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Bull. Soc. Photogr. Imag. Japan. (2014) Vol. 24 No. 2: 19–26

Original Paper

Improving the Perception of Image Sharpness Using Noise Addition
Xiazi Wan*, Naokazu Aoki*, and Hiroyuki Kobayashi*

Abstract:

In our previous paper, we investigated the effects of image noise on the perception of image sharpness using white noise, andone- and two-dimensional (1D and 2D, respectively) single-frequency sinusoidal patterns as stimuli. Our results showed thatwith high-frequency stimuli, sharpness decreased as noise level increased; whereas, with low-frequency stimuli, sharpness
reached a maximum value at a certain level. The sharpness of the rectangular grating and the checkerboard pattern, both ofwhich have clear edges, decreases more drastically even than the sinusoidal wave with the highest frequency. This paper builds
on our previous study by evaluating color natural images rather than black-and-white, single-frequency patterns. Our results
indicate that the effects of noise are more remarkable in images of objects containing more low-frequency components, in blurredrather than sharp images, and in strongly blurred images. The dependence of sharpness on frequency, as found in this study, isconsistent with results from the preceding study; the results we obtained using black-and-white, single-frequency patterns wereverified using color images of natural objects. Furthermore, we acquired new information on the influence of texture, which we
did not investigate in our previous studies, i.e., noise has a negligible effect on images with a large number of edges; whereas, weobserved the most significant effects for images without such a texture.

Key words:

Noise addition, Perception of image sharpness, Spatial frequency dependence

1. Introduction
1.1 Current Knowledge
Currently, the digital photograph has become comparable tothe silver halide photograph in information capacity. However,when considered as a target of appreciation, silver halide photographic prints are excellent in the subjective region, i.e., the region that cannot be physically evaluated. A possible cause is that
digital photographs are said to be considerably smooth—there isno granular noise; these photographs appear as a picture for coloring. Some professional photographers intentionally add granular
noise to images captured using digital cameras to improve thetexture quality of digital photographs because granular noise resembles the graininess of a silver-halide film or photograph 1).
Some studies have suggested the possibility of improving image
quality through the addition of noise 2). Other studies have suggested improvements in likeability by noise addition 3). There arealso studies that highlight the relationship between noise addition
and memory of texture 4), with the authors of one study proposingthat textures can be recalled in association with familiar objects,
in a similar manner as memory color 5).
Further, Kurihara et al. investigated the effects of noise on the
sharpness of an image by adding white noise to one- (1D) andtwo-dimensional (2D) single-frequency sinusoidal gratings as
stimuli and comparing them with rectangular and checkerboard

Fig. 1. Stimuli used in the study of Kurihara et al.1)

patterns, respectively 6). The stimuli are shown in Fig. 1.
The results of this experiment indicate that the addition ofnoise improves the sharpness more effectively when low-frequency
stimuli, rather than high-frequency stimuli, are used. Addition ofnoise is not particularly effective in images that contain clear

Received 9th, June 2014; Accepted 26th, November 2014
*Graduate School of Advanced Integration Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan

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Fig. 3.

Interface of frequency analysis program

and their blurred images as stimuli, and then added white noise tothese images.

Fig. 2.

Sample images

edges, such as rectangular and checkerboard patterns. This effectis more pronounced with 2D than with 1D patterns.
1.2 Objective
This paper further develops the ideas of Kurihara et al.’s previously mentioned study by evaluating natural color images as opposed to black-and-white, single-frequency patterns. Our goal is
to find whether the results for simple patterns also apply to color
images.

2. ExperimentBecause sinusoidal gratings can be regarded as blurred rectangular or checkerboard patterns, we used focused original images

2.1 Original sample images
We chose rice crackers and cookies because they are familiar
items that have various textures. Fig. 2 shows the images used.
To prevent shadows, we captured photos under diffuse light.
We took photos using a NIKON D800 (Nikon Corp., Tokyo,
Japan) with 7360 × 4912 pixels JPEG file, fine-image quality,
shutter speed 1/250, F16, and ISO-100. The settings related to
sharpness are standard and the Vibration Reduction (VR) of thelens is turned on.
The spatial frequency region where the Visual Transfer Function (VTF) of human eye shows significant values is 0–10 cycles/
mm when people observe at the distance of distinct vision (a distance where distinct vision was possible. 25–30 cm in the normaleye). Because 10 cycles/mm = 500 dpi, we cut 2048 × 2048 pixels
with 500 dpi (10.4 × 10.4 cm) out from the original photos andall images were adjusted to the actual size of the objects.
2.2 Power spectrum measuring tool and the power spectra of
the original images
We used a software frequency analysis program as a power spectrum measuring tool (Fig. 3).
The method of calculating the power spectrum is to take theaverage of the values of all angles (0°–180°) by performing a twodimensional FFT.
Figure 4 shows the power spectra of the images. The abscissa is

Fig. 4. Power spectra of the sample images

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Improving the Perception of Image Sharpness using Noise Addition

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Fig. 5. Interface of color graininess program

Fig. 6. White noise and its power spectrum

Fig. 8.

