Supplemental Material for DeepFovea: Neural Reconstruction ... · dering, foveated rendering, deep...
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Supplemental Material for DeepFovea: Neural Reconstruction for Foveated Rendering and Video Compression using Learned Statistics of Natural Videos ANTON S. KAPLANYAN, ANTON SOCHENOV, THOMAS LEIMKÜHLER ∗ , MIKHAIL OKUNEV, TODD GOODALL, and GIZEM RUFO, Facebook Reality Labs CCS Concepts: • Computing methodologies → Neural networks; Per- ception; Virtual reality; Image compression. Additional Key Words and Phrases: generative networks, perceptual ren- dering, foveated rendering, deep learning, virtual reality, gaze-contingent rendering, video compression, video generation ACM Reference Format: Anton S. Kaplanyan, Anton Sochenov, Thomas Leimkühler, Mikhail Okunev, Todd Goodall, and Gizem Rufo. 2019. Supplemental Material for DeepFovea: Neural Reconstruction for Foveated Rendering and Video Compression using Learned Statistics of Natural Videos. ACM Trans. Graph. 38, 4, Article 212 (July 2019), 5 pages. https://doi.org/10.1145/3355089.3356557 Fig. 1. User study setup. Leſt: display setup; right: HMD setup 1 COMPRESSION DENSITY FOR A DISPLAY From the CSF, a function of maximum perceptible frequency f m (e ) (cycles/degree) vs. eccentricity can be derived by equating to maxi- mum contrast and solving for frequency. This function, parameter- ized by fixation distance e , is defined as f m (e ) = e 2 ln(1/ CT 0 ) α (e + e 2 ) (1) ∗ Joint affiliation: Facebook Reality Labs, MPI Informatik. Authors’ address: Anton S. Kaplanyan, [email protected]; Anton Sochenov, anton. [email protected]; Thomas Leimkühler, [email protected]; Mikhail Okunev, [email protected]; Todd Goodall, [email protected]; Gizem Rufo, Facebook Reality Labs, [email protected]. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the owner/author(s). © 2019 Copyright held by the owner/author(s). 0730-0301/2019/7-ART212 https://doi.org/10.1145/3355089.3356557 where e 2 , the half-resolution eccentricity distance, is 2.3 ◦ , CT 0 , the minimum contrast threshold, is 1/64, and α , a sensitivity falloff parameter, is 0.106. The pixel distance of a point x from the point of fixation x f is d ( p) = || x f − x|| 2 . (2) The minimum angular displacement between adjacent pixels at point x informs critical display frequency and is provided by θ (x) = min cos −1 AB || A|| 2 || B|| 2 , cos −1 AC || A|| 2 || C|| 2 , where A(x) = ⟨(x 0 − x c )∗ q, (x 1 − y c )∗ q, D⟩ B(x) = ⟨(x 0 − x c + 1)∗ q, (x 1 − y c )∗ q, D⟩ C (x) = ⟨(x 0 − x c )∗ q, (x 1 − y c + 1)∗ q, D⟩, q is the pixel pitch estimated by dividing physical display width by horizontal resolution, D is the distance between observer and display, and x c and y c are the horizontal and vertical center pixel coordinates respectively. Finally, the minimum angular pixel size at particular eccentricity is f d (cycles/degree) is f d (x) = 1 2|θ (x)| . The ratio of f m to f d describes the amount of resolution that the eye can pick up vs what the display can deliver. The number of pixels that are needed according to the perceptual falloff follows the sampling rate R R(x) = min 1.0, p r f m ( m(x)) f d (x) , where m(x) is the angle between a point on the display ⟨x 0 , x 1 , D⟩ and the fixation point ⟨x f 0 , x f 1 , D⟩, and p r is the subsampling rate used for controlling sampling rate. Note that R is continuous and bounded on [0, 1]. Under this formulation, the number of samples V pix needed to fully cover the retina for a given screen of NxM resolution is provided by V pix = 1 MN x ∈X [1 − R(x)] , where X is the set of pixel locations, M is vertical resolution, and N is horizontal resolution. Note that p r is monotonic with sampling rate, allowing us to map desired sampling rate to p r , giving direct control over the average sampling rate computed over an entire frame. ACM Trans. Graph., Vol. 38, No. 4, Article 212. Publication date: July 2019.
Transcript of Supplemental Material for DeepFovea: Neural Reconstruction ... · dering, foveated rendering, deep...
