1

Converting Celsius to Fahrenheit

C

1.8

32

+ F

10

1850

325

9 CF

2

Converting Fahrenheit to Celsius

C

1.8

32

+ F

10

1850

325

9 CF

)32(9

5 FC

3

Addition Box

+p

qr

qpr

qrp

prq

4

Muliplication Box

p

qr

qpr

0 if qq

rp

0 if pp

rq

0 if 0 pr

0q if 0 r

5

Local Propagation is Not Enough

yx

100?

6

Barometric Measurements with Varying Confidence

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Confidencelevels

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Actualterrain

Barometerreadings

7

Constraint Propagation by Relaxation

Barometer readings

0123456789

10

After first iteration

0123456789

10

After fifth iteration

0123456789

10

After tenth iteration

0123456789

10

After twentieth iteration

0123456789

10

After fortieth iteration

0123456789

10

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

8

GENINFER: Genetic Reasoning

9

GENINFER Results

Nothing known about uncles and

brothers

Uncles OKnothing

known about brothers

Both uncles and brothers

OK

12.5%

2.8%

0.7%

10

Line Drawing Analysis

11

Classification of Lines

Alllines

Interiorlines

Boundarylines

Convexedges

Concaveedges

12

Line Interpretation

13

Common Junctions

L

Arrow

T

Fork

X

Peak

K

Psi

Multi

Kk

14

Possible Inputs

15

Excluded Input

16

Impossible Junctions

17

Identifying Three-Faced Junctions

18

Full/Empty: 7/1, 1/7

19

1 Full, 7 Empty (Low Views)

L R

R

T

L

RL

20

1 Full, 7 Empty (High Views)

RL

L R

21

3 Full, 5 Empty

22

Junction Dictionary

Ljunctions

Forkjunctions

Tjunctions

Arrowjunctions

Alljunctions

23

Labeling a Drawing

24

A Two-Tiered Figure

25

Starting From the Middle

26

Impossible Objects?

Not possible

27

Waltz’s Algorithm

A B

C

DE

F

A B

C

DE

F

A B

C

DE

F

A B

C

DE

F

(a) (b)

(c) (d)

28

Waltz Example

AB

CD

C

B

A

D

29

The Need for More Information

30

Shadows

31

Concave Edges

32

Extended Line Catalog

C

C

Alledges

Realedges

Interioredges

Boundaryedges

Shadowedges

Pseudoedges

Crackedges

Convexedges

Concaveedges

33

Face Catalog

Illuminated

Illuminated

Illuminated

Shadowed

Self-Shadowed

34

Effects of Constraints(Basic Lines)

VertexType

Number ofunconstrained

possible junctions

Number ofphysically

realizable junctions

Ratio(%)

L 16 6 37.5

Fork 64 5 7.8

T 64 4 6.2

Arrow 64 3 4.7

35

Effects of Constraints(Expanded Categories)

VertexType

Number ofunconstrained

possible junctions

Number ofphysically

realizable junctions

Ratio (%)

L 2.5103 80 3.2Fork 1.2105 500 4.010-1

T 1.2105 500 4.010-1

Arrow 1.2105 70 5.610-2

Psi 6.2106 300 4.810-3

K 6.2106 100 1.610-3

X 6.2106 100 1.610-3

Multi 6.2106 100 1.610-3

Peak 6.2106 10 1.610-4

Kk 3.1108 30 9.610-6

36

Example

37

Waltz in Action

1 A — 123 16 E 79 33 31 C 20 2 61 P 5 1 76 T — 123

2 A 123 76 17 D 15 14 32 B 14 2 62 O 2 1 77 T 123 4

3 B — 79 18 F — 123 33 A 20 2 63 Q — 123 78 T 4 1

4 B 79 52 19 F 123 28 34 H — 79 64 Q 123 5 79 J 4 1

5 A 76 32 20 G — 593 35 H 79 1 65 Q 5 1 80 R 4 1

6 C — 388 21 G 593 42 36 I — 123 66 L 3 1

7 C 388 78 22 G 42 18 37 I 123 2 67 K 5 2

8 B 52 34 23 F 28 11 38 J — 593 68 R — 388

9 A 32 26 24 E 33 7 39 J 593 9 69 R 388 20

10 D — 79 25 D 14 6 40 K — 79 70 R 20 4

11 D 79 15 26 F 11 2 41 K 79 7 71 J 6 4

12 C 78 20 27 G 18 1 42 J 9 8 72 K 2 1

13 B 34 14 28 E 7 1 43 L — 593 73 S — 1391

14 A 26 20 29 D 6 1 44 L 593 12 74 S 1391 5

15 E — 79 30 F 2 1 45 K 7 5 75 S 5 1

38

Time Intervals

before

A

B

A B

39

Interval Arithmetic

beforeA

beforeB C

beforeA

beforeB C

before

?

40

Constraint Propagation for Time Intervals

B

A

C D Z

b e f o r e b e f o r e b e f o r e b e f o r e

b e f o r e b e f o r eb e f o r eb e f o r e

41

Using Reference Nodes

MEETS

MORNING AFTERNOON

X

Y

DURING

MEETS

MORNING AFTERNOON

X

Y

DURING

BEFORE

BEFORE

BEFORE

BEFORE

BEFORE