Depth Estimation and Focus Recovery

Reporter: Wade ChangAdvisor: Jian-Jiun Ding1Depth Estimation and Focus Recovery1Outline2MotivationOverview Blurring model and geometric opticsBlurring functionFourier opticsLinear canonical transform (LCT) Depth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

2Outline3MotivationOverview Blurring model and geometric opticsBlurring functionFourier opticsLinear canonical transform (LCT) Depth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

3Motivation4Focus recovery is important, it can help users to know the detail of original defocused image.Depth is a important information for focus restoration.

4Outline5MotivationOverview Blurring model and geometric opticsFourier opticsLinear canonical transform (LCT) Blurring functionDepth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

5Blurring Model and Geometric Optics(1)6What is the perfect focus distance?

Why does the blurring image generate?

lenssensorPosition of objectEffective depth of field intervalFThis area is too small for the HVS and results in an effective focused plane

6Blurring Model and Geometric Optics(2)7Ideal and real spherical convex lens Ideal spherical convex lensReal spherical convex lensAspherical convex lens7Blurring Model and Geometric Optics(3)8 combination of the convex lens and the concave lensConvex lensConcave lensIncident raysF1F28Blurring Model and Geometric Optics(4)9Effective focal length of the combination of lensesF4l1l2F3F2F1Combination of the thin convex lenses9Outline10MotivationOverview Blurring model and geometric opticsBlurring functionFourier opticsLinear canonical transform (LCT) Depth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

10Blurring Function (1)11screenFD/2FusvBiconvex2R : R0screenv11Blurring Function (2)12Blurring radius relates to depth value:

Considering of diffraction, we may suppose a blurring function as:

:diffusion parameter

12Outline13MotivationOverview Blurring model and geometric opticsBlurring functionFourier opticsLinear canonical transform (LCT) Depth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference13Fourier Optics(1)14Aperture effect(Huygens-Fresnel transform)When a plane wave progress through aperture, the observed field is a diffractive wave generated from the rim of aperture.

......14Fourier Optics(2)15Where the examples are through Huygens-Fresnel transform at z=1 meter, z=14 meters and z=20 meters respectively.

15Outline16MotivationOverview Blurring model and geometric opticsBlurring functionFourier opticsLinear canonical transform (LCT) Depth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

16Linear Canonical Transform (1)17Why we use Linear canonical transform?Definition

17Linear Canonical Transform (2)18Effects on time frequency analysis can help us realize most properties by changing those four parameters.Let us consider one of time frequency analysis-Gabor transform:

After is substituted as a LCT signal, the result in a new coordinate on time and frequency is as follows.

18Linear Canonical Transform (3)19CharacteristicsFunction representationTransforming parametersChirp multiplicationChirp convolutionFractional Fourier transformFourier transformScaling

19Linear Canonical Transform (4)20Consider a simple optical system.

The equivalent LCT parameter:

UoUlUlUis

20Linear Canonical Transform (4)21Special case of an optical system

UoUlUlUif : focal length

21Outline22MotivationOverview Blurring model and geometric opticsBlurring functionFourier opticsLinear canonical transform (LCT) Depth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

22Binocular Vision System(1)23

23Binocular Vision System(2)24Binocular vision at a gazing point.

Gazing point(Corresponding point)Baseline (B)B/2B/2Depth (u)

24Outline25MotivationOverview Blurring model and geometric opticsBlurring functionFourier opticsLinear canonical transform (LCT) Depth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

25Monocular Vision System(1)26Method 1:Utilizing diffusion parameter to calculate depth value.

Blurring radius: R>0FD/2Fus2R : R>0screenv26Monocular Vision System(2)27Using power spectral density to calculate depth value.

27Monocular Vision System(3)28Method 2:Take differentiation on equation I which respect to .

28Monocular Vision System(4)29Method 3:Using LCT blurring models UoUlUlUis

29Outline30MotivationOverview Fourier opticsLinear canonical transform (LCT) Blurring functionDepth estimation methodsBinocular vision systemMonocular vision system Focus recovery methods Reference

30Focus Recovery Methods(1)31Derive MMSE filter

31Focus Recovery Methods(2)32Derive MMSE filter

32Focus Recovery Methods(3)33Derive Wiener Filter:

33Reference34[1] M. Robinson, D. Stork, Joint Design Lens Systems and Digital Image Processing[2] P. C. Chen, C. H. Liu, Digital Decoding Design for Phase Coded Imaging[3] Y. C. Lin, Depth Estimation and Focus Recovery3435Thank You for Listening35