Supplemental Material for DeepFovea: Neural Reconstruction forFoveated Rendering and Video Compression using Learned Statistics ofNatural Videos
ANTON S. KAPLANYAN, ANTON SOCHENOV, THOMAS LEIMKÜHLER∗, MIKHAIL OKUNEV, TODDGOODALL, and GIZEM RUFO, Facebook Reality Labs
CCS Concepts: • Computing methodologies → Neural networks; Per-ception; Virtual reality; Image compression.
Additional Key Words and Phrases: generative networks, perceptual ren-dering, foveated rendering, deep learning, virtual reality, gaze-contingentrendering, video compression, video generation
ACM Reference Format:Anton S. Kaplanyan, Anton Sochenov, Thomas Leimkühler, Mikhail Okunev,Todd Goodall, and Gizem Rufo. 2019. Supplemental Material for DeepFovea:Neural Reconstruction for Foveated Rendering and Video Compression usingLearned Statistics of Natural Videos. ACM Trans. Graph. 38, 4, Article 212(July 2019), 5 pages. https://doi.org/10.1145/3355089.3356557
Fig. 1. User study setup. Left: display setup; right: HMD setup
1 COMPRESSION DENSITY FOR A DISPLAYFrom the CSF, a function of maximum perceptible frequency fm (e)(cycles/degree) vs. eccentricity can be derived by equating to maxi-mum contrast and solving for frequency. This function, parameter-ized by fixation distance e , is defined as
fm (e) =e2 ln(1/CT0)α(e + e2)
(1)
∗Joint affiliation: Facebook Reality Labs, MPI Informatik.
Authors’ address: Anton S. Kaplanyan, [email protected]; Anton Sochenov, [email protected]; Thomas Leimkühler, [email protected]; MikhailOkunev, [email protected]; Todd Goodall, [email protected]; Gizem Rufo,Facebook Reality Labs, [email protected].
Permission to make digital or hard copies of part or all of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for third-party components of this work must be honored.For all other uses, contact the owner/author(s).© 2019 Copyright held by the owner/author(s).0730-0301/2019/7-ART212https://doi.org/10.1145/3355089.3356557
where e2, the half-resolution eccentricity distance, is 2.3◦, CT0, theminimum contrast threshold, is 1/64, and α , a sensitivity falloffparameter, is 0.106.
The pixel distance of a point x from the point of fixation xf is
d(p) = | |xf − x| |2. (2)
The minimum angular displacement between adjacent pixels atpoint x informs critical display frequency and is provided by
θ (x) = min[cos−1
AB| |A| |2 | |B| |2
, cos−1AC
| |A| |2 | |C| |2
],
where
A(x) = ⟨(x0 − xc ) ∗ q, (x1 − yc ) ∗ q,D⟩
B(x) = ⟨(x0 − xc + 1) ∗ q, (x1 − yc ) ∗ q,D⟩
C(x) = ⟨(x0 − xc ) ∗ q, (x1 − yc + 1) ∗ q,D⟩,
q is the pixel pitch estimated by dividing physical display widthby horizontal resolution, D is the distance between observer anddisplay, and xc and yc are the horizontal and vertical center pixelcoordinates respectively. Finally, the minimum angular pixel size atparticular eccentricity is fd (cycles/degree) is
fd (x) =1
2|θ (x)|.
The ratio of fm to fd describes the amount of resolution that theeye can pick up vs what the display can deliver. The number ofpixels that are needed according to the perceptual falloff followsthe sampling rate R
R(x) = min[1.0,
pr fm (m(x))fd (x)
],
wherem(x) is the angle between a point on the display ⟨x0, x1,D⟩
and the fixation point ⟨x f0 , xf1 ,D⟩, and pr is the subsampling rate
used for controlling sampling rate. Note that R is continuous andbounded on [0, 1]. Under this formulation, the number of samplesVpix needed to fully cover the retina for a given screen of NxMresolution is provided by
Vpix =1
MN
∑x∈X
[1 − R(x)] ,
where X is the set of pixel locations,M is vertical resolution, and Nis horizontal resolution. Note that pr is monotonic with samplingrate, allowing us to map desired sampling rate to pr , giving directcontrol over the average sampling rate computed over an entireframe.
ACM Trans. Graph., Vol. 38, No. 4, Article 212. Publication date: July 2019.
