depth from X: defocus blur and binocular disparity Tues. Feb. 13, - - PowerPoint PPT Presentation

β–Ά
depth from x defocus blur and binocular disparity
SMART_READER_LITE
LIVE PREVIEW

depth from X: defocus blur and binocular disparity Tues. Feb. 13, - - PowerPoint PPT Presentation

Aug 14, 2023 148 likes β€’559 views

COMP 546 Lecture 10 depth from X: defocus blur and binocular disparity Tues. Feb. 13, 2018 1 Depth from defocus blur 2 The eye controls , so it knows . 1 1 1 1

slide-1
SLIDE 1

1

COMP 546

Lecture 10

depth from X: defocus blur and binocular disparity

  • Tues. Feb. 13, 2018
slide-2
SLIDE 2

Depth from defocus blur

2

slide-3
SLIDE 3

3

1 𝑔

π‘‘π‘π‘ π‘œπ‘“π‘ +

1 π‘”π‘šπ‘“π‘œπ‘‘ = 1

π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ + 1 π‘Žπ‘‘π‘“π‘œπ‘‘π‘π‘ 

The eye controls 𝑔

π‘šπ‘“π‘œπ‘‘, so it β€œknows” π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“.

π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“

slide-4
SLIDE 4

Recall: Depth and Defocus Blur

1 π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ βˆ’ 1 π‘Ž0

(See Exercise 2 Q 6 & Assignment 1)

4

blur width = aperture

π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ π‘Ž0

slide-5
SLIDE 5

Estimating Depth from Defocus Blur

1 π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ βˆ’ 1 π‘Ž0

5

blur width = aperture

3.) estimated 2.) measured

(details omitted)

1.) known

(controlled by vision system)

π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ π‘Ž0

slide-6
SLIDE 6

Estimating Depth from Defocus Blur

1 π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ βˆ’ 1 π‘Ž0

blur width = aperture

π‘Žπ‘”π‘π‘‘π‘π‘šπ‘žπ‘šπ‘π‘œπ‘“ π‘Ž0 ? π‘Ž0 ?

There is a two-fold depth ambiguity.

slide-7
SLIDE 7

7

Varying accommodation resolves the two-fold ambiguity.

Estimating Depth from Defocus Blur

slide-8
SLIDE 8

Blur on a slanted plane

blur gradient focal plane intersection

8

slide-9
SLIDE 9

slanted plane

Blur on a slanted plane

focal plane sensor plane

9

π‘Ž = 𝑛 𝑍 + π‘Ž0

slide-10
SLIDE 10

slanted plane image of slanted plane

Blur on a slanted plane

focal plane sensor plane

10

See lecture notes: blur width radians = 𝐡 𝑛

π‘Ž0 𝑧 𝑔

π‘Ž = 𝑛 𝑍 + π‘Ž0

slide-11
SLIDE 11

slanted plane image of slanted plane

ASIDE: tricks with a tilt-shift lens in photography

focal plane sensor plane

Tilt-shift lens can increase (or decrease) blur gradient

11

slide-12
SLIDE 12

Tilt-shift Illusion (Miniaturization)

12

slide-13
SLIDE 13

Tilt-shift Illusion (Miniaturization)

13

slide-14
SLIDE 14

14

We next examine how defocus blur is related to binocular disparity.

slide-15
SLIDE 15

Recall: Binocular disparity and depth

15

π‘ˆ

𝑦

(π‘Œ0, π‘Ž0)

π‘Ž π‘Œπ‘  π‘Ž

(π‘¦π‘š , 𝑔 )

π‘Œπ‘š

(𝑦𝑠 , 𝑔)

disparity ≑

π‘¦π‘š 𝑔 βˆ’ 𝑦𝑠 𝑔 = π‘ˆ

𝑦

π‘Ž0

slide-16
SLIDE 16

Recall: Binocular vergence

16

π‘ˆ

𝑦

(π‘Œπ‘€, π‘Žπ‘€) πœ„π‘  < 0 πœ„π‘š > 0

Vergence point

slide-17
SLIDE 17

(π‘Œπ‘€, π‘Žπ‘€) πœ„π‘  < 0 πœ„π‘š > 0 πœ„π‘š - πœ„π‘ 

Vergence angle πœ„π‘€ determines depth

πœ„π‘€ ≑ πœ„π‘š - πœ„π‘  β‰ˆ

π‘¦π‘š 𝑔 βˆ’ 𝑦𝑠 𝑔

= π‘ˆ

𝑦

π‘Žπ‘€

17

Vergence point

slide-18
SLIDE 18

18

π‘ˆ

𝑦

(π‘Œπ‘€, π‘Žπ‘€)

