Variantes figuradas recogidas en el diccionario

Module 2 extracts theintensitychannel fromIPTout (see Figure 7.3). Theintensity infor- mation when linearly scaled and discretised for 10-bit encoding exhibits visible contouring artefacts due to rounding errors. Thus, to minimise the quantisation errors, the scaledI′

channel was perceptually encoded by any of the previously mentioned PTFs such that the resultant JND quantised luma satisfies the properties mentioned in Section 7.1.2. Since I_∈(0,1], it can be scaled to any range, suitable for a chosen PTF. The linear scaling op-

eration is performed by a multiplying factor ψfollowed by the application of the PTF as shown in equation 7.6.

For instance, ifI_∈(0,1], f(_·)is the chosen PTF (say GDF) andLis the 10-bit JND quantised luma then the scaling and JND mapping operation is given as in equation 7.6.

I′_{=I·ψsuch thatI}′_{∈[0.05,4000]}

∴L=f(I′)such thatL∈[0,1023]

(7.6)

To determine theintensityencoding efficiency of each PTF and to evaluate the reconstruc- tion quality of the algorithm (as a whole) upon the application of the PTF, the scaled I′

channel is encoded using each of the four existing PTFs (one at a time). The rest of the data flow remains unchanged (see Figure 7.3). Subsequently, the algorithm is used to determine the reconstruction quality of the 39 HDR sequences using the evaluation methodology de- scribed later in Section 7.3.2. The RD characteristics across a set of different quality levels determines the overall HDR reconstruction quality of the algorithm when using each of the four PTFs. This indirectly indicates theintensitychannel encoding efficiency of each PTF.

The RD characteristics discussed later in Section 5.5 show that amongst the exist- ing PTFs, the algorithm exhibits the best reconstruction quality using either GCRM or the modified Ferwarda’st.v.i. However, both PTFs have certain issues as previously discussed in Section 7.1.2. Further details about the shape and characteristics of the PTFs have been discussed previously in Section 3.2.1. To mitigate those issues, this Chapter proposes a novel PTF which incorporates the advantages of both along with the added advantage of a straightforward analytical solution.

Design of the proposed PTF

Following recommendation REC 1886 [Ser11], the proposed PTF has been designed as a three-part analytical solution such that f(_·):I′_{−→L. The conditional equation 7.7 bears}

includes a logarithmic segment to encode highintensityvalues. L=          a_·I′ _ifI′_<I′ s; b_·I′(1_c)_{+d ifI}′_∈[I′ s,Ip′); e_·log10(I′) +fc ifI′∈[Ip′,Ih′]; (7.7)

Similarly, f−1_{(·)can be formulated as in equation 7.8.}

I′₌          L a ifL<Ls; (L−d b )c ifL∈[Ls,Lp); 10(L−fc e ) ifL∈[Lp,Lh]; (7.8)

The boundary value conditionsI′ _{was assumed to be similar to [MND13]. There-}

fore, I _∈(0,1] is scaled by ψ such that I′ _{∈ [10}−5_,104_{]. Also, the JND quantised} L_∈[0,1023]. The goal of the proposed PTF was to facilitate a conservative quantisation

throughout the range ofI′ _{for low-, mid- and high-intensity regions. Since the shape of}

GCRM shows biasedness towards preservation of high-intensity regions, it was taken out of consideration. Now, amongst the existing PTFs, the shape of Ferwarda’st.v.i is a very close fit to the analytical model proposed in Daly’s VDP [Dal92] for the power segment and also a close fit to Barten’s CSF based PTF for the logarithmic segment. Therefore, the proposed analytical model was initially fitted to Ferwarda’st.v.iusing non-linear regression techniques for initial calculation of the interval boundariesI′

sandI′p.Ih′ was always fixed to 104_{as the upper bound of theintensity, considered in this work. Such an excercise produces}

the intial interval boundaries as well as the co-factors in equation 7.7. Using the co-factors and interval boundaries,LsandLpwere computed. Similar toI′

h,Lhwas again fixed to 1023 as the upper bound for 10-bit encoding.

Since the analytical model is a piecewise-nonlinear model, it is important to enforce C0_{continuity at the intervals boundsI}′

sandI′p. Also, it is important to test the function for large jumps and discontinuities using a Contrast vs. Intensity (c.v.i) plot and correspond- ing adjust the parameters to not only enforceC0 _{continuity but also eliminate jumps and}

discontinuities. This ensures the elimination of undesirable visible contouring artefacts. Therefore, following the completion of equation 7.7, the analytical model was re-verified using ac.v.iplot and discontinuities and large contrast jumps were found especially at the

low-intensity regions. Correspondingly after iterative trials, the co-factors in equation 7.7

were adjusted to elimnate the contrast jumps and discontinuities. Using ac.v.i plot also provides an advantage in measuring the effectiveness of the bit-depth allocation inL. Re- plotting thec.v.iwith the proposed PTF’s modified co-factors showed that the bit-depth al- location was not optimal. Therefore, a second round of optimisation was performed on both the boundary values and co-factors to ensure optimal bit-depth allocation with re-modified

co-factors to eliminate contrast jumps and discontinuities. Furthermore, theC0_continuity

was re-enforced thus arriving to the final configuration of the proposed PTF in equation 7.7. Correspondingly the co-factors of equation 7.8 was computed. The interval boundaries and co-factors are given in Table 7.1.

a=2285.712 b=224.1745 c=5

d=₋67.1009 e=263.5 fc=₋31

I′

s=0.007 I′p=100 Ih′ =104

Ls=16 Lp=496 Lh=1023

Table 7.1:Co-factors used for the proposed PTF.

This PTF when plotted with the final configuration, shows interval boundariesI′

s,I′p and I′

h in equation 7.7 represent the brightness (in this case the scaled intensity chan- nel) values where the HVS exhibits linear, power and logarithmic response, respectively [SYD87]. Correspondingly, the c.v.i plot ensured that the JND space Lwas divided into three blocks with optimal bit-depth allocation within intervals whereL_∈(0,Ls),L∈[Ls,Lp) andL_∈[Lp,Lh]such that each block can facilitate a conservative quantisation of low-, mid- and high-intensityregions. Also, when the modified PTF was plotted with a semilog plot (I′

vs. L) and compared with the existing PTFs, the shape of the curve showed the following characteristics:

• In the low-intensityregions, the curve exhibits an optimal quantisation where it per- forms more conservative quantisation than exhibited by the modified Ferwarda’st.v.i while not as conservative as a logarithmic PTF.

• In the mid-intensityregions, the curve exhibits a similar quantisation to the modified Ferwarda’st.v.i.

• In the high-intensityregions, the curve exhibits a conservative quantisation similar to Barten’s CSF based PTF.

Furthermore, the bit-depth allocation effectiveness was tested against existing EOTFs and found to be a close fit with the EOTF used in the PQ algorithm [MND13].

The c.v.i plot is given Figure 7.4. For a further confirmation, the proposed PTF and its

inverse were rigorously tested by using them in the algorithm and evaluating the same us- ing the same methodology described in Section 7.3. Results obtained from the evaluation showed that the performance of the proposed algorithm using the proposed PTF is better than the existing PTF used for theintensity channel encoding. The evaluation results are given later in Figure 7.7.