renng thesis

7/30/2019 Renng Thesis

1/203

D I G I T A L L I G H T F I E L D P H O T O G R A P H Y

a dissertation

submitted to the department of computer science

and the committee on graduate studies

of stanford university

in partial fulfillment of the requirementsfor the degree of

doctor of philosophy

R N

J


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C R N

A R R


3/203

I I , ,

D

P.

P H P A

I I , , D

P.

M L

I I , ,

D

P.

M H

A U C G S.


4/203


5/203

Acknowledgments

I P H, M

L M H , I

. P ,

, I

. I . M L

, ,

. M H

.

I .

I B W D N -

. D S.

I

. M B

, . G D

,

. A A M Y -

. K F

,

.

A . S

K W K I S S -

, T J C M, S P A R

A O A, M H Z I.


6/203

I , I H G A G S-

G L - , J G .

T P C, B C, J F, K F, A E G,

J G, B H, B O, D O

.

A M R F . T

,

. A S B G

. I

S U S C

.

I S G L.

I K F,

. M K -

, I . J K

. I

: E C, M H, G H, B

M, K P, R R, P S R W. S

J O, M P B W

.

I , ,

, M B, S C, A C,

P F, N H, L H, J J, S M, E M, M

P, J R, M R, D W M W. S

N , ,

.

F, I , Y F, B L C K N,

. M ,

. T .


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'PS.BNBBOE1BQB


8/203


9/203


10/203

contents

4 Digital Refocusing 49

. P W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I S A . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. T R P . . . . . . . . . . . . . . . . . . . . . . .

. T N P . . . . . . . . . . . . . . . . . . . . . . . . . .

. E P . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. P A . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Signal Processing Framework 79

. P W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. O . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. P I F D . . . . . . . . . . . . . . . . .

.. G F S T . . . . . . . . . . . . . .

.. F S P T . . . . . . . . . . . . . . . . . . .

.. P E F L F . . . . . . . . . . . .

. B-L A R P . . . . . . . . . . . . . .

. F S D R . . . . . . . . . . . . . . . . . . . . . . . . .

. L F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Selectable Refocusing Power 113

. S P G L F C . . . . . . . . . . .

. O F P L . . . . . . . . . . . . . . . . . . .

. E P C . . . . . . . . . . . . . . . . . . . . . . .

. E R- S . . . . . . . . . . . . . . . . . . . . .

7 Digital Correction of Lens Aberrations 131

. P W . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. N . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. V A R L F . . . . . . . . . . . . . . . .

. R O C . . . . . . . . . . . . . . . . . . . .

. D C A . . . . . . . . . . . . . . . . . . . . . . . . . .


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contents

. C R A P-C L . . . . . . . . . .

. S C P . . . . . . . . . . . . . . . . . . . . . . . . .. M I Q M . . . . . . . . . . . . . . . . . .

.. C A: C L . . . . . . . . . . . . . . . . . . .

.. C P A D L . . . . . . . . .

8 Conclusion 167

A Proofs 171

a. G F S T . . . . . . . . . . . . . . . . . . . . . . . .

a. F L F I T . . . . . . . . . . . . . . . . . . . . . . a. P F-D S L F . . . . . . . . . . . . . .

Bibliography 177


12/203


13/203

List of Figures

1 Introduction 1

. C . . . . . . . . . . . . . . .

. D . . . . . . . . . . . . . . . . . . . . . . . . .

. R . . . . . . . . . . .

. D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Light Fields and Photographs 11

. P . . . . . . . . . .

. T . . . . . . . . . . . . . . . . . . . .

. P . . . . . . . . . . . . . . . . . P . . . . . . . . . . .

. - . . . . . . . . . . . . . . . . . . . . . . .

3 Recording a Photographs Light Field 23

. S . . . .

. O . . . . . . . . . . . . . . . . .

. R . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. C . . . .

. S- . . . . . . . . . . . . . . .

. E . . . . . . . . . . . . . . . . . .

. M . . . . . . . . . . . .

. G : - . . . . . . . . . . . . . . .

. G : . . . . . . . . . . . . . . . . .


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list of figures

. P . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. M . . . . . . . . . . . . . . . . . . . . . . . . S . . . . . . . . . . . . . . .

4 Digital Refocusing 49

. E . . . . . . . . . . . . . .

. S-- . . . . . . . . . . . . . . . . . . . . . . . . .

. A - -- . . . . . . . . . .

. C - . .

. I . . . . . . .

. E : . . . . . . .

. E : . . . . . .

. E . . . . . . . . . .

. R . . . . . . . . . . . . . . . . . . .

. L . . . . . . . . . . . . .

. F - . . . . . . . . . . . . . . . . . . . . . . . . . . .

. M . . . . . . . .

. T . . . . . . . . . . . . . . . . . . .

. H- . . . . . . . . . . . . . . . . . . . . . . . .

. E . . . . . . . . . . . . .

