32
Bull. Soc. Photogr. Imag. Japan. (2017) Vol. 27 No. 2: 32–39

Original Paper

Memory Texture as an Important Factor Affecting Improvement of Subjective
Image Sharpness by Using Noise Addition
Xiazi Wan, Hiroyuki Kobayashi, and Makoto Ichikawa

Abstract: ur earlier study demonstrated that the subjective sharpness of blurred images is improved by superimposing granular noise on it.
O
We proposed that we have memory of textures of certain familiar objects encountered in daily life, similar to memory color. As described herein, for five objects, we used sample images of six kinds: the original image, a white-noise-added original image, a 1/
f-noise-added original image, a blurred original image, a white-noise-added blurred image, and a 1/f-noise-added blurred image.
First, observers were asked to recall an object’s texture without seeing the real object and to sort the images in descending order,
starting with the one closest to the recalled texture. While viewing the actual object, observers were asked to rearrange the images indescending order, starting with the one closest to the actual texture. Finally, observers were asked to rearrange the images in descending order of subjective sharpness. Correlation analysis, partial analysis, and path analysis were conducted for this reported ordering.
Correlation was found between the memory texture and subjective sharpness. Results demonstrate that subjective sharpness improved when the texture of the objects in images came to approximate the remembered texture.

Key words:

Noise addition, Subjective sharpness, Memory texture

1. Introduction

2. Earlier studies“Memory texture” refers to the texture that one remembers for an
object surface. It is a concept similar to “memory color,” which is thecolor that one associates with and then remembers for specificthings, especially familiar objects in daily life. For instance, the red
associated with apple, and the yellow associated with banana1).
Memory colors are formed in everyday life when we experience familiar objects and situations, as are memory textures.
As part of an individual’s recollection for familiar objects2), memory colors have an important characteristic by which people living inthe same environment tend to have similar memory colors. An earlier study of memory color revealed that preservation of the actual
colors of sky, vegetation, and other natural objects have high preference, whereas reproducing memory colors of facial skin reveals more
preferred images than those with the actual color. Not only do memory colors vary greatly among regions or nations, they also vary
among genders, generations, and economic conditions3).
We propose memory texture as another recollection for familiar
objects. It is formed by the same mechanism as that of memory color4).
The memory texture concept was obtained after noticing that, preference was actually increased by adding image noise to some images.
Fig. as1 unnecessary and as best
Such noise has heretofore been regarded
eliminated to improve preferability of the images5). Specifically, thetexture of familiar objects is more preferred when textures are presented after adding noise to the images.

2.1 Earlier study of image subjective sharpness using single-frequency sinusoidal gratings
Kurihara et al. investigated noise effects on the sharpness perception of an image by superimposing white noise on one-dimensional(1D) and two-dimensional (2D) single-frequency sinusoidal gratings as stimuli6). Stimuli are presented in Figure 1.
Results of this experiment indicate that the noise addition improves the subjective sharpness more effectively when low-frequency
stimuli, rather than high-frequency stimuli, are observed. Noise addition is not particularly effective for images that include clear edges.
This effect is more pronounced with 2D patterns than with 1D patterns.

Received: 13th, October 2017; Accepted: 21st, October 2017

Graduate School of Advanced Integration Science, Chiba University
1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

Fig. 22.2 Previous study of subjective sharpness using natural color images
Wan et al. extended Kurihara’s study using natural color images(Fig. 2) rather than black and white, single-frequency patterns7). Because sinusoidal gratings can be regarded as blurred rectangular or

Fig. 1 Stimuli and noise used by Kurihara et al.

