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Vision-correcting Displays @ SIGGRAPH 2014
- 1. Eyeglasses-free Display: Towards Correcting Visual Aberrations with Computational Light Field Displays Fu-Chung Huang1,+ Gordon Wetzstein2,# Brian A. Barsky1 Ramesh Raskar2 University of California, Berkeley MIT Media Lab now at Microsoft now at Stanford University 1 2 + #
- 2. shown at 350mm normal display distance to display focal range
- 3. perceived image normal display distance to display focal range
- 4. pinhole array mask parallax barrier based light field display
- 11. 25% U.S. population of hyperopia (far-sightedness) [Krachmer et al. 2005]
- 12. 43% age 40 U.S. population of presbyopia (need reading eyeglasses) [Katz et al. 1997]
- 13. 68% age 80+ [Katz et al. 1997] U.S. population of presbyopia (need reading eyeglasses) 43% age 40
- 14. U.S. population of myopia (near-sightedness) 41.6% [Vitale et al. 2009]
- 15. Myopia in some Asian countries 60% ~ 90% [Rajan et al. 1995] [Wong et al. 2000] [Takashima et al. 2001] [Lin et al. 2004]
- 16. Irregular Blurring in Vision PSF PSF PSF caused by higher-order aberrations
- 17. Nirmud lens (?) 9th century reading stone 1284 Salvino D’Armato 1508 concept 1760 Benjamin Franklin 1880 August Mueller 1983 PRK and LASIK now 934 B.C.
- 18. Computational light field display (eye-tracking) (input data)
- 19. Prior Work Projector Precompensation - Brown et al. [2006] - Zhang and Nayer [2006] - Oyamada et al. [2007] - Grosse et al. [2010] Computational Displays - Lanman et al. [2010] - Wetzstein et al. [2012] - Maimone et al. [2013] - Hirsch et al. [2014] - Akeley et al. [2004] Computational Vision Correction - Alonso and Barreto [2003] - Yellot and Yellot [2007] - Huang et al. [2012] - Pamplona et al. [2012] - Ji et al. [2014] - Huang and Barsky [2011]
- 20. How to Build a Vision Correcting Display
- 21. Spatial domain Frequency domain
- 22. = ⊗ ∗ = 𝑖𝑚𝑔 ∗ 𝑝𝑠𝑓 = 𝑏𝑙𝑢𝑟𝑖𝑚𝑔 ⊗ 𝑝𝑠𝑓 = 𝑏𝑙𝑢𝑟 Spatial domain Frequency domain
- 23. ∗ = −1 𝑖𝑚𝑔 ∗ 𝑝𝑠𝑓 = 𝑝𝑟𝑒 = 𝑖𝑚𝑔 ⊗ 𝑝𝑠𝑓 = 𝑝𝑟𝑒 ⊗ −1 Spatial domain Frequency domain
- 24. prefiltered perceived = 𝑖𝑚𝑔 ⊗ 𝑝𝑠𝑓 = 𝑝𝑟𝑒 ⊗ −1 Spatial domain
- 25. plane of focus time-multiplexed PSFPSF [Huang et al. 2012] without correction multilayer displayconventional display (simple inversion)