. D . . . . . . . . . . . . . . . . . . . .

. M . . . . . . . . . . . . . . . . . .

5 Signal Processing Framework 79

. F- . . . . . .

. F- . . . . . .

. R F . . . . . . . . . . . . . . . . . . . . P I O . . . . . . . . . . . . . . . . . . . . . . . . .

. C F S T . . . . . . . . . . . . . . . . . . . . . . . . . .

. G F S T . . . . . . . . . . . . . . . . . . . . . . . .

. F S P T . . . . . . . . . . . . . . . . . . . . . . . .

. F L F P T . . . . . . . . . . . . . . . . . . .


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16/203

list of figures

. C . . . .

. C . . . . . . . . . . psf rms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. A - - C . . . . . . . . . . .

. S . . . . . . . . . . . . . . . . . . . . . . . . . . .

. H - psf . . . . . . . . . . . .

. mtf ( ) . . . . . . . .

. mtf ( ) . . . . . . . .

. R- . . . . . . . . . . . . . .

. D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. P . . . . . . . . . . . . . . .

8 Conclusion 167

A Proofs 171


17/203

1Introduction

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18/203

chapter . introduction

1.1 The Focus Problem in Photography

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19/203

.. the focus problem in photography

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21/203

.. trends in digital photography

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23/203


24/203


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1.4 Dissertation Overview

Organizational Themes

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25/203

.. dissertation overview

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27/203

2Light Fields and Photographs

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28/203

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.. the light field flowing into the camera

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.. photograph formation

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.. photograph formation

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34/203


(a) (b)

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35/203

.. imaging equations

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36/203


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.. imaging equations

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3Recording a Photographs Light Field

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chapter . recording a photographs light field

3.1 A Plenoptic Camera Records the Light Field

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.. a plenoptic camera records the light field

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.

3.2 Computing Photographs from the Light Field

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44/203


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45/203

.. three views of the recorded light field

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48/203


(z) (z)

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50/203


3.4 Resolution Limits of the Plenoptic Camera

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.. generalizing the plenoptic camera

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59/203

.. prototype light field camera

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Integral Photography, Plenoptic Cameras and Shack-Hartmann Sensors

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61/203

.. related work and further reading

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62/203


63/203


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65/203

4Digital Refocusing

T :

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66/203

chapter . digital refocusing

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68/203


Focus and Depth from Defocus and Auto-Focus

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.. image synthesis algorithms

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70/203


71/203


(a): N (b): R (c): R

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72/203


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A - , -

. T - . T - F . c.

T - .


73/203


Q d . T

- E ..A

. Vignetting F . c. T

- (

F .b c). A

E . . T

, ,

LF .

A

. F ,

. D

. F . c

, F . c.

Extending the Depth of Field

T . P-

- . T digitally stopping down the lens,

. S

. T

, ,

. T snr ( F .b).

I . L

,

. T , . A -

, ,.

I -

. T ,

, . B


74/203


(a): U (b): S- (c): E dof

F .: C - - .

E ., snr , . T , F .c,

- , . I -

, digitally extending the depth o feld

snr .

T F . z .

O -

, C . T F .a . I

,

. F .b F . z

.

T

. F ,


75/203

.. theoretical refocusing performance

F . . C

, S ., I digital photomontage A . []

.

D

. I

. I

graph-cut optimization [B . ] ,

gradient-domain diusion [P . ] . F

,

. B ,

, .

4.3 Theoretical Refocusing Performance

T -

. T -

- - . A

N , - N

, N .

C F . T -

- d . B-

,

. T -

C ,

.

F,

N - . A

N= . I

,


76/203


. I

, , .A

. S

- N,

N

. I , / N= ,

/ . P

,

.F . . I I b,

, . I

, - :

. T, ,

. I I c,

. O

I a. T

. I, ,

, .

D .

T eective depth o ocus

. T

. I

- . I

- . I

, eective

, -

. F


77/203

.. theoretical noise performance

-FOT%FTJSFE

GPDBMQMBOF%FQUIPGGPDVTPGBDPOWFOUJPOBMDBNFSB

&FDUJWFEFQUIPGGPDVTPGUIFMJHIUmFMEDBNFSB

F .: I . T , .

(..

, N ). T -

N. T N -

.

T N ,

F .. T - N

,

. T : -

- .

4.4 Theoretical Noise Performance

A -

. F ,

(.. -

). H,


78/203


NN (..

N2

).L -

/A /(A N), /A . A ,

-

. F,

/(A N) .H, N2

. I 1/N2

- . A, ,

N2 .

A , snr -

? T , N2

? T ,

, - ,

. T

P [G],

. F , , ,

. G , -

P ,

. U - , snr

N , N2 , P

N .

T , . L ,

, NN . I , -

N . T


79/203

.. experimental performance

. T

. T ,

. I , N2

, 1/N2 1/N2

. T snr N. O

- -

, .

4.5 Experimental Performance

T

. I ,

,

.