212:2 • Kaplanyan, A. S. et al.
(a) Source Video (b) Region one
(c) Region two (d) Region three
Fig. 2. Regions of interest for both multiscale and H.265 methods.
2 CONCENTRIC H.265 PERCEPTUAL BIT-BUDGETALLOCATION
The number of bits per second is capped at
B ≤ crHWbpp fr ,
where H andW are the vertical and horizontal resolution respec-tively, bpp , bits per pixel, is set to 12 throughout, cr is the compres-sion rate, and fr is frame rate. We have three concentric regionsthat must be allocated from this shared B/1024 kbits, according toB = w1B1 +w2B2 +w3B3, where w1, w2 and w3 are proportionalweights according to region size one, two, and three respectively.For each video and compression rate used in H.265, we use the sameregion radii, defined as the same multiresolution radii. A visualdemonstration of these radii is provided in Fig. 2.Given fixed radii and fixed bitrate, we must finally decide on
the bit allocation for each spatial region. To remain comparable toDeepFovea, we use the ganglion cell density function to developthe relative weights corresponding to region size and retinotopiclocations. In other words, we use the normalized midget ganglioncell density map to produce a perceptual importance weighting,which is a simple strategy for bit allocation by keeping the allocationdecision in terms of receptor density. This density of cells in theretina correlates highly with the size of brain regions dedicatedto each eccentric region [Duncan and Boynton 2003]. The samestrategy is repeated when creating the compressed videos for theHMD experiment.
3 DEEPFOVEA RECONSTRUCTION VS INPAINTINGRecent work demonstrates that sparsely sampled scenes can bereconstructed using radial basis functions (RBF) interpolation toachieve a foveated image. In Figure 3, we compare Delaunay-basedinterpolation, RBF interpolation, and DeepFovea as suggested in[Sun et al. 2017] using identical sampling conditions. For RBF andDelaunay, sampled video frames were reconstructed on a per-framebasis.We found that RBF and Delaunay-based interpolationmethodsintroduce high levels of flicker and spatial noise throughout the
(a) DeepFovea (b) Delaunay (c) RBF
Fig. 3. Comparison among DeepFovea reconstruction, Delaunay, and RBFinpainting from identical sparse samples, using unseen content.
250000 500000 750000 1000000 1250000 1500000 1750000 2000000Minibatches
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Fig. 4. FWQI graph for networks with different depth of the U-net (numberof encoder blocks).
whole video, including the foveal regions. Higher-quality spatio-temporal reconstruction can be achieved from both in-hallucinationand temporal accumulation using DeepFovea.
4 ABLATION STUDY ADDITIONAL PLOTSFigure 4 provides an analysis of DeepFovea performance for dif-ferent numbers of encoding blocks. We use the FWQI foveatedframe-quality metric to measure performance, and we find that thereconstruction quality greatly improves when the number of encod-ing layers is increased from 1 to 3, but not much when increasedfrom 3 to 5.
5 CORRELATION WITH FWQI AND FA-SSIMWe computed mean gaze from the recorded gaze locations in bothscreen and hmd subjective studies for each content, method, andsampling rate. First, we treated each gaze location from each subject
ACM Trans. Graph., Vol. 38, No. 4, Article 212. Publication date: July 2019.
Supplemental Material for DeepFovea: Neural Reconstruction for Foveated Rendering and Video Compression using Learned Statistics of Natural Videos • 212:3
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Fig. 5. Scatterplot between FWQI and ground truth DMOS for DeepFovea,Multiresolution, and H.265 methods. Different colors indicate differentcontent.
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Fig. 6. Scatterplot between FA-SSIM and ground truthDMOS for DeepFovea,Multiresolution, and H.265 methods. Different colors indicate differentcontent.
as a unit impulse located at pixel locations in a frame. Second, weconvolved these impulses with a Gaussian window with standarddeviation 100, corresponding to 3.34◦ [Rai et al. 2017]. Finally, wepicked the maximum point, which isolates the “most seen” pointamongst observers.Feeding these mean gaze points into FWQI [Wang et al. 2001]
and FA-SSIM [Rimac-Drlje et al. 2011] allowed us to compute eachmetric based on the gaze of an average observer on each frame ofeach video. Figure 5 compares FWQI with mean gaze to the groundtruth DMOS for both DeepFovea and Multiresolution. We find asignificant correlation between the metric and our subjective scores.For FA-SSIM, we observe a poor correlation with our computed
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Fig. 7. A summary of detectability results from HMD experiment. Greenshows mean detectability for five compression rates measured for Deep-Fovea. Red shows Multiresolution. Dashed brown line shows H.265 and thedashed black line represents reference videos. The x-axis represents com-pression rate. Error bars represent bootstrapped 95% confidence intervals.
