𝑡𝑟𝑢𝑡ℎ 𝑖𝑚𝑎𝑔𝑒
𝐶vQ: 𝑔𝑟𝑜𝑢𝑛𝑑 𝑡𝑟𝑢𝑡ℎ 𝑒𝑑𝑔𝑒 𝑚𝑎𝑝
𝐼v‰Pd: 𝑔𝑟𝑎𝑦𝑠𝑐𝑎𝑙𝑒 𝑖𝑚𝑎𝑔𝑒
𝑀: 𝑖𝑚𝑎𝑔𝑒 𝑚𝑎𝑠𝑘
𝐼v‰Pd
i = 𝐼v‰Pd⊙ 1 − 𝑀 : 𝑚𝑎𝑠𝑘𝑒𝑑 𝑔𝑟𝑎𝑦𝑠𝑐𝑎𝑙𝑒 𝑖𝑚𝑎𝑔𝑒
𝐶vQ
i
= 𝐶vQ⊙ 1 − 𝑀 : 𝑚𝑎𝑠𝑘𝑒𝑑 𝑒𝑑𝑔𝑒 𝑚𝑎𝑝
𝐶8‰ŽO = 𝐺k 𝐼v‰Pd
i , 𝐶vQ
i
, 𝑀
min
.•
max
1•
𝐿.•
= min
.•
(𝜆PO‘,k max
1•
𝐿PO‘,k + 𝜆’“ 𝐿’“)
𝐿PO‘,k = 𝐸”|;,•|–:—
𝑙𝑜𝑔𝐷k 𝐶vQ, 𝐼v‰Pd + 𝐸•|–:—
1 − 𝐷k 𝐶8‰ŽO, 𝐼v‰Pd
𝐿’“ = 𝐸[˜
™šk
›
1
𝑁™
∥ 𝐷k
™
𝐶vQ − 𝐷k
™
𝐶8‰ŽO ∥{]

51. Edge Conne c t – I m a ge C om pl e t i on
Stage2: Image Completion Network𝐼vQ: 𝑔𝑟𝑜𝑢𝑛𝑑 𝑡𝑟𝑢𝑡ℎ 𝑖𝑚𝑎𝑔𝑒
𝐶vQ: 𝑔𝑟𝑜𝑢𝑛𝑑 𝑡𝑟𝑢𝑡ℎ 𝑒𝑑𝑔𝑒 𝑚𝑎𝑝
𝐼v‰Pd: 𝑔𝑟𝑎𝑦𝑠𝑐𝑎𝑙𝑒 𝑖𝑚𝑎𝑔𝑒
𝑀: 𝑖𝑚𝑎𝑔𝑒 𝑚𝑎𝑠𝑘
𝐼v‰Pd
i = 𝐼v‰Pd⊙ 1 − 𝑀 : 𝑚𝑎𝑠𝑘𝑒𝑑 𝑔𝑟𝑎𝑦𝑠𝑐𝑎𝑙𝑒
𝐶vQ
i
= 𝐶vQ⊙ 1 − 𝑀 : 𝑚𝑎𝑠𝑘𝑒𝑑 𝑒𝑑𝑔𝑒 𝑚𝑎𝑝
𝐼vQ
i
= 𝐼vQ⊙ 1 − 𝑀 : 𝑚𝑎𝑠𝑘𝑒𝑑 𝑐𝑜𝑙𝑜𝑟 𝑖𝑚𝑎𝑔𝑒
𝐶žŸ 8 = 𝐶vQ⊙ 1 − 𝑀 + 𝐶8‰ŽO⊙𝑀
𝐼8‰ŽO = 𝐺{ 𝐼vQ
i
, 𝐶žŸ 8
𝐿PO‘,{ = 𝐸”¡¢£¤,•|;
𝑙𝑜𝑔𝐷k 𝐼vQ, 𝐶žŸ 8 + 𝐸”¡¢£¤
1 − 𝐷k 𝐼8‰ŽO, 𝐶žŸ 8
𝐿8Ž‰ž = 𝐸 ˜
™
1
𝑁™
∥ 𝜙™ 𝐼vQ − 𝜙™ 𝐼8‰ŽO ∥k
𝐿¦Qd§Ž = 𝐸¨ ∥ 𝐺¨
©
𝐼8‰ŽO
i
− 𝐺¨
©
𝐼vQ
i
∥k
𝐿.ª
= 𝜆§•
𝐿§•
+ 𝜆PO‘,{ 𝐿PO‘,{ + 𝜆8Ž‰ž 𝐿8Ž‰ž + 𝜆¦Qd§Ž 𝐿¦Qd§Ž

52. Pe r c e pt ua l Los s a nd St y l e Los s

53. Pr ogr e s s i v e G r ow i ng of G AN

54. St y l e G AN

55. Thank You!