Article
A Flexible Coding Scheme Based on Block Krylov Subspace
Approximation for Light Field Displays with Stacked
Multiplicative Layers
Joshitha Ravishankar
†
, Mansi Sharma *
,†
and Pradeep Gopalakrishnan
Citation: Ravishankar, J.; Sharma,
M.; Gopalakrishnan, P. A Flexible
Coding Scheme Based on Block
Krylov Subspace Approximation for
Light Field Displays with Stacked
Multiplicative Layers. Sensors 2021,
21, 4574. https://doi.org/10.3390/
s21134574
Academic Editors: Nikolaos Thomos,
Eirina Bourtsoulatze and Xianbin
Wang
Received: 22 March 2021
Accepted: 18 June 2021
Published: 4 July 2021
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Attribution (CC BY) license (https://
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4.0/).
Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai 600036, India;
ee19d401@smail.iitm.ac.in (J.R.); pradeepgopalakrishnan32@gmail.com (P.G.)
* Correspondence: mansisharma@ee.iitm.ac.in or mansisharmaiitd@gmail.com
† These authors contributed equally to this work.
Abstract:
To create a realistic 3D perception on glasses-free displays, it is critical to support continuous
motion parallax, greater depths of field, and wider fields of view. A new type of Layered or Tensor
light field 3D display has attracted greater attention these days. Using only a few light-attenuating
pixelized layers (e.g., LCD panels), it supports many views from different viewing directions that
can be displayed simultaneously with a high resolution. This paper presents a novel flexible scheme
for efficient layer-based representation and lossy compression of light fields on layered displays.
The proposed scheme learns stacked multiplicative layers optimized using a convolutional neural
network (CNN). The intrinsic redundancy in light field data is efficiently removed by analyzing
the hidden low-rank structure of multiplicative layers on a Krylov subspace. Factorization derived
from Block Krylov singular value decomposition (BK-SVD) exploits the spatial correlation in layer
patterns for multiplicative layers with varying low ranks. Further, encoding with HEVC eliminates
inter-frame and intra-frame redundancies in the low-rank approximated representation of layers
and improves the compression efficiency. The scheme is flexible to realize multiple bitrates at the
decoder by adjusting the ranks of BK-SVD representation and HEVC quantization. Thus, it would
complement the generality and flexibility of a data-driven CNN-based method for coding with
multiple bitrates within a single training framework for practical display applications. Extensive
experiments demonstrate that the proposed coding scheme achieves substantial bitrate savings
compared with pseudo-sequence-based light field compression approaches and state-of-the-art JPEG
and HEVC coders.
Keywords:
light field; lossy compression; layered tensor 3D displays; convolutional neural network;
Krylov subspace; low-rank approximation; randomized block Krylov singular value decomposition;
rank analysis; rate distortion
1. Introduction
Realistic presentation of a three-dimensional world on displays has been a long-
standing challenge for researchers in the areas of plenoptics, light field, and full parallax
imaging [
1
–
3
]. Glasses-free or naked-eye autostereoscopic displays have replaced stereo-
scopic displays which offer motion parallax for different viewing directions [
4
]. However,
current naked-eye displays fall far short of truly recreating continuous motion parallax,
greater depth-of-field, and a wider field-of-view for visual reality [5–8].
Designs based on a single display panel attached with a parallax barrier or special
lens (lenticular screen or integral photography lens) usually suffer from inherent resolution
limitations. The resolution for each view decreases with an increase in multiple viewing
directions. Thus, supporting a full parallax visualization of the 3D scene is impractical [
4
].
On the other hand, both monitor-style and large-scale systems based on several projectors
introduce a wide viewing approach, but such light field displays do not maintain a thin
Sensors 2021, 21, 4574. https://doi.org/10.3390/s21134574 https://www.mdpi.com/journal/sensors