Experimental Method

T ,

. , I

away . I ,

.

I I

- . T, ,

?

A -

, - . I

.

S -


80/203


,

- .A

- -

. T

,

. I I ,

,

.

A

. N, , P

. T snr

.

Refocusing Results

I / , -

/ /. T - . T -

. T

-.

F .

. N / -

/ . T

/ , /. I

/ .F . ,

(mtf) . I mtf

F [W ].

F , I ,

, F .


81/203


/ R L F / C

/ C / C / C

F .: E : .


82/203


$POWFOUJPOBM

3FGPDVTFE-JHIU'JFME

F .: E : mtf . H 0 N .

F . mtf . T

mtf . T

- , ., , , , . A

- , ,

mtf. T , /

/ . T mtf

/ ,

F ..

A , , -

, / . I ,

/ , -

.

T . A F .,

,

. A, -

, S .. W

/ ,


83/203


/ , -

.

Noise Results

I . A -

, I snr /

/ . T -

snr ., (

. / ). T

snr P , S-

.. I snr

- , I -

. T snr --

- .

/ C / C / R L F

F .: E .


84/203


(a): C

(b): U (b): R (b): E dof

F .: R .

F . . T - F .,

,

. I F ., / -

- . T /

, . N /


85/203

.. technical summary

(a): /, / L F, E dof

(b): /, / C P

(c): /, / C P

F .: C .

/ . T / ,

. N , / . T

snr . / /

.

4.6 Technical Summary

T

- .

F . ,

. N

I b ,

/


86/203


- / . H,

/ . I I b, . N, ,

. W .

I b

.

F .

. T

F . F .a. I I b,

/ , I ( /)

. A ,

. I

I a,

P . I , I c, I / ,

- /

I a. T -

. T

. H, I c

. F .

-

.

I ,

. T

. T

.

4.7 Photographic Applications

,

. T -

.


87/203

.. photographic applications

Portraiture

G

. I , -

. F

, -- ,

,

. I , .

I , . O

, .

U . H, ,

. W

,

, . F .a ,

- ,

. S ,

, F .c.

(a): M- (b): R (c): R -

F .: F -

A ,

. I ,


88/203


89/203


F .: T .

Action Photography

A

. L ,

. T -

, ,

.

F . . T

a-a b-b

. T / .

I c-c .

T ,

/ .

Landscape Photography

W , . T

,

. I

.


90/203


(a) (a) (a)

(b) (b) (b)

(c) (c) (c)

F .: D - .


91/203


A ,

, . S . C ,

. F , -

,

.

T , -

,

- -

.

(a): R (a): R (a): E dof

(b): R (b): R (b): E dof

F .: E .

F . . I ,


92/203


(a) (a) (a)

(b) (b) (b)

F .: D .

, . T

- ,

.

Macro photography

T ,

, ,

. , : , -

,


93/203


(a): H (b): L

(c): F (d): C

F .: M

.

F , ,

.

B ,

. M - . I , ,

. T ,

. A , -

, ,


94/203


95/203

5Signal Processing Framework

A , F -

-

. T F

. F ,

. I

,

C .

S . , F

. T ,

F . L ,

F

, B [].

5.1 Previous Work

T F C . [].

T , , - -

. T

- ,

.


96/203

chapter . signal processing framework

I I . []. T

F , . T -

, -

.

M , S . []

- - . T -

-- . I ,

- . A

, .

F, D . [] F

,

, . W

,

.

5.2 Overview

T F -

. W

(C ) ,

. I , F

d d .

T , F d

d F . T F S P T,

S ., .

F . -

, F . T

, ,


97/203

.. overview

N R R

F .: T ( ) F ( ).


98/203


-. T -

F . F . T - F ,

(mr) . I , kx ku

F- x u ( ky

kv). T F-

F . T . T

,

, .

T F - - R B [] F

S T ( C S T F P-S

T). B -

. H,

,

(ct) (pet) [M

], (mr) [N ].

T d d , -

d -

d . N,

, - -

. F , mr

S .

F-.

P F S P T-

-

. S . -

, . I ,

S .

-.

F .c -:


99/203

.. overview

$POUJOVPVTMJHIUFME 1FSGFDUQIPUPHSBQI 3FDPSEFEMJHIUFME

1IPUPHSBQIDPNQVUFEXJUIPVUSFGPDVTJOH

3FGPDVTFEQIPUPHSBQIXJUIGVMMTQBUJBMSFTPMVUJPO

3FGPDVTFEUPPGBSXJUIMPTTJOTQBUJBMSFTPMVUJPO

3FEVDFEQIPUPCBOEXJEUI

F .: F- .

,

. T F-

. . I , , -

. W -

, -

,

,

.

W - , -

. F . , d


100/203


. S

-, - (F .df).

T , ,

(F .b). T -

- . B -

- ,

.

T S ., F .e f

. T ,

F .: T

F

.

,

- . U ,

-,

(

) . H, -

,

(-

). T

F .. A

. S-

. , C

.