- 26. 7x7 views into the eye [Pamplona et al. 2012] without correction corrected vision pupil aperture
- 27. Inversely Prefilter the Light Field target image prefiltered light field
- 28. Flatland Light Field Projection retina 𝐼(𝑥) = −∞ +∞ 𝑙 𝑥, 𝑢 𝐴 𝑢 𝑑𝑢Retinal image: 𝒙𝒖 𝒙 𝒖 display focus plane (1D image + 1D direction)
- 29. Light Field Projection 𝐼(𝑥) = −∞ +∞ 𝑙 𝑥, 𝑢 𝐴 𝑢 𝑑𝑢Retinal image: 𝒙 𝒖 retinadisplay focus plane 𝒙𝒖
- 30. “Defocus” Light Field Projection focus plane 𝒙 𝒖 retinadisplay 𝒙𝒖
- 31. “Defocus” Light Field Projection focus plane 𝒙 𝒖 retinadisplay 𝒙𝒖 convolution
- 32. “Defocus” Light Field Projection focus plane 𝒙 𝒖 retinadisplay 𝒙𝒖 convolution 𝝎 𝒙 𝝎 𝒖 frequency domain analysis (in the paper)
- 33. Using a Light Field Display 𝒙 𝒖 𝒍 𝒅 = −𝑟/2 𝑟/2 𝑙 𝑑 Ψ 𝑥 𝑢 𝑑𝑢 𝐼(𝑥) = −∞ +∞ 𝑙 𝑥, 𝑢 𝐴 𝑢 𝑑𝑢Retinal image: more degrees of freedom focus plane retina 𝒙𝒖
- 34. Using a Light Field Display 𝒍 𝒅 = −𝑟/2 𝑟/2 𝑙 𝑑 Ψ 𝑥 𝑢 𝑑𝑢 𝐼(𝑥) = −∞ +∞ 𝑙 𝑥, 𝑢 𝐴 𝑢 𝑑𝑢Retinal image: focus plane retina 𝒙𝒖 ?
- 35. Using a Light Field Display 𝒍 𝒅 𝒙𝒖 ? 𝐏 ∙ 𝐋 𝒅 𝐈=
- 36. Using a Light Field Display 𝒍 𝒅 𝒙𝒖 ? 𝐋 𝒅 𝐈= 𝐏−𝟏 𝐏 ∙
- 37. Using a Light Field Display 𝒙 𝒖 𝒍 𝒅 more degrees of freedom focus plane retina 𝒙𝒖 𝐋 𝒅 𝐈= 𝐏−𝟏
- 38. Using a Light Field Display 𝒙 𝒖 𝒍 𝒅 more degrees of freedom focus plane retina 𝒙𝒖 𝐋 𝒅 𝐈= 𝐏−𝟏 become well-posed?
- 39. Using a Light Field Display 𝒙 𝒖 𝒍 𝒅 more degrees of freedom focus plane retina 𝒙𝒖 𝐋 𝒅 𝐈= 𝐏−𝟏 become well-posed?
- 40. Using a Light Field Display 𝒙 𝒖 𝒍 𝒅 more degrees of freedom focus plane retina 𝒙𝒖 𝐋 𝒅 𝐈= 𝐏−𝟏 become well-posed?
- 43. 250mm focus380mm f = 50 mm a = 6 mm
- 46. without correction Pamplona et al. 2012multilayer prefilteringtarget image light field prefiltering HDR-VDP2 Low error detection
- 48. * = : : : : Display light fieldProjection matrices Axial or lateral movement
- 50. conventional display multilayer display [Pamplona et al.2012][Huang et al.2012] Proposed method Method Inverse prefiltering Direct ray tracing Prefiltered light field Spatial Resolution Very High Very Low High Image Contrast Very Low Full (100%) High Building Cost High Very High Very Low light field display light field display
- 51. Shortcomings • Contrast and brightness loss – Content-dependent • Resolution loss – 3-to-1(DroidDNA), 5-to-1(iPhone) – about 150 PPI • Computation – GPU, Mobile • Calibration – Eye-tracking – Off-Axis Opt.
