ObjectiveEvaluation

In the previous section, the subjective evaluation was performed with respect to the simulated print image displayed on the high resolution LCD. The simulated image o(x, y;λ) can also be applied to the objective evaluation. In this section, a new physical criterion is proposed to objectively evaluate the image quality of halftone print.

5.4.1 Conventional criteria

Inoue has proposed a physical criterion named as IQF_paper [Inoue 1998] to evaluate the image quality of halftone print, defined by

IQF_paper =

where CSF_v(u) is the contrast sensitivity function of human eye. SinceIQF_paper has MTF_p(u) in its formula,IQF_paper mainly evaluates the sharpness of halftone print.

However, as mentioned in the previous section, the granularity would also affect the image quality of halftone print significantly in the case of AM screening especially.

The criterion IQF_paper does not consider the granularity.

Miyake et al. have proposed a physical criterion named as the Digital image Quality Factor (DQF) [Miyake et al. 1986] with respect to not the halftone print but the digital image, defined by

DQF = (DQF₁)²·log₂DQF₂, (5.12)

where MTF_s(u) is the MTF of imaging system,D_L is the density range which can be represented by the imaging system, Qis the number of quantization levels, and σ is the RMS granularity of the system. In Eq. 5.14, is σ is zero then DQF₂ will be equal to Q. As σ becomes larger, the effective number of quantization levels in the digital image will decrease. Therefore, this function is similar to the definition of information capacity for photographic film by Altman ans Zweig [Altman and Zweig 1963]. Since DQF has MTF_s(u) andσ in its formula, DQF evaluates both the sharpness and the granularity of digital image.

Let us consider how DQF is applied to the halftone print image. With respect to the sharpness, (DQF₁)² can be alternated to IQF_paper. With respect to the

granularity, however, it is difficult to define σ of halftone print image since the granularity caused by the halftone micro-structure is significantly dependent on the tone level. In other words, the granularity significantly changes with the spatial position of halftone print image.

5.4.2 Proposed full reference RMS granularity

In order to define the RMS granularity of halftone print image changing with the spatial position, a full reference RMS granularity is proposed. The full reference RMS granularity is given by

σ_dv = 1 where l_x andl_y are the horizontal and vertical lengths of image, respectively, and CSF_v(u, v) is the two dimensional CSF of human eye calculated from the CSF_v(u) assuming the spatial isotropy. Equations (5.16) and (5.17) indicate the translation to the density space. The functionY(x, y) is the CIEY image corresponding toY_v(x, y) in Eq. (5.6) calculated fromo(x, y;λ). The functionY^ref(x, y) is the reference image ofY(x, y), whereY^ref(x, y) is not affected by the granularity caused by the halftone micro-structure. In the print simulation in this chapter, one pixel of input digital image where the range of value is [0 - 255] is converted to one dot on–off image having 16×16 pixels. Hence,Y^ref(x, y) was obtained as follows in this research.

1. Letl_x=l_x/16 andl_y =l_y/16.

2. The imageY(x, y) is down-sampled tol_x×l_y by the area average.

3. The down-sampled image is up-sampled to l_x ×l_y by the nearest-neighbor interpolation. The up-sampled image isY^ref(x, y).

Since the proposed RMS granularityσ_dv considers the change of granularity with the spatial position, it would be suitable to evaluate the granularity of halftone print image.

5.4.3 CSF of human eye

As the CSF of human eye, a model proposed by Mannoset al.[Mannos and Sakrison 1974] was introduced because of its simplicity, which is given by

CSF_v(f) =

1 when f = 0 2.6 (0.0192 + 0.114f) exp

−(0.114f)^1.1

otherwise , (5.18)

wheref denotes the spatial frequency expressed in cycles/degree. One has to trans-late cycles/degree to cycles/mm.

u[cycles/mm] =f[cycles/degree]·180

πd, (5.19)

wheredis the viewing distance which was set to 300 mm in the subjective evaluation.

The function CSF(u) expressed in cycles/mm is applied to Eqs. (5.16) and (5.17) by extending to two dimensional CSF(u, v) assuming spatial isotropy.

5.4.4 Proposed criterion

By applying the proposed full reference RMS granularity σ_dv to the conventional criterion DQF defined in Eqs. (5.12), (5.13) and (5.14), a new physical criterion DQF_{half tone} is proposed to evaluate not only the sharpness but also the granularity of halftone print image. The proposed criterion DQF_{half tone} is given by

DQF_{half tone} =IQF_paper·log₂DQF_dv, (5.20)

DQF_dv = D_L

(D_L/Q) + 2σ_dv. (5.21)

5.4.5 Validity of proposed criterion

In order to compare the validity of conventional and proposed criteriaIQF_paper and DQF_{half tone}, the correlation was analyzed between these criteria and the average observer rating value (ORV) obtained in the previous section.

Figure 5.11 shows the correlation betweenIQF_paper and the ORV. In the case of FM screening, IQF_paper was well correlated to the ORV since the correlation coef-ficients were 0.97 (Face) and 0.94 (Flower). In the case of AM screening,IQF_paper was also well correlated to the ORV since the correlation coefficients were 0.79 (Face) and 0.91 (Flower), however, the correlation coefficients were lower than the case of FM screening. It is considered thatIQF_paper does not consider the granularity and AM screening causes the high granularity.

Figure 5.12 shows the correlation betweenDQF_{half tone} and the ORV. The cor-relation coefficients in AM screening were 0.87 (Face) and 0.98 (Flower). These are significantly higher compared to IQF_paper. It is considered that DQF_{half tone} accu-rately evaluates the granularity. On the other hand, The correlation coefficients in FM screening were 0.95 (Face) and 0.90 (Flower). These are a little lower compared to IQF_paper. The granularity in FM screening is distributed at the high spatial frequency, however, the decimation filtering in Sub-section 5.3.1 erases the high spa-tial frequency components in order to display the simulated halftone print image on the LCD. From this reason, it is considered that observers underestimated the granularity of FM screening in the subjective evaluation.

0 0.5 1

Figure 5.11: Correlation betweenIQF_paper and ORV (CC: correlation coefficient).

0.5 1 1.5 2

Figure 5.12: Correlation betweenDQF_{half tone} and ORV.

5.5 Relationship between Amount of Ink and Optical