S . F S P T

F S D R . T -

d F -

d F . T

O(n2 log n), n . T


101/203

.. photographic imaging in the fourier domain

O(n4) , -

d .

5.3 Photographic Imaging in the Fourier Domain

P>1P


102/203


A ,

F S T. T F S T [D ] d d F F -

d . T

, F .. C,

dc ( ) ,

. F ,

. I

,

.

T ,

, d

d F . W , S .. ..

,

E . ..

5.3.1 Generalization of the Fourier Slice Theorem

L -, d . A

R [L M ], -

N M . T

-

change o basis (.. N- ). T

.

I Pj L INM N- M-

N M : INM [f] (x1, . . . , xM) =f(x1, . . . , xN) dxM+1 . . . dxN.

S L SNM N- M - NM -: SNM [f] (x1, . . . , xM) = f(x1, . . . , xM, 0 , . . . , 0).


103/203


C B L B

N- . I B N- NN, B[f] (x) = f(B1x), x N- , B1 B.

S L a

, a[f](x) = a f(x).

F T L FN N- F -, FN . FN [f] (u) =

f(x) exp (2i (x u)) dx,

x u N- ,

N- .

W , :

generalized fourier slice theorem Let fbe an N-dimensional unction. I we

change the basis of, integral-project it down toM o its dimensions, and Fourier transorm the

resulting unction, the result is equivalent to Fourier transorming f, changing the basis with

the normalized inverse transpose o the original basis, and slicing it down to M dimensions.

Compactly in terms o operators, the theorem says:

FM INM B= SNM BT|BT| F

N, (.)

where the transpose o the inverse oBis denoted byBT, andBT is its scalar determinant.A A a..

F . N-

, M- , F . O ( F .

.) N= , M = d (B= R). I , (R = RT), RT

1. A , F .


104/203


105/203


, . R

A a.. A , () -

.

T . F -

,

N- , GN, F , GN. F

, M ,

GM. A F ., ( -

) O(n

N

) , n N. A GN ( ) -

F ( ), O(nM log n)

F F .

F ,

. F ,

ct , - -

. I ,

F F . W

.

5.3.2 Fourier Slice Photograph Theorem

T F S P T,

. T IO G F S T.

T I O (E .) -

():

P [LF] = 12F2

I42 B [LF] , (.)


106/203


:

I C B B d :

B =

0 1 00 0 1 0 0 1 0

0 0 0 1

B1 =

1/ 0 1 1/ 00 1/ 0 1 1/0 0 1 0

0 0 0 1

N B B1 , B,

generic G F S T. D I42 E . E ..

W G F S T (E .) -

E . F- . F, - E .

P = 12F2

F2 (F2 I42 B).

I , G F S T (E .)

,

P = 12F2

F2 S42 B

TBT F

4

.

F, BT

= B1 = 1/2, :

P = 1F2

F2 S42 BT F4, (.)

(P) d F : d (S42 BT), d (F2), (1/F2).

B ,

F :


107/203


F P I O

P =1F2

S42 BT. (.)

I P ,

S42 B. T :

P[G](kx, ky) =1

F2G( kx, ky, (1 ) kx, (1 ) ky). (.)

A E . E . , , :

fourier slice photograph theorem

P = F2 P F4. (.)

A photograph is the inverse d Fourier transorm o a dilatedd slice in the d Fourier trans-

orm o the light feld.

F .

. T P F- P. T , F .

I ,P F F

F . I

,

.

T P, ,

P, . T

P (E .) P (E .). B F- -,

. I , F S P T C-

T, .

F ,

. T


108/203


2P

LF .F

EF 'F

O(n4)

O(n4 logn)

O(n2)

O(n2 logn)

4QBUJBMEPNBJO*NBHJOH

F4

F2

'PVSJFS5SBOTGPSN

'PVSJFS5SBOTGPSN

'PVSJFSEPNBJO*NBHJOH

F .: F S P T. d LF, - d EF, F ,LF EF.

F ., n d .

T P (O(n2))

P (O(n4)). T S ..

5.3.3 Photographic Effect of Filtering the Light Field

A E .. I

, ,

, ? T -

.

filtered light field imaging theorem A d convolution o a light feld results

in a d convolution o each photograph. Te d flter kernel is simply the photograph o the dflter kernel ocused at the same depth. Compactly in terms o operators,

P C4h = C2P[h] P, (.)

where we have expressed convolution with the ollowing operator:


109/203


Cv CNh N-

h, CN

h [F](x

) =F(x

u

) h(u

) du

x

u

N- , F h N- .

F . . O , LF d

, LF d d h. EF EF

, . T EF d

EF, d d , h.

I , ,

. A a. . A ,

F S P T C T

F . I ,

, .

I

P

LF

EF

$POWPMVUJPO

$POWPMVUJPO

P

LF

EF

C4h

'JMUFSLFSOFM

C2P [h]

'JMUFSLFSOFM

P

F .: F L F P T. d LF, , LF, EF EF.