( π‘¦π‘š 𝑔 βˆ’ πœ„π‘š ) βˆ’ ( 𝑦𝑠 𝑔 βˆ’ πœ„π‘ ) = 0 βˆ’ 0 = 0

πœ„π‘  < 0 πœ„π‘š > 0

Vergence point

Binocular disparity of vergence point is 0 (obvious).

slide-19
SLIDE 19

(π‘Œπ‘€, π‘Žπ‘€)

19

π‘’π‘—π‘‘π‘žπ‘π‘ π‘—π‘’π‘§ = π‘ˆ

𝑦( 1 π‘Žπ‘‘ βˆ’ 1 π‘Žπ‘€) > 0

(π‘Œπ‘‘, π‘Žπ‘‘)

Binocular disparity depends on distance (diopters) from vergence depth.

Near (crossed) Disparity

slide-20
SLIDE 20

20

π‘’π‘—π‘‘π‘žπ‘π‘ π‘—π‘’π‘§ = π‘ˆ

𝑦( 1 π‘Žπ‘£ βˆ’ 1 π‘Žπ‘€) < 0

Binocular disparity depends on distance (diopters) from vergence depth.

(π‘Œπ‘€, π‘Žπ‘€) (π‘Œπ‘£, π‘Žπ‘£)

Far (uncrossed) disparity

slide-21
SLIDE 21

Binocular Fusion (β€œCyclopean Vision”)

If disparity is sufficiently small, then we fuse the left and right eye images. Otherwise, we perceive two images ( β€œdiplopia”).

21

slide-22
SLIDE 22

Panum’s fusional area

disparity β‰ˆ π‘ˆ

𝑦

1 π‘Žπ‘ βˆ’ 1 π‘Žπ‘€ < 𝑒𝑛𝑏𝑦

(π‘Œπ‘€, π‘Žπ‘€) (π‘Œπ‘, π‘Žπ‘)

22

slide-23
SLIDE 23

Panum’s fusional area in disparity space

23

π‘¦π‘šπ‘“π‘”π‘’ π‘¦π‘ π‘—π‘•β„Žπ‘’

𝑒 = 0 𝑒 > 0 𝑒 < 0

slide-24
SLIDE 24

Binocular disparity and blur

disparity =

IOD

1

  • bject dist

βˆ’

1 vergence dist

24

interocular distance or π‘ˆ

π‘Œ

blur width =

1

  • bject dist

βˆ’

1 focal dist

aperture

slide-25
SLIDE 25

Binocular disparity and blur

| disparity | blur = IOD aperture β‰ˆ 10

25

If vergence distance = focal distance then

blur width =

1

  • bject dist

βˆ’

1 focal dist

aperture disparity =

IOD

1

  • bject dist

βˆ’

1 vergence dist

slide-26
SLIDE 26

26

Vergence and accommodation systems are coupled. We verge at the same depth as we focus (even if one eye is closed) and vice-versa.

slide-27
SLIDE 27

focal plane vergence plane

Monocular Binocular

β‰ˆ

slide-28
SLIDE 28

Limitations on 3D cinema

vergence plane

28

slide-29
SLIDE 29

3D stereo displays can create accommodation-vergence conflict

[Hoffman et al 2008]

29

slide-30
SLIDE 30

How to study binocular stereo vision ?

Neuroscience

  • Show cats or monkeys different images to the left and

right eyes and measure brain activity. Computational modelling

  • Write a computer program that finds matching points

in left and right images, in a biologically plausible way Psychology

  • Show people different images to the left and right eyes

and measure how well the people judge depth.

30

slide-31
SLIDE 31

Random Dot Stereogram

Bela Julesz, β€œBinocular depth perception without familiarity cues” Science 1964.

31

slide-32
SLIDE 32

32

slide-33
SLIDE 33

33

slide-34
SLIDE 34

How to make a random dot stereogram?

1.) shift patch left image for left eye image for right eye 2.) Fill empty patch

34

slide-35
SLIDE 35

image for left eye image for right eye background background right eye only left eye only foreground square

35

slide-36
SLIDE 36

image for left eye image for right eye background background right eye only left eye only foreground square perceived depths

36

slide-37
SLIDE 37

37

left eye only right eye only neither eye

slide-38
SLIDE 38

38

π‘¦π‘šπ‘“π‘”π‘’ π‘¦π‘ π‘—π‘•β„Žπ‘’

𝑒 = 0 𝑒 > 0

𝑒 < 0

Disparity Space

slide-39
SLIDE 39

39

Q: where are the eyes verging?

π‘¦π‘šπ‘“π‘”π‘’ π‘¦π‘ π‘—π‘•β„Žπ‘’

Disparity Space