- 52. Future Work • Higher Resolution & Large Display – e.g. tensor displays • Multi-way correction • Other applications – AR/VR, 3D, Cryptography • Theoretical analysis – Higher order aberrations
- 53. Eyeglasses-free Display http://web.media.mit.edu/~gordonw/VisionCorrectingDisplay/ http://graphics.berkeley.edu/papers/Huang-EFD-2014-08/ Fu-Chung Huang Gordon Wetzstein Brian A. Barsky Ramesh Raskar http://displayblocks.org/
- 58. 𝝎 𝒙 𝝎 𝒖 (a) conventional display (in-focus) spatialdomainfrequencydomain no angular variations only spatial energy 𝒙 𝒖
- 59. 𝝎 𝒙 𝝎 𝒖 𝒙 𝒖 (a) conventional display (in-focus) spatialdomainfrequencydomain pupil function is a rect(), in u multiplication ( just spreading ) pupil response is a sinc(), in 𝜔 𝑢 convolution
- 60. 𝝎 𝒙 𝝎 𝒖 𝒙 𝒖 (a) conventional display (in-focus) spatialdomainfrequencydomain retinal projection integration in u slicing at 𝜔 𝑢 = 0 𝐼 𝑥 𝐼 𝜔 𝑥 Fourier Slice Theorem
- 61. 𝝎 𝒙 𝝎 𝒖 𝝎 𝒙 𝝎 𝒖 𝒙 𝒖 𝒙 𝒖 (a) conventional display (in-focus) (b) conventional display (out-of-focus) spatialdomainfrequencydomain retinal projection
- 62. 𝝎 𝒙 𝝎 𝒖 𝝎 𝒙 𝝎 𝒖 𝝎 𝒙 𝝎 𝒖 𝒙 𝒖 𝒙 𝒖 𝒙 𝒖 (a) conventional display (in-focus) (b) conventional display (out-of-focus) (c) multilayer display (out-of-focus) spatialdomainfrequencydomain retinal projection
- 63. 𝝎 𝒙 𝝎 𝒖 𝝎 𝒙 𝝎 𝒖 𝝎 𝒙 𝝎 𝒖 𝒙 𝒖 𝒙 𝒖 𝒙 𝒖 (a) conventional display (in-focus) (b) conventional display (out-of-focus) (c) multilayer display (out-of-focus) spatialdomainfrequencydomain retinal projection 𝝎 𝒖 (d) light field display (out-of-focus) 𝒙 𝒖 𝝎 𝒙 (d) light field display (out-of-focus)
Editor's Notes
- Imagine you are near-sighted, When the display is shown outside your focal range,
- everything appears blurred
- We built a parallax barrier based light field display using a printed pinhole mask on a ipod touch And the construction is quite thin, just a few milimeters,
- And using computation to correct vision problem! This does not require the observer to wear eyeglasses. And we did not change the optics of the eye and display Once the display has been built, all the corrections are done through computation! So let me introduce where you can use this kind of technology…
- So, this is a technology that has a very broad impact….. But let me go more specific on who can benefit from this. It is estimated that about 25% of people in the US , are far-sighted
- And since the ability to accommodate will decreases over time, At age of 40, the population of people having presbyopia is about 43%,
- And the number increases to almost 70% at the age of 80, This is an inevitable aging process that everyone has to face. That we will need a pair of reading glasses
- In the mean time, recent study shows that myopia in the US has increased to 41% Which is also high
- But the number in some Asia countries is approaching to a crazy 60%~90%. Although these “conditions” can be solved with eyeglasses They are not always convenient (click)
- And there are also certain people having HOA, that the blur they perceive are irregular, and are very difficult to correct. So maybe we need a new solution, Before that, let me briefly review what options people have so far.
- The earliest form of correction is the reading stone, or just a magnifier. (click)But really the first revolution is the eyeglasses; (click) The second category is the contact lenses, but it took a long time to become what it is today. (click) Finally, the third category is refractive surgery, and it has become quite popular these days.
- In this paper, we introduce the 4th option, which is a computation based correction. (click) This eye-glasses free vision correcting display modifies the content shown on the display according to your prescription (click) When paired with standard eye tracking technology, the display can generate a sharp perception to the user’s eye. This capability is unlocked by solving a deconvolution problem in the light field domain. So let me first introduce some prior work that leads to this idea
- The idea of pre-correction is not new. Early work pre-compensate a defocused projector, such that the projected image will become sharp. (click) We are also inspired by the concept of computational display, that modifying the optical components and the added computation give us more degree of freedoms. (click) Finally, correcting vision through computation has existed for quite some time, but modern approaches using computational display can give better results.