110/203


. A ,

. I d,

(x,y, u, v) = (x) (y) (u) (v), d :

(x) =

1 |x| < 120

.

W (x,y, u, v) ,

P [LF ] = (P C4) [LF]

= (C2P[] P) [LF]= P [] P [LF] .

F , , fg d d f g, a b d - d a b.

T

. T (P [LF]) d P []. T d d . W d ? T

d .

T


111/203


. T d , - ,

, .

B d , d d

, - . E , , d .

T F L F I T

. F ,

, ,

d , h(x,y, u, v). A ,

, (..

) h(x,y, u, v). G ,

P[h]. C d : . A

.

O , -

. F, ,

F -

. T

(C ), , - . A

-, -

. I , -

,

.


112/203


5.4 Band-Limited Analysis of Refocusing Performance

T F L F I T

, . W -

? H ,

-

?

T , S .,

- . S . -

-. T ,

F L F I T.

T - F

d , (x,y, u, v). B C T, F

F .

I F - ,

. L - , sinc(x,y, u, v) = sinc(x) sinc(y) sinc(u) sinc(v),

sinc(x) =sin x

x.

I , - , LF,

exact , LF, d sinc:

LF =C

4lowpass [LF] , where

lowpass(x,y, u, v) =1

(xu)2 sinc

xx

,y

x,u

u,v

u

.

I , x u

, . T 1/(xu)2 - -

sinc.


113/203

.. band-limited analysis of refocusing performance

Analytic Form for Refocused Photographs

O , EF ,

- , LF. T F L F P

T. L = F/F,

EF = PLF

= P

C4lowpass [LF]

= C2P[lowpass] [P [LF]] = C2P[lowpass] [EF ] ,

EF exact F. T -

d- . T d d sinc , P [lowpass].

I d sinc d sinc :

P [lowpass] = P

1

(xu)2 sinc

xx

,y

x,u

u,v

u

=1

D2x sinc

x

Dx,y

Dx

, (.)

N d sinc , :

Dx = max(x, |1 |u). (.)

T , F S P

T , ( A a.).

T d sinc, -

- . T

d (E .)

.

Interpretation of Refocusing Performance

R x u. L

Wx,


114/203


Wu. W , Nx = Wx/x

Nu =Wu/

u.

S = (F/F) u =Wu/Nu,

|x| |(1 )u|

|F F| xNuF

Wu. (.)

T , F,

, .. . W

N- ,

- .

P, E . E .,

(x). N,

, Wx, (Wx). T

( E .). I > 1, ,

, S ..

T, N

Wxx

=Wxx

. (.)

T ,

. T

E .. N

, Nu, S ..

I , ..

|F F| > xNuF

Wu,

- , EF , |1 |u,


115/203

.. fourier slice digital refocusing

x ( E .). T ,

Wx|1 |u ,

,Wx/x. I ,

, N- .

R- -

. S = F/F u =Wu/Nu,

|1

|

Wxu

=Wx

Wu

NuF |F

F|

. (.)

B NuFWu

f- Nu

, WuNuF |F F| - -

|F F|.I , ,

, Nu , S .. N

, Nu. D ,

.

I , - -

-

C .

5.5 Fourier Slice Digital Refocusing

T F S P T ,

. T

: - (

). T , ..


116/203


117/203


wwww

F

wwww2>

wwww2=

wwww2>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

1

3

-JHIU'JFME'PVSJFS4QFDUSVN

'PVSJFS4MJDF&YUSBDUJPO

'PVSJFS4MJDFT

*OWFSTF'PVSJFS5SBOTGPSN

3FGPDVTFE1IPUPHSBQIT

-JHIU'JFME

'PVSJFS5SBOTGPSN

F .: F S D R .


118/203


119/203


120/203


(a): W - (b): W -

F .: R .

F [M ], -

d F .

T d F -

. F . - K-

B , .

U, -

,

.

Suppressing Aliasing Artifacts

T , -

-. O

, - d F (PF F4) [LF]. I- F

. T - .

E

F . S,

. H,

,


121/203


. A ,

.

(a): (F ) (b): I F (a)

(c): N (d): C (b)

F .: R F .

F . . I a F . I b

. S

, I d. F , c

. T

.


122/203


O , -

. T , -

.

T : .

A , sinc -

. O - -

. T -

- ,

J . [] , M [] F .

(a): Q ( )

(b): K-B ( .)

(c): K-B ( .)

F .: A . R .

J . , -, K-

B . T K-B

. F .

K-B . S, K-

B . .

A , bokeh

. U


123/203


(a): W (b): W

F .: A . K-B - .

LF(x,y, u, v) A(u, v) -

. F , A(u, v)

(u, v) . I F ,

F

A(u, v). T F [L ].

T -

- F [L ;

M ]. T ,

- .. I F .,

I a -

I b -.