Xiazi Wan, Hiroyuki Kobayashi, and Makoto Ichikawa

Memory Texture as an Important Factor Affecting Improvement of Subjective Image Sharpness by Using Noise Addition33

4.1 Original images of objects
Figure 3 depicts original images we used in this experiment. The
objects have various distinctive textures and different spatial frequency characteristics. We used deep-fried rice crackers, round ricecrackers, and buckwheat biscuits, as in our previous study7) of subjective sharpness. Additionally, we used sweet potatoes and tissue formore texture variety. They are similar to the samples used in an earlier study8) of the memory texture. As the same with our previous
study7), the evaluation experiment was conducted using hard copies.
We cut 2048 * 2048 pixels out from the original digital photos tomake the hard copies have a resolution of 500 dpi when printed out
in 10.4 * 10.4 cm, and all images were adjusted to the actual size ofthe objects. The images were printed on gloss photographic papers(EPSON KA4100PSKR, Seiko Epson Corp., Nagano, Japan), using
an ink-jet printer (EPSON MAXART PX5500, Seiko Epson
Corp., Nagano, Japan).
Figure 4 presents the power spectra of the original images. The
power spectra of (c) deep-fried rice cracker, (d) round rice cracker,
and (e) buckwheat biscuit were slightly different from those in ourprevious study7). (c) was another kind of deep-fried rice cracker alittle differed from that used in our previous study7). (d) and (e) were
the same kinds with those used in our previous study7) but different
individuals.
The order from high mean value to low mean value of power was
the following: sweet potato, buckwheat biscuit, deep-fried ricecracker, round rice cracker, and tissue. The objects are divisible into
two groups. The first group includes the buckwheat biscuit anddeep-fried rice cracker. Their textures are readily apparent: The buckwheat biscuit has a characteristically porous surface. In addition, theFig. 2 Objects and noise used by Wan et al.

checkerboard patterns, we used not only clearly focused original images, but also their blurred images as stimuli. Then we added white
noise to these images.
The results demonstrate clearly that the noise effects are considerable for images that include clear low-frequency components, and inblurred rather than sharp images. The dependence of subjective
sharpness on frequency, as found in this study, is consistent with results obtained from the study conducted by Kurihara et al.
2.3 Previous studies of improvement in preference by noise addition
Kashibuchi et al. suggested improvements in preference achieved
through noise addition5). Zhao et al. proposed memory textures as afactor affecting the improvement of texture preference8). Potatoes,
cardboard, tissue, newspaper, onions, wooden chopsticks, and wooden boards were used for the study.
The results are the following: (1) No consistency was found between memory texture and actual texture in evaluations conductedwith various scales. (2) Correlation was found between the memory
texture and preferred texture of the objects in images.

3. Objective
By examining the observers’ individual data in the experiment on
subjective sharpness, we found conspicuous individual differences inthe subjective sharpness improvement by noise addition to the images. A few observers for whom the effect was strong had some experience with enlarging a negative to produce black and white prints,
where the result of focus adjustment can be determined by the appearance of silver grains. Based on this result, we propose that a relation exists between the effect of noise addition and a person’s
memory: we hypothesized that adding noise to a blurred imageFig. 4
causes observers to recall the object texture from memory, and that
this recall exaggerates the subjective sharpness of the image. Improvement of the subjective sharpness if the texture occurs as thenoise addition comes to approximate the memory texture. This study
examined the relation between the subjective sharpness and memory
texture that have not been investigated.
Fig. 3 (a)Fig. 3 (b)（a）
Sweet potato

Fig. 3 (d)Fig. 3 (c)（b）
TissueFig. 3 (e)（c）
Deep-friedrice cracker（d）Round ricecracker（e）
BuckwheatbiscuitFig. 3 Objects used for this study.

4. Experiment
We took photos using a NIKON D800 (Nikon Corp., Tokyo, Japan) with 7360 * 4912 pixels JPEG file, fine-image quality, F22, andISO-200. The settings related to sharpness are standard and the Vibration Reduction (VR) of the lens is turned on. The image processing software used in this study were the same as the ones used in ourprevious study7).