DMOS, as depicted in Fig. 6. We also observe that the scores andFWQI both independently demonstrate a systematic difference be-tween DeepFovea and Multiresolution. Since FWQI does not modeltemporal information or masking, it mispredicts on content withhigh motion and details, such as “DucksTakingOff.”
6 HMD DETECTABILITY EXPERIMENT RESULTSSUMMARY
From Fig. 7, we find that DeepFovea is much less detectable thanMultiresolution. Also, for lower compression rates, we find thatDeepFovea is statistically indistiguishable from H.265 and referenceup until 25x compression, which corresponds to a sampling rate of4%.
7 CORRELATION WITH FWQI AND FA-SSIM PER VIDEOFigures 8 and 9 depict a per-content breakdown of DMOS resultswith 95% confidence intervals for the screen and hmd studies re-spectively. Across the contents and display types, we noticed that“cosmoslaundromat” and “duckstakingoff” had the highest degreeof overlap in confidence intervals amongst the methods. In the caseof “cosmoslaundromat,” most of the content away from the cen-ter of the image is part of the out-of-focus background, which caneasily be captured by each approach. For “duckstakingoff,” most ofthe content contains rippling water waves, which tends to maskspatial-temporal artifacts.
8 SCREEN EXPERIMENT: DETECTABILITY RESULTSFOR EACH VIDEO
Figure 10 analyzes detectability performance of DeepFovea com-pared to H.265 andMultiresolution for each video in the screen study.We find that the contents “NetflixToddler” and “DucksTakingOff”
ACM Trans. Graph., Vol. 38, No. 4, Article 212. Publication date: July 2019.
212:4 • Kaplanyan, A. S. et al.
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Fig. 8. Scatterplots between FWQI and ground truth DMOS for DeepFovea, Multiresolution, and H.265 methods. Different colors indicate different content.Error bars indicate 95% confidence intervals.
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Fig. 9. Scatterplots between FWQI and ground truth DMOS for DeepFovea, Multiresolution, and H.265 methods. Different colors indicate different methods.Error bars indicate 95% confidence intervals.
are tend to mask artifacts, sometimes causing methods to becomevisually indistinguishable. Contents with high camera and object mo-tion such as “OldTownCross” and “CrowdRunning” are particularlydifficult for both Multiresolution and DeepFovea, with relativelyhigher visibility of artifacts when compared to other content.
9 HMD EXPERIMENT: DETECTABILITY RESULTS FOREACH VIDEO
Figure 11 analyzes detectability performance of DeepFovea com-pared to H.265 and Multiresolution for each video in the HMD study.We find that multiple contents are indistinguishable for subjectswhen comparing DeepFovea with H.265. When looking specificallyat “Assemble2” and “Trolley” we noticed that artifact detectability is
higher than for other contents. These contents, like before, demon-strate a large degree of motion, which is not represented naturallyin the viewed reconstructions.
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movements for 360 degree images. In Proceedings of the 8th ACM on MultimediaSystems Conference. ACM, 205–210.
S. Rimac-Drlje, G. Martinović, and B. Zovko-Cihlar. 2011. Foveation-based contentAdaptive Structural Similarity index. International Conference on Systems, Signalsand Image Processing (2011), 1–4.
Qi Sun, Fu-Chung Huang, Joohwan Kim, Li-Yi Wei, David Luebke, and Arie Kaufman.2017. Perceptually-guided Foveation for Light Field Displays. ACM Trans. Graph.(Proc. SIGGRAPH) 36, 6, Article 192 (2017), 192:1–192:13 pages.
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Fig. 11. Per-video results for HMD study. Error bars indicate 95% confidence intervals.
Zhou Wang, Alan Conrad Bovik, Ligang Lu, and Jack L Kouloheris. 2001. Foveatedwavelet image quality index. Proc. SPIE 4472 (2001), 42–53.
ACM Trans. Graph., Vol. 38, No. 4, Article 212. Publication date: July 2019.