Implementation Summary

I S ., . I

- ,

. P (..) .

. P- F

.


124/203


F

S

F .: C F .

I , d F ,

. U - K-B . A .

. F , .

( ) .

. O d F . A F , -

.

Performance Summary

T - F S

- C .

D , F . .


125/203


F

S

F .: C F II.

F . T

( = ). F .

F ,

- . R

,

, .

N, F- .. A , -

F- .

I , cpu F

. W , F [N ]. T F


126/203


S uv ,

, F .

5.6 Light Field Tomography

T -

F . T

. T light feld tomography ct -

.

L d d . W

, F d -,

, . A

, /2 /2. H, d d ,

F . A

d R [D ] . T d

F S T d R

.

A

,

F . I ,

d .

I , d

. I F S P T ( E-

. ) - d

d d F :

( kx, ky, (1 ) kx, (1 ) ky)where [0,), and kx, ky R

. (.)


127/203

.. light field tomography

I , d

d . I d F .O d

. D d

. O d slit light feld d

. T

d d (

). B ,

d d

.


128/203


129/203

6Selectable Refocusing Power

T -

,

. T

. C

-,

. T generalized light feld camera.

O - -

. T

,

. H, ,

, - -

. F .

. N

,

.

T - F .


130/203


131/203

.. sampling pattern of the generalized light field camera

(a): = 1 (b): = . (c): = . (d): = 0

F .: D .

= 0. A S .,

beyond .

F . -. T

F .. N

F . . - , -. A

F . , -

. T

( x ), ( u ). A

-


132/203

chapter . selectable refocusing power

, . H, -

.

R ,

. H,

. A = 0

, .

T ,

. I ,

MM M

M,

MM,

M = max((1 )M, M). (.)

Deriving the Sampling Pattern

F . - , -

- . T

.A F .

. E -

. D

-,

C . T

-, , -

.F .a , , i,

. F .b -

, . L

- :

, xi, , si, , wi. I


133/203


134/203


135/203

.. optimal focusing of the photographic lens

.

N -. F .e

, . A

, F .f

u

.

A , ,

- - . T

F .f

F . . T

, .

The Problem with Focusing the Microlenses Too Close

T

( < ). A -

closer ,

urther ( > ). T - . T

, . B

() , - -

,

-. F ,

.

6.2 Optimal Focusing of the Photographic Lens

A -

. I

. I , -


136/203


137/203


138/203


, E . (1 ),

. H (1 ). T , . E

(1 ).I , , -

F, Fopt. D -

F

max((1 )M,M).

6.3 Experiments with Prototype Camera

T ., -

. I

. T -

S .: I -,

. I , I

.F . - : -

( ), -

( ). T -

/ iso

. W .

. O -

.

N = .

, -

. I , = .,

- . H, -,


139/203

.. experiments with prototype camera

= .

= .

W-

0

F .: D .

. I, - . .

( ) .

T

. T

, . F . . E . . ,

. , -

, F ..

A , 0 -

- [M N ] . T

,

- . N

-


140/203


C R- C R-

F .: C

-, = . ( ), = 1.

, - -

- .

6.4 Experiments with Ray-Trace Simulator

,

P H - [] . F .

-. T

- F ., , -

. T F . = ., = .. T

. T


141/203


142/203


T -

. T - iso . T

-. A -

, ,

.

MTF Analysis

T - mtf ,

- . T .

A

. B -

,

.

T mtf

. F ,

, - -. T

. T

F mtf -

-.

T mtf

. T

mtf . A

mtf, , mtf .

F .a

. T - -

, .


143/203

.. experiments with ray-trace simulator

. N .

F .a . F, ( ) , . T -

- = ( = 0, ., ., .

), , -

(1 ) . T , -. T

. T

, E-

.. A , (

). T ,

.

F .b - E-

., ,

F .c. T

,

E .. T F .c .

F . - F .b F .c -. T ,

. T

. T F .a

= .

.

T E ..

T F .b,

.c .d. R

E ..

T

,

. I F .b, .c .d, -

,


144/203


(FOFSBMJ[FEMJHIU

FMEDBNFSBDPOHVSBUJPOT

$FOUFSFEWFSTJPO

$VTUPNJ[FEQMFOPQUJDDBNFSBT

3FMBUJWFPQUJDBMNJTGPDVTJNBHFTJEF

4QBUJBMGSFRVFODZGPS

DVUPDZDMFTNN

NJDSPONJDSPONJDSPO

NJDSPONJDSPO

F .: mtf .

( ). I

, between ,

. T , , 1

, F .e.


145/203

.. experiments with ray-trace simulator

NJDSPO

NJDSPO

NJDSPO

NJDSPO

NJDSPO

NJDSPO

NJDSPO

NJDSPO

3FMBUJWFPQUJDBMNJTGPDVTJNBHFTJEF

4QBUJBM

GSFRVFODZGPSDVUPD

ZDMFTNN

F .: mtf II.