Fig. 4 Power spectra of the original images for respective objects.
Table 1 Mean of power of the original images for each object

Mean of
power

Sweet
potato2.0

Buckwheat Deep-fried Round ricebiscuitrice cracker
cracker
1.9

1.8

1.3

Tissue1.1

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Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)

deep-fried rice cracker texture is that of a surface covered withcracks in a linear shape.
The second group includes sweet potato, round rice cracker, andtissue. Their textures appear to be smooth. Although the power spectra demonstrate that sweet potato images contain more high powerin wide frequency range, the sweet potato appears to be smooth at a
glance. Details of the texture would be difficult for human observers
to notice because of its deep color and low brightness.

within which only the object was chosen using the Magic WandTool in Photoshop, and combined it with the background of theoriginal sample image. This clipping and combining were done toprevent changes in the object edge and the background from affecting evaluation of the texture and subjective sharpness.
Six images were evaluated for each of the five objects, including
images without noise. Consequently, 30 images were evaluated. Figure 7 presents power spectra of the original image and the blurred
original image of each object.

4.2 Image noise
According to earlier studies of memory texture, there is a suitablenoise for the texture of some objects, and that could be white noiseor 1/f noise. So we used white noise and 1/f noise as image noise inthis experiment. Figure 5 shows the power spectra of white noiseand 1/f noise. White noise is characterized by constant power in thespatial frequency region. 1/f noise is characterized by descent powerin the spatial frequency region (as shown in (i)). When taking thelogarithm of both power and spatial frequency, the slope becomes -1(as shown in (ii)).

Fig. 5

Fig. 5

4.4 Evaluation environment
The evaluation environment was the same as that used in our previous subjective sharpness experiment7). Evaluation was conducted
at 700 lx under a natural color evaluation fluorescent lamp with acolor temperature of 5000 K (Toshiba Corp., Tokyo, Japan). Participants were asked to observe the images at the distance of distinct
vision (about 25 cm for normal vision).
4.5 Evaluation procedures
Experiments evaluating the memory texture, the actual texture,and subjective sharpness were conducted using a normalized rank
approach. First, participants were asked to recall the texture of an
object in each image without seeing the real object, and to sort theimages in descending order, starting with the one most closely approximating the recalled texture. Subsequently, they viewed the real
object with a black background identical to that in the stimulus im-

4.3 Stimulus images for evaluation
In our previous study7) using noise of one kind, we used two blurlevels (radius (described later) 8 or 12) and two noise levels (RMS
granularity9) 10 or 20 (referred to RMS 10 or 20 later)). In this study,
because we used noise of two kinds, we used one blur level and one
noise level to avoid overwhelming the observers with too many images to evaluate. Figure 6 portrays stimulus images forFig.evaluation.
6
Images were prepared for evaluation as follows: first, the original
images (no-0) were blurred (blur-0) using the Lens Blur feature of
the Blur Filter tool in Photoshop™ (CS4, Adobe Systems Inc.). For
this study, we set the blur level at radius 8. The radius setting sets thestrength of the lens-blur effect and has a pseudo effect that resembles f-stop setting of lens. Other settings about Lens Blur were all
default (speed: Faster, Source: none, Iris Shape: Hexagon, Circularity of the aperture: 0, Rotation: 0, Brightness: 0, Threshold: 255,
Amount of noise: 0, Distribution: Uniform, Monochromatic: uncheck). Then white noise and 1/f noise were added, respectively, atlevel RMS 20.
After blurring the image and adding noise, we clipped the area

white noise

Fig. 7

Fig. 6 Images for evaluation. Words before “-” denote blurring. “no” denotes
no blur images. “blur” denotes blurred images. Words after “-” denotenoise. “0” denotes no noise. “1/f ” denotes 1/f noise addition. “white”
denotes white noise addition. Therefore, “no-0” denotes no blur image
with no noise addition. “no-1/f “signifies that no blur image was combined with 1/f noise. “no-white” signifies that no blur image was combined with white noise. “blur-0” denotes a blurred image with no noise
addition. “blur-1/f ” signifies that a blurred image was combined with
1/f noise. “blur-white” signifies that a blurred image was combinedwith white noise. We treated no-0, no-1/f, and no-white as original
conditions, and treated blur-0, blur-1/f, and blur-white as blurred conditions.