- So let me briefly describe how to build a display that can potentially correct your vision
- Let’s consider a 1D scan line of the watch face, its diagram is shown on the right
- For we know the blur can be modeled using convolution, (click) In the frequency domain, the operator becomes a pairwise multiplication of their spatial frequencies
- A simple idea of prefiltering is to invert the kernel in frequency domain, multiply with the signal spectrum (click)And then transform it back to the spatial domain This is a very simple idea, and can be implemented in just 3 lines of code
- The result looks very strange. But the ringing artifacts will be canceled out by a final stage of the blur, which happens inside the eye. Unfortunately the perceived image has very low contrast. This is because inverting the kernel, or deconvolution, is a well-known ill-posed problem. So how can we solve the problem?
- Our prior work uses a multilayer display, (click)such that the point spread functions at different layers have different sizes In the frequency domain, they give different response, thus we have more degrees of freedom. (click) Here are the photograph comparing with conventional display. Multilayer display can generate higher contrast and sharper image. But the contrast is still not perfect, so let’s look at another approach.
- Pamplona et al. construct a high angular resolution light field display. (click)When shown to a patient with blurred vision, the display can generate a sharp perception. (click) In their solution, all the light rays hitting the same retinal cell will be assigned to the same value. (click) But since they requires all 49 views entering the eye, thus the hardware construction can be very challenging, and the spatial resolution is low. So there must be some way to have both high contrast and high resolution image.
- And actually it’s quite simple: We use a light field display, and inversely prefilter the 4D space, And you can see the prefiltered images inside each view have the amplified frequencies. So let me briefly describe how that is done.
- Let’s say you have a simple set up that the rays leaving the display are focused on the retina. To obtain the perceived image I, (click) we have to consider the retinal light field L, where the rays are expressed using the spatial location x and the angular direction u. (click) the retinal image pixel is obtained by integrating rays along the angular direction,
- And Finally, since some rays are blocked by the pupil, we have to multiply a binary aperture function A, That limits the integration. This gives us the basic projection equation
- Now let’s consider the case where the display is out of focus, (click) since the rays converge at a plane before the retina plane, the retinal light field is now sheared.
- Integrating along the angular direction changes the formulation into a convolution:
- There are some interesting frequency domain analysis, please refer to the paper. But basically we know that the inversion in the frequency domain is ill-posed, since we don’t have enough degrees of freedoms.
- So using a light field display allows us to control the angular variation, thus we have more flexibility. (click) so let’s go back to look again at the projection equation (click) Since we know the exact geometry, we can always express the integral using the display light field
- So the question is: how can we solve for the display light field such that the eye will see a sharp target image? Well, The first step is to discretize the integral equation
- Into a matrix-vector multiplication. (click) The projection matrix P can be obtained by sampling the light transport. And P times the light field gives the target image
- A very simple way to solve for the prefiltered display light field is to move the projection matrix to the right, And that’s it. The solution is almost just that simple. But we might ask ourselve is there any condition allowing us to solve this problem in such a simple way?
- Remember that we said using the light field display gives more degree of freedoms
- So does that mean we can solve it with just two rays per pixel?
- Or do we need 3 rays?
- Or maybe 4? To answer these question, (click) we can take a look at the property of the projection matrix P. Since we want to invert the matrix, it is a good idea to look at its condition number
- By changing the numbers of rays entering the pupil, and varying the blur size in screen pixels What we found is that the decrease of the condition number slows down (click) as the angular sampling rate is higher than 2, so we decide 2 rays per pixel is good enough to implement on a regular display This number gives the guideline for hardware construction,
- So let me show you the experiments and results(click)
- And we simulate a hyperopic eye using a camera. On the right is the direct comparison of a battery with our correction.