146/203


Summary

T

-

. T

, - -

. A

. T ,

,

.F , -

. A

. T

-

,

.

T ,

. T

-

. F ,

,

.

T - :

. B ,

.


147/203


148/203

chapter . digital correction of lens aberrations

. T -

, W [K ]. I -

. I , C

. F, ,

D , .

-

. Z

F .: S

.

. Z -

,

. H, -

-

,

[M ]. A ,

,

[D L ]! ,

- [S ],

.

O

[K ].

T -

. T -

. T :

, -

. D

.

F ,


149/203

.. previous work

( = 1) . I ,

, . T - , -

. T ,

, - .

7.1 Previous Work

R- . P

- . I S E P,

C L H [ A ] -

[K ]. A - ,

, /., . T

, ,

- ,

[N ].

K -

[K ]. T

. O

- - lasl

L A [B ].

I , -

- [P

C ; C . ], - - [K . ]. T C .

P C M-

C [K ]. I

, - ,

- [P H ] I


150/203


. O

- - .I , -

[M . ]. T

.

7.2 Terminology and Notation

T -

. T two - :

ideal-, , aberrated-

, . I

,

. T ,

-. L

(x,y, u, v)

(x,y, u, v).

T - . A -

. I ,

. I

, G ,

[S ]. T G -

, -

. T

G .

T , C, -

:


151/203


152/203


153/203

.. visualizing aberrations in recorded light fields

F .: A - - .


154/203


F .d.

F .b :

. T . A

- . F, S .,

.

T - ,

.

E - F .. T . F .

- ,

. I

,

.

7.4 Review of Optical Correction Techniques

T -

.

, .

F . . T - ,

. T -

ray-intercept curves

,

, - . T F . . T

( u -

), . S

, x . O

, .


155/203


156/203


I ,

. T , , F . .

(F .).

7.5 Digital Correction Algorithms

A ,

: . -

,

- . I ,

,

.

F . -,

. F .a

, - . T . F .b

(x, u) - , (x, u) -

. E

. T F .a.

F .c

. T

. I , F .d

. N

, , - F .c.

F .ac : pixel-order

, . A -

ray-order, .


157/203

.. digital correction algorithms

(a) (b)

(c) (d)

F .: R- .

T -

. T :

-

. T . T

- . T -

.

Pixel-Order Image Synthesis

T -

. I

.

. S . A M-C


158/203


.

. C - .

. R -

,

.

. E

. T

d . L- -

. S, .

. A .

Ray-Order Re-Projection of the Light Field

T - -

. I

.

. S

. A M-C

,

.

. , , -

.

. R

.

. I . A ,

.

A , ,

.


159/203


Confidence Weighting for Increased Contrast Enhancement

T -

. W

. F, - F .,

. S, -

,

, . F , F .d

.

T -

, . T

-

. T

weighted - .

I , I ,

x y .

F , .

w(x,y) = h(x) h(y), where

h(x) =

1, x 1exp

(1x)2

22

, x > 1

. (.)

I , G -

. T x y

, . I

= G -. C

x

y, (x,y, u, v), .

F . . E

. T

,

. A


160/203


(z) (z) (z)

F .: W ( ) . E .


161/203


- , (z z).

C , .

R -

. E . ,

. C

. T -, ,

( 1) -

. F ,

F . , -

. H,

- . W

. A -

, .

Computing the Projected 2D Size of Light Field Samples

C x y E .

d . I ,

,

C, . I , x

- :

x 1x

Cxx x +

Cxy y +

Cxu u +

Cxv v

, (.)

I C :

Cx,y, u, v

=

Cx(x

,y, u, v),

Cy(x,y, u, v),

Cu(x,y, u, v),

Cv(x,y, u, v)

= (x,y, u, v) . (.)


162/203


163/203

.. correcting recorded aberrations in a plano-convex lens

(a) (b)

F .: S- - .

F .a. T

- .

I -

- ( ). A

, / . I

-

, F .,

.

I M-C -. T

,

. T

-. A -, I

.


164/203


165/203


166/203


167/203

.. simulated correction performance

7.7 Simulated Correction Performance

I ,

. T , [S ]

- (psf)

. T psf

. I -

, . O

. I

- ?

,

.

7.7.1 Methods and Image Quality Metrics

T . A

, -

. T , ,

(. mp). A NN , N= (), N= . S

, N . N= , . -

, [A

]. . [M ],

, N= ,

. .

T psf

. C psf ,

. I ,

. F psf -

, - ,


168/203


psf .

A psf , -. T

(a): S

(b): C

F .: psf rms

.

psf d

, . F ,

psf

. A ,

( -

). F -, psf .

I , , I

psf.

T

(rms) ,

. T rms

psf

. A ,

rms - . O

,

:

. F .a

psf , rms .

O , rms ,

. F

, F .b psf coma.

T - psf

psf . C

[S ]. T rms

, .

T rms , d


169/203


. T rms

d , - -. A , -

,

.