1/f noise(i)Fig. 5 Power spectra of white noise and 1/f noise.

(ii)

Fig. 7 Power spectra of the original image and the blurred original image ofeach object

Xiazi Wan, Hiroyuki Kobayashi, and Makoto Ichikawa

Memory Texture as an Important Factor Affecting Improvement of Subjective Image Sharpness by Using Noise Addition

ages. Participants were asked to rearrange the images in descendingorder, starting with the one nearest to the actual texture. Finally, they
were asked to rearrange the images in descending order of subjective
sharpness. We conducted correlation analysis, partial correlation
analysis and path analysis with results obtained from the two groupsof experiments. Fifteen participants conducted these evaluations.

5. Results and discussion
5.1 Kendall's coefficient of concordance W
We calculated Kendall's coefficient of concordance W. Table 2
presents the values and results of significance test10) of W (Chisquared test). Values in cells with color were found to be significant(significance level 0.5%, 1% or 10%). Deeper colors represent stronger significance (0.5% indicates stronger significance than 1%). ValTable 2 Values and significance of Kendall's coefficient of concordance W foreach object. Values in cells with color were found to be significant.
Deeper colors represent stronger significance. Values in cells with nocolor were not significant.

Sweet potato

Memorytexture0.297 (0.5%)

Tissue0.128 (10%)

Round rice cracker

0.127 (10%)

Deep-fried rice cracker 0.228 (1%)

Buckwheat biscuit

0.112

Actualtexture

0.065

0.044

0.225 (0.5%)

0.273 (0.5%)

0.306 (0.5%)

Subjective
sharpness

0.699 (0.5%)

0.289 (0.5%)

0.362 (0.5%)

0.359 (0.5%)

0.594 (0.5%)

Fig. 8 (b). 8 (a)Fig. 8 (d)35ues in cells with no color were not significant.
The low W for the buckwheat biscuit memory texture indicatesthat the individual variance in ratings was large. This large individual variance might derive from differences in participants’ familiarity
with buckwheat biscuits, which are not a widely appreciated snack.
The individual variances in ratings for actual textures of sweet potato and tissue were large. Surface textures of sweet potato and tissue
were difficult for participants to notice. The way to recognize thetexture would differ greatly among participants.
5.2 Results of a normalized rank approach
To investigate the memory texture, the actual texture, and subjective sharpness of each object, we obtained scale values of the normalized rank approach and discussed the characteristics. Figure 8 presents the scale values of the normalized rank approach for therespective objects.
In terms of memory texture, the actual texture, and subjective
sharpness, scale values of normalized rank approach which show awide spread in the plot and clear significant differences in Figure 8,
also show a large coefficient of concordance in Table 2.
From Figure 8, we can see the stimuli of the blurred condition(blur-0, blur-1/f, blur-white) correspond to the respective stimuli ofthe original condition (no-0, no-1/f, no-white) eliciting lower ranksof memory texture, actual texture, and subjective sharpness.
In the blurred condition, the stimuli with noise elicited higher
subjective sharpness rankings than the stimuli with no noise. That

Fig. 8 (c)Fig. 8 (e)Fig. 8 Results of the normalized rank approach for the respective objects. The abscissa is the scale values. Higher scale value represents higher rank. The mark (*)
indicates significant differences with a significance level of 5%, and (**) indicates 1%.