- And here is the video I showed you earlier.(click) Here we compare with the prior light field solution by pamplona et al. On the same low resolution hardware, we can still manage to create a sharp image.
- The hardware construction is quite straightforward, and we will show how to build it in a few seconds First we show a light field image, When the display is out of focused, everything is blurred. Putting a pinhole array mask on top, a sharp image is revealed after some alignment.
- We also evaluate the standard Michaelson contrast The multilayer prefiltering gives sharp correction, but contrast is very low. (click) On the other hand, Pamplona et al. has full contrast, but using the same low resolution prototype, their results are still quite blurry. (click) Our method gives a good balance between sharpness and contrast. (click) We also test with the perceptual metric HDR-VDP2, and our method has low probability of differences detection
- Finally, we also show that it is possible to correct higher order aberrations. You can see the spherical is quite different from the defocus term, and both are difficult to correct. (click)The coma is more difficult with a cone shape PSF. (click)Finally, not all higher order term are difficult; For example, trefoil has 3 legs, and preserves more high frequency information making the prefiltering easier.
- Our method can also account for slight deviation in the lateral and axial movement. This is done by stacking multiple projection matrices into the linear system and solving an over-constrained optimization.
- On the top right is the prefiltered light field with an over-constrained lateral movement. Since the light field display also has repetitive viewing zones, this allows the display to be viewed with two eyes separated by 65mms.
- Finally, to summarize the features and problems with different approaches, The first multilayer display deconvolve the optical blur of the eye, the resolution is higher, but the contrast is low. Building a multilayer display is non-trivial. (click)Pamplona et al require a super high resolution display, so its spatial resolution is quite low, even it provides the full image contrast. Build such high resolution display is extremely difficult and expensive. (click)The last technology prefilters the 4D light filed, so it has both higher resolution and higher contrast, and the cost is just a few dollars
- But of course, we also still have some problems. First, the prefiltering is content dependent: so if you have a lot of high frequencies, the contrast and brightness will be lower. (click) Second, our parallax barrier implementation will introduce some resolution loss, and the highest resolution we built is about 150PPI (click)processing light field requires a lot of computation, but we think it shouldn’t be too hard to port to GPU (click)Finally, the vision correcting require a good calibration between the eye and the display. But fortunately Amazon just announce a very cool firephone and SDK to do that, And in the paper, we also implemented an off-axis optimization to deal with the problem
- However, there are still some future work to be done. First, we anticipate higher resolution on a larger display to be built, and we believe this could be achieve using the tensor display architecture. (click)And it would be also interesting to provide a multi-way correction for a shared display. (click) extending the prefiltering to other applications like AR/VR, 3D content, or even cryptography can be very interesting (click) and finally, we believe a more thorough theoretical analysis is required for higher order aberrations.
- But even I just told you how to solve for the light field with a simple equation, The frequency analysis is actually more interesting than the equation.
- Let’s first look at the frequency domain light field, For a in-focus diffuse object, its spectrum is simply a line.
- But remember there is a pupil aperture blocking the light, In the spatial domain it’s a multiplication with the pupil function (click)And in the frequency domain it’s a “convolution” with the pupil response, which is a “sinc” function Since the original light field spectrum is only a line, (click)the convolution is just a spreading of the line vertically.
- The final step to obtain the image is the integration of light rays over the angular direction. If you are familiar with computational tomography, the integration is a slicing in the freq. domain. So the target image spectrum is the slicing on the axis.
- For an out of focus diffuse object, its representation is sheared, and so does its frequency spectrum. If you just slice the axis, there will be nothing left except for the DC term. But the spreading due to the pupil aperture will deliver some information to the slicing axis. Unfortunately not all spatial frequencies are preserved, since the spreading is due to a “sinc” function.
- In the multilayer prefiltering case, the missing frequencies are covered by the other layer, so you can still preserve all spatial frequencies
- Finally, the light field display is a bit different, You have a full convolution with the entire frequency spectrum, but you also have a lot more flexibility.