A , rms eective res-

olution. T . I

F .: E

.

, ,

rms (F .). T . I

,

(

2R)2,

R rms ( ),

2R

. T

-

psf

. E psf-

.

T mtf. T mtf

,

. I

F . I, I

mtf : psf

F . A

mtf [P . ].

T mtf N

.

S mtf F psf, - psf.


170/203


T mtf,

. I ,

mtf. A mtf

.

7.7.2 Case Analysis: Cooke Triplet Lens

L psf . T /.

C [ E ]. F . psf. C a,

b c : ,

- , .

T

. ,

. T -

. T

. I , . F , D a

. I , D c

, .

T F . , -.

T , x, , , u,

. T N= . T

.

I D c,

. I ,

. I ,

D c ,

- , .

T -


171/203


(a)

(a)

(a)

(b)

(b)

(b)

(c)

(c)

(c)

F .: A - - C .

. I , -

. C, -

. T

, ,


172/203


MICRONS

(a): C

NJDSPOT

(b): M

NJDSPOT

(c): E

U C psf.

MICRONS

(d): C

NJDSPOT

(e): M

NJDSPOT

(f): E

F .: D C psf.

, . T

: -

,

.

F . psf

F .. T rms . W

(), rms , . mp .

F .

. I psf

, .

F .


173/203


TQPUSBEJVTQJ

YFMT /

/

'SBDUJPOPGFMEPGWJFX

/

/

/

F .: H - psf .

(NN) N= ( ) . T N rms

. T . F -

, N= , rms

. T psf -

( ) . , rms psf.

T rms

. T

, -

. T . mp

. mp N= . T ,

. O -

-, . S,

. I ,

,

.

T -

, . F .

, mtf . W ,


174/203


%JTUBODFGSPNPQUJDBMBYJTNN

6ODPSSFDUFENN6ODPSSFDUFENN6ODPSSFDUFENN$PSSFDUFENN$PSSFDUFENN$PSSFDUFENN

F .: mtf ( ).

%JTUBODFGSPNPQUJDBMBYJTNN

6ODPSSFDUFENN6ODPSSFDUFENN6ODPSSFDUFENN$PSSFDUFENN$PSSFDUFENN$PSSFDUFENN

F .: mtf ( ).

N . T mtf

: /, / / N . T / N

, . C

. T

. G mtf

,

.

F . , ,

, .

S, , , .


175/203


D , -

.

F . ,

: (.. ). T

, . T

- , M

. T

( ), . T

.

T mtf F .

. T extends the useul ocal range

. H, ,

. T -. F,

. F . -

F .. F

,

.

U,

. T F .

d-f a-c. T

. A ,

,

.

T ,

-

. H

.


176/203


(a): C (b): M (c): E

R- , .

(d): C (e): M (f): E

F .: R- .

7.7.3 Correction Performance Across a Database of Lenses

T -

- . I -

-

.

,

. T

-- Z [Z ]

.

T Z . F,


177/203


, -

- . S,

. T

. F ,

,

. F . ,

.

T , , G

, - . T

-. M

, . N, ,

. T

,

.

I , - . T

- .

F . . E ,

. F , -

. T

NN, N= 1 ( ), - N= , . N

.

T

. E ,

-. I

, -

.

A -

. I ,


178/203


L F D G F A R

e- C /. e- /. e- usp ,, /.

e- C usp ,, /.

f- W usp ,, /. f- W- /.

g- /. g- slr /. i- P /. l- D G /.

l- D G

/.

l- P usp ,, /. l- P usp ,, /.

l- L usp ,, /.

l- M G usp ,, /. l- L usp ,, /.

l- L. . usp ,, /. l- G usp ,, /. l- D usp ,, /.

l- - G usp ,, /. l- M usp ,, /.

l- D G /.

I F ..

F .: D .

-

. F , , vlsi ,

. , ( ). ,

. F -

. T ,

.


179/203


,FZ

&FDUJWF3FTPMVUJPO

F .: I .


180/203


A (

- ) . T . F

. mp .

A ,

( ) ,

-, . I

,

[A ]. O

, . T

-

.

In Closing

, -

, . O

: . A

. I , -

(.. )

.

I ,

. A -

, F . ,

. F

-,

u, . O

,


181/203


. O ,

, .

T

: ? ,

- S .

. W

. M

. T -

F .d . R

, , . W

, . A

- -

F .. I ,

. I , ,

.

T - -

. C

,

.


182/203


183/203

8Conclusion

T , H C-B

( ) , , -

Decisive Moment .

T , --,

.

A L, ,

, , C-B

.

B . I , I -

. T

-. O

. F D , - ,

-, A S ,

,

. B - ,

.


184/203


185/203

. H

.T -

. A d -

[L . ], -

. -

. W -

- [ ],

? I ,

.

T . W

: ,

. I I

, I

.

B , . P

,

. ,

is

. R

,

. I

renng thesis

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