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Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)

result is consistent with results obtained from our previous study7).
For objects with lower frequency and for which the texture was
not clearly visible, such as tissues and round rice crackers, little difference was found between the original (no-0) and the blurred original (blur-0). However, for objects with higher frequency such as
sweet potato, deep-fried rice cracker, and buckwheat biscuit, a great
difference was found between original and blurred images.
For (a) sweet potato, blur-white was ranked higher than blur-1/f,
and there was significant difference between blur-white and blur-1/f
in subjective sharpness. For (b) tissue, no-1/f was ranked high inmemory texture, actual texture and subjective sharpness. There wassignificant difference between blur-white and blur-1/f in subjective
sharpness. For (c) deep-fried rice cracker, there were significant differences between no-1/f and no-white both in actual texture and insubjective sharpness. For (d) round rice cracker, both no-1/f andblur-1/f were ranked high in memory texture and subjective sharpness. There was significant difference between blur-1/f and blurwhite in subjective sharpness. For (e) buckwheat biscuit, no-white
was ranked high in memory texture, actual texture and subjective
sharpness. There were significant differences both between no-whiteand no-1/f and between blur-white and blur-1/f in subjective sharpness. Table 3 presents the first place of images in the original condition and in the blurred condition for each object in terms of thememory texture, the actual texture, and subjective sharpness.
The stimuli with noise elicited higher ranking in terms of the subjective sharpness. The first places of the blurred condition on mem-ory texture are the same as first places of blurred condition for subjective sharpness. The stimulus evaluated as the most subjectively
sharp was the nearest to the memory texture. The noise effects weremore evident in blurred images. These results are consistent withresults obtained from our previous study7).
Actually, 1/f noise did not appear for sweet potato or buckwheat
biscuit in Table 3. In some cases, the 1/f noise also had some effect,
but not as much as white noise. This result demonstrates that white
noise is more suitable for textures of sweet potatoes and buckwheat
biscuits. However, for round rice cracker, only 1/f noise appeared inmemory texture or subjective sharpness in Table 3. These results suggest that using two kinds of noise was meaningful.
5.3 Correlation analysis
The scale values obtained from the normalized rank approach fitted a normal distribution. Therefore, we can calculate Pearson's correlation coefficient (Pearson product-moment correlation coefficient) r between the scale values. Between the ranks of the scalevalue, we can calculate Spearman's rank correlation coefficient ρ and
Kendall's rank correlation coefficient τ. We calculated the threekinds of correlation coefficients to see whether the results of themwere the same.
First, we calculated the correlation coefficient for each object. For
instance, for sweet potatoes, we collected the scale values of memory
texture, actual texture, and subjective sharpness, and obtained a rank,
respectively, as Table 4 shows.

Table 3 First place of original condition and blurred condition for each object on memory texture, actual texture, and subjective sharpness
Memory texture

Sweet potato

Actual texture

Subjective sharpness

Original condition

Blurred condition

Original condition

Blurred condition

Original condition

Blurred condition

1/f

white

1/f

1/f

1/f

white

0

TissueDeep-fried rice cracker

white

0

Round rice cracker

white

1/f

Buckwheat biscuit

0

1/f

1/f

white

white
1/f

0

white

white
1/f

white

white

white

1/f

white

white

1/f

white

white

Table 4 Scale values and ranks of memory texture, actual texture, and subjective sharpness for sweet potato. Each column has six
values because six stimulus images exist for each object.
scale value

stimuli

Memory texture Actual texture Subjective sharpness

no-0

0.642

no-1/f

0.320

0.344

0.321

0.851

0.290

-0.187blur-0-1.004-0.234-1.307blur-white

0.112-0.026-0.101

no-white

0.171

blur-1/f-0.2100.751-0.194rank

Memory texture Actual texture Subjective sharpness
1

2

3

3

1

1

2

4

6

-0.539

6

5

5

4

3

2

6

5

4

Ranks, scale values and corresponding stimulus images for sweet potato on memory texture, actual texture, and subjective sharpness. Each column has six values because six stimulus images exist for each object.
Memory texture

rank scale value
1

2

3

4

5

6

0.642

0.290

0.171

0.112

-0.210-1.004stimuli

no-0

no-1/fno-whiteblur-whiteblur-1/f

blur-0

Actual texture

rank scale value
1

2

3

4

5

6

0.321

0.320

-0.026-0.187-0.194-0.234stimuli

no-whiteno-0

blur-whiteno-1/fblur-1/f

blur-0Subjective sharpness

rank scale value
1

2

3

4

5

6

0.851

0.751

0.344

-0.101-0.539-1.307stimuli

no-whiteno-1/fno-0

blur-whiteblur-1/f

blur-0Xiazi Wan, Hiroyuki Kobayashi, and Makoto Ichikawa

Memory Texture as an Important Factor Affecting Improvement of Subjective Image Sharpness by Using Noise Addition

