TMO optimization for HDR compression |
contact: D. Gommelet, A. Roumy, C. Guillemot, M. Ropert, J. Le Tanou
This webpage brings additional results to the paper "Rate-Distortion Optimization of a Tone Mapping with SDR Quality Constraint for Backward-Compatible High Dynamic Range Compression" [1] submitted to icip 2016. The following figure recalls the scheme used to encode the HDR content:
To remind how the test is done, first the original HDR image is transformed such that the quantization becomes uniform
with respect to the human eye contrast sensitivity. More precisely, the HDR signal is perceptually transformed with SMPTE-2084
and uniformly quantized to 12 bits. This builds the input HDR signal X. For this image, the pixel distribution is computed and
one TMO is computed per SDR rate value according to the optimization problem (21) in the paper [1]. Then, this image X is
tone-mapped to produce the 8 bit base layer Y. The SDR image is encoded with the HEVC reference software HM 16.2 (18 ≤ QP ≤ 34)
and inverse tone-mapped to obtain an HDR image X_{E}.
The SDR reference signal is generated using the PTR operator proposed in [2], known to give good visual quality. Several images of different sizes and dynamic
ranges have been tested with different constraint value D0. The results are shown for the input images AtriumNight, Nancy,
FireEater and Tibul. These images are tone-mapped with the PTR [2] and shown on the following figure:
For all these images, we test with the D0 constraint adjusted to 34.2dB (MSE=25). The second minimization aims to find the best rate allocation for the base and enhancement layers. The quality of the inverse tone mapped HDR image is improved by adding the enhancement layer Z, that is the residue represented on 12 bits. This residue is also encoded with the HM 16.2. Multiple encodings have been performed, with different combinations of base and enhancement QPs to test different rate allocations. For each value of the sum rate (RSDR + RHDR), the pair (QPSDR, QPHDR) leading to the best PSNR is retained, thus yielding the best R-D curve for each TMO. In the following section, we show results for the all of them.
In all the following figures, (a) plots the PSNR of the inverse tone mapped HDR image versus the SDR image bitrate, (b) plots the corresponding SDR PSNR with respect to the reference, and (c) plots the PSNR of the enhancement layer versus the total bitrate (SDR + HDR).
The proposed TMO gives the best R-D performance and the smallest distortion with respect to the SDR reference,
especially at low bitrates. [17] and [18] solve a similar optimization problem, with however a simplified model
of the variance of the residue, which leads to suboptimality and worst results in (a).
Concerning (c), the gap between R-D curves is reduced, compared to (a), where only the base layer is encoded.
The enhancement layer helps the least efficient TMO to improve the HDR reconstruction, since we choose the best repartition for each TMO.
However, the proposed TMO still keeps the best R-D performance although it respects a stricter constraint on the
SDR perceptual quality, especially at low bitrates. The gain is around 0.1dB, for rates in the range (0.5, 1) bpp, compared to [17] or [18].
The following table shows all the SDR images obtained with each TMO at different QP. These images are comparable
with the SDR image obtained with the Reinhard TMO
The conclusions remains the same: the proposed TMO gives the best R-D performance and the smallest distortion with
respect to the SDR reference.
Concerning (c), the gap between R-D curves is further reduced. In this case, [14] performs a bit better however this TMO is not constrained to a SDR reference.
The proposed TMO still keeps good R-D performance although it respects a stricter constraint on the SDR perceptual quality.
The following table shows all the SDR images obtained with each TMO at different QP. These images are comparable
with the SDR image obtained with the Reinhard TMO
Interestingly, in this case, we observe that our optimization is easier to tune in order to meet the constraint on the SDR signal.
Since [18] change the constrained optimization into an unconstrained optimization, where the tuning has to be done through the
lagrangian multiplier, the distortion with the reference will depend on the image distribution.
The proposed TMO does not give the best R-D performance but respect a much stricter constraint with respect to the SDR reference.
For these reason we did not perform the second optimization on this case.
The following table shows all the SDR images obtained with each TMO at different QP. These images are comparable
with the SDR image obtained with the Reinhard TMO
Here, we adjusted our constraint to 26dB to match the constraint from [18].
In this case, we observe that the proposed TMO still gives the best tradeoff between R-D performance and distortion with
respect to the SDR reference.
Concerning (c), the gap between R-D curves is still very reduced. In this case too, [14] performs a bit better however this TMO is not constrained to a SDR reference.
The proposed TMO still keeps good R-D performance although it respects a stricter constraint on the SDR perceptual quality.
The following table shows all the SDR images obtained with [17] and the proposed TMO (The only ones who change with the new constraint) at different QP. These images are comparable
with the SDR image obtained with the Reinhard TMO
As for the FireEater image, we see that our optimization is easier to tune in order to meet the constraint on the SDR signal.
The proposed TMO does not give the best R-D performance but respect a much stricter constraint with respect to the SDR reference.
For these reason we did not perform the second optimization on this case.
The following table shows all the SDR images obtained with each TMO at different QP. These images are comparable
with the SDR image obtained with the Reinhard TMO
Here, we adjusted our constraint to 29.5dB to match the constraint from [18].
In this case, we observe that the proposed TMO still gives the best tradeoff between R-D performance and distortion withrespect to the SDR reference.
Concerning (c), the gap between R-D curves is still very reduced, however, the proposed TMO still respects a stricter constraint on the SDR perceptual quality, especially at low bitrates.
The following table shows all the SDR images obtained with [17] and the proposed TMO (The only ones who change with the new constraint) at different QP. These images are comparable
with the SDR image obtained with the Reinhard TMO