We calculated the correlation between the memory texture andthe actual texture. We obtained Pearson's correlation coefficient r
using scale values. Then we calculated Spearman's rank correlation
coefficient ρ and Kendall's rank correlation coefficient τ using ranks.
Additionally, we obtained the respective significance probabilities pof these correlation coefficients. We calculated the correlation between memory texture and subjective sharpness and the correlation
between actual texture and subjective sharpness. Additionally, we
calculated correlation coefficients in the same way as sweet potato
for the other four objects. Finally, we calculated correlation using
data from five objects with six image conditions.
The values of correlation coefficients and results of significancetest (t - test) are presented in Table 5. We show cells of p < 0.001, p< 0.01, p < 0.05, and p < 0.1 in different colors. Cells with color are
significant. Deeper colors represent greater significance.
From the differences in color of the cells, we can see that there
were differences among the results of Pearson's correlation coefficient, Spearman's rank correlation coefficient and Kendall's rankcorrelation coefficient. It might be because that the participants were
not enough to result significances for all the three kinds of correlation coefficients.
The results of correlation for each object (Table 5) show correlation between the memory texture and subjective sharpness. For tissues and round rice crackers, correlation was found only between thememory texture and subjective sharpness. Aside from memory, thetexture is an important clue for judging subjective sharpness. For
objects with more low frequency and for the texture of which was
not clearly visible, such as tissues and round rice crackers, there waslittle texture as a clue for subjective sharpness. Therefore, memoryshows a consistent influence on subjective sharpness.
Results of all stimuli showed strong correlation between thememory texture and subjective sharpness. Strong correlation was
also found between the actual texture and subjective sharpness, andbetween the memory texture and the actual texture.
Objects for which no correlation was found between memory texture and actual texture, such as tissue and round rice crackers, revealed little correlation, little partial correlation (Table 6) and little
casual relation (Table 7) between actual texture and subjective
sharpness. From these results, we infer that correlation existed between the actual texture and subjective sharpness for the other objects (sweet potato, deep-fried rice cracker and buckwheat biscuit) incorrelation analysis is a consequence of the correlation between theactual texture and the memory texture. Moreover, this idea is supported by the result that no object was found with correlation only
between the actual texture and subjective sharpness.
5.4 Partial correlation analysis
Partial correlation analysis is often used as a method of multivariate analysis. As seen in the results of correlation analysis, correlation
existed both between memory texture and subjective sharpness, andbetween actual texture and subjective sharpness. In order to further
clarify the correlation between memory texture and subjective
sharpness, and between actual texture and subjective sharpness, weused subjective sharpness as the dependent variable, with memory

37

Table 5 Correlation coefficients and their significance level for each object
and all stimuli. We show cells of p < 0.001, p < 0.01, p < 0.05, and p< 0.1 in different colors. Cells with color are significant. Deeper
colors represent greater significance. Significance level of cells without a p value are p values greater than 0.1.
Sweet potato

PearsonSpearmanKendallTissuePearsonSpearmanKendall

Deep-friedrice cracker

PearsonSpearmanKendallRoundrice cracker

PearsonSpearmanKendall

BuckwheatbiscuitPearsonSpearmanKendall

All stimuli

PearsonSpearmanKendall

Memory texture vs. Actual texture vs.
Memory texture vs.
Subjective sharpness Subjective sharpness Actual texture
0.857 (p < 0.05)

0.615

0.658

0.600 (p < 0.1)

0.733 (p < 0.05)

0.600 (p < 0.1)

0.771 (p < 0.1)

0.829 (p < 0.05)

0.714

Memory texture vs. wActual texture vs. Memory texture vs.
Subjective sharpness Subjective sharpness Actual texture
0.858 (p < 0.05)

0.317

0.670

1 (p < 0.01)

0.200

0.200

1 (p < 0.001)

0.429

0.429

Memory texture vs. Actual texture vs.
Memory texture vs.
Subjective sharpness Subjective sharpness Actual texture
0.601

0.682

0.762 (p < 0.1)

0.733 (p < 0.05)

0.600 (p < 0.1)

0.600 (p < 0.1)

0.829 (p < 0.05)

0.771 (p < 0.1)

0.771 (p < 0.1)

Memory texture vs. Actual texture vs.
Memory texture vs.
Subjective sharpness Subjective sharpness Actual texture
0.960 (p <0.01)

0.162

0.270

0.867 (p < 0.05)-0.0670.067

0.943 (p <0.01)-0.086

0.086

Memory texture vs. Actual texture vs.
Memory texture vs.
Subjective sharpness Subjective sharpness Actual texture
0.910 (p < 0.05)

0.931 (p < 0.01)

0.781 (p < 0.1)

0.733 (p < 0.05)

0.867 (p < 0.05)

0.600 (p < 0.1)

0.826 (p < 0.05)

0.943 (p <0.01)

0.771 (p < 0.1)

Memory texture vs. Actual texture vs.
Memory texture vs.
Subjective sharpness Subjective sharpness Actual texture
0.813 (p < 0.001)

0.563 (p < 0.01)

0.568 (p < 0.01)

0.651 (p < 0.001)

0.398 (p < 0.01)

0.389 (p < 0.01)

0.836 (p < 0.001)

0.543 (p < 0.01)

0.547 (p < 0.01)

texture and the actual texture as independent variables.
We calculated the partial correlation coefficient between thememory texture and subjective sharpness, with the effect of the actual texture removed, and the partial correlation coefficient between
the actual texture and subjective sharpness, with the effect of memory texture removed, using scale values. Results of a comparison with
the Pearson’s correlation coefficient are presented in Table 6.
Results for the respective objects (Table 6) were consistent for
both single correlation and partial correlation. Results of all stimuli
indicate partial correlation between memory texture and subjective
sharpness; although no partial correlation was found between actual

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Bull. Soc. Photogr. Imag. Japan. Vol. 27 No. 2 (2017)

Fig. 9

Table 6 Comparison of single correlation and partial correlation

Sweet potato
TissueDeep-friedrice cracker
Round ricecracker
BuckwheatbiscuitAll stimuli

Single correlation

Partial correlation
Single correlation

Partial correlation
Single correlation

Partial correlation
Single correlation

Partial correlation
Single correlation

Partial correlation
Single correlation

Partial correlation

Memory texture vs. Actual texture vs.
Subjective sharpness Subjective sharpness
0.857 (p < 0.05)

0.615

0.858 (p < 0.05)

0.317

0.763 (p < 0.1)

0.916 (p < 0.05)
0.601
0.172

0.960 (p <0.01)

0.964 (p < 0.01)
0.910 (p < 0.05)
0.803 (p < 0.1)

0.813 (p < 0.001)
0.724 (p < 0.001)

0.132-0.673
0.682
0.434
0.162

-0.3590.931 (p < 0.01)

Fig. 9 Path diagram. Effects of the memory texture and the actual texture on
subjective sharpness are the following. Pya represents the direct effectof memory texture on subjective sharpness. Pyb denotes the direct effect of the actual texture on subjective sharpness. The correlation effectof memory texture on subjective sharpness through the actual texture
is rab* Pyb. Correlation effects of the actual texture on subjective sharpness through memory texture is rab* Pys. Total effects of memory texture on subjective sharpness is Pya+ rab* Pyb (=ray). Total effects of Actual texture on subjective sharpness is Pyb+ rab* Pya (=rby).

0.850 (p < 0.05)

0.398 (p < 0.01)
0.211

Table 7 Direct effect, correlative effect, total effect, and coefficient of determination (R2) of memory texture and actual texture
for each object and all stimuli

Sweet potato
TissueDeep-fried rice cracker
Round rice cracker
Buckwheat biscuit
All stimuli

Memory texture

Actual texture

Memory texture

DirecteffectCorrelative
effectTotal
effect

0.090

0.525

0.615

0.798

1.170

Actual texture-0.466

Actual texture

0.535

Memory texture

Memory texture

0.194

0.988

Actual texture-0.105

Actual texture

0.563

Memory texture

Memory texture

Actual texture

0.470

0.728

0.150

texture and subjective sharpness. Results support a relation between
the memory texture and subjective sharpness.
5.5 Path analysis
Path analysis is another common method of multivariate analysis.
It provides estimates of the magnitude of hypothesized causal connections between sets of variables. We investigated the magnitude ofeffects of memory texture on subjective sharpness and the magnitude of effects of actual texture on subjective sharpness, using pathanalysis. Figure 9 depicts the path diagram of the path analysis, withsubjective sharpness as the dependent variable, and the memory texture and the actual texture as independent variables. Results of pathanalysis are presented in Table 7.
For sweet potato, tissue, and round rice cracker images, both large
direct effects and total effects of memory texture on subjective
sharpness were found. As grouping with spatial frequency characteristics and surface textures, the textures of the three objects appear tobe smooth. For the tissue and round rice cracker, a large difference indirect effects was found between the memory texture and the actual
texture, and the same for total effect. No such a large difference was

0.059-0.312
0.784

0.408

0.148

-0.028
0.267

0.440

0.367

0.085

0.414

0.857

0.858

0.318

0.602

0.683

0.960

0.162

0.910

0.930

0.813

0.564

Coefficient ofdetermination (R2)

Effect of
unexplained terms

0.740

0.510

0.855

0.380

0.481

0.720

0.931

0.262

0.953

0.218

0.676

0.570

found for sweet potato, which is possibly true because, as the power
spectra indicates, tissue, and round rice cracker showed lower power
in a wide frequency range, whereas sweet potato showed higher
power in a wide frequency range.
For the deep-fried rice cracker and buckwheat biscuit, a large direct effect of the actual texture on subjective sharpness was found.
The textures of the two objects were clearly visible. However, little
difference was found between the total effects of memory texture
and actual texture. For buckwheat biscuit, both total effects werelarge. For deep-fried rice cracker, both total effects were small. The
coefficient of determination R2 was small, meaning that other factors played a great role in the judgment of subjective sharpness ofthe deep-fried rice cracker. Small R2 is expected to result from thesurface property of deep-fried rice crackers, which are covered withlinear cracks. The appearance of lines served as clues for judgment ofsubjective sharpness. Moreover, it might be true because the contrast
and stereoscopic effects are evaluated differently among stimuli.
Those differences affected the evaluation of the subjective sharpness.
For all stimuli, both direct effects and total effects of memory
texture on subjective sharpness were large. Memory strongly affectedXiazi Wan, Hiroyuki Kobayashi, and Makoto Ichikawa

Memory Texture as an Important Factor Affecting Improvement of Subjective Image Sharpness by Using Noise Addition

the subjective sharpness.

6. Conclusion
Results of correlation analysis, partial correlation analysis andpath analysis were mutually consistent, demonstrating consistently
that subjective sharpness is related to the memory texture. These results suggest that the memory texture of objects is an important factor affecting the subjective sharpness of images.
The influences of other factors which could affect the judgment ofsubjective sharpness cannot be ignored either, as seen in the pathanalysis. And it is also because that there was effect of noise on subjective sharpness in the experiment used sinusoidal gratings whichhave no texture.

Acknowledgment

The authors wish to express their appreciation to Mr. Shinji Maeda (Chiba University) for his assistance with experiments.

39

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