Examples of blur levels (magnified twice)

had many low-frequency components, and the buckwheat cookie(Fig. 4(d)) had many high-frequency components. Surprisingly,
the surface of the deep-fried rice cracker (Fig. 4(b)) was not flat,and it did not have many high-frequency components; however, it
did have many lines and a distinct texture. Because there are notmany high-frequency images in rice crackers and cookies, wechose one high-frequency image and three low-frequency images,
all of which have different surfaces.
Fig. 7. Preparation of the images for the evaluation: The original images
were blurred at two different levels (1 and 2), and then noise wasadded at two different levels (w10 and w20). For each sample,
there were nine images to be evaluated, including images without
noise.

the spatial frequency region where the VTF of human eye shows
significant values (0–10 cycles/mm) and the ordinate is a logarithm of a power.
In general, images with many edges have more high-frequency
components than images with fewer edges. As expected, theround rice cracker (Fig. 4(a)) and the square cookie (Fig. 4(c))

2.3 Noise addition tool
We used a software color graininess program as a noise addition
tool (Fig. 5). “a” is a constant that can change the amplitude ofnoise. “b” is the slope of the double logarithmic power spectrumof the noise. By setting the value of “b” to zero, we can add white
noise to the image. Further, we can control the RMS granularity
value by changing the value of the standard deviation field.
The first step of the creation of white noise is to generate a
two-dimensional noise using a Gaussian random number, andthen the two-dimensional noise is added to the image data.

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Bull. Soc. Photogr. Imag. Japan. Vol. 24 No. 2 (2014)

Fig. 9. (a) (b)Blur level012Power spectra of images for evaluation
0012Graph ①

Noise level
w10
0_w10
1_w10
2_w10

w20
0_w20
1_w20
2_w20

Graph ②Graph ③

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Improving the Perception of Image Sharpness using Noise Addition

Fig. 9. (c) (d)Power spectra of images for evaluation

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2.4 White noise image
Figure 6 shows the image and power spectrum of white noise.
White noise is characterized by constant power in the spatial
frequency region, where the VTF shows significant values. We
generated the noise image by adding white noise to a gray patch ofdigital value 128, and then measured the power spectrum of it
using the frequency analysis program.
2.5 Images for evaluation
The images for the evaluation were prepared by the following
process: first, the original images were blurred at two different
levels, and then, noise was added at two different levels, RMS 10
and 20 (Fig. 7).
We blurred the images using the Lens Blur feature of the Blur
Filter tool in Photoshop. We can change the blur level by adjusting the Radius value. In this study, we set radius 8 as blur level 1,
and radius 12 as blur level 2.
Figure 8 shows the local enlarged views of the deep-fried ricecracker so that it is easier to observe the different blur levels.
For each of the four samples, there were nine images to be evaluated, including images without noise; therefore, there were atotal of 36 images.
All 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). We checked the printed image of black lines
cleared 500 dpi.
2.6 Power spectra of images for evaluation
Figure 9 shows the power spectra of the images for the evaluation of (a), (b), (c), and (d), respectively. The low-frequency images(a), (b), and (c) show the same characteristics; whereas the highfrequency image (d) shows different characteristics.
For each sample, graph ① shows power spectra of the original(0), blur level 1 (1), and blur level 2 (2). The power spectra ofblurred images decrease. Graph ② shows the power spectra ofimages with noise RMS10 compared with white noise RMS10.
Graph ③ shows the images of noise RMS20. We can observethat following the addition of noise, the power spectra of the lowfrequency images are almost the same as the power spectra ofwhite noise.
2.7 Evaluation environment
The evaluation was carried out at 700 lx under a natural color
evaluation lamp of 5000 K (Toshiba Corp., Tokyo, Japan). The
subjects were asked to observe the samples at the distance ofdistinct vision, but the distance was not specified.
2.8 Evaluation method
Images were evaluated using a normalized ranking method.
The research participants were asked to rearrange images according to the following instructions: “A sharp image means that animage appears to be clear, and in focus. Please sort these images
in the descending order of sharpness for each sample (nine imag-

Fig. 10. Results for the subjective evaluation of image sharpness.
Sharpness depends on noise level and blur level.

Wan, Aoki, and Kobayashi

Fig. 11.

Improving the Perception of Image Sharpness using Noise Addition

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Results for the subjective evaluation of image sharpness. The mark (*) indicates significant differences, with a significance level of 5%.

es) at the distance of distinct vision.” Participants had to rearrange
nine images per each sample, for (a), (b) (c) and (d). Based on theiranswers, we calculated the sharpness values.
2.9 Observers
Seventy-eight subjects, between the age group of 10 and 60
years, participated in this experiment.

3. Results and discussion
Figure 10 shows the results of the sharpness evaluation. The
abscissa is the noise level (w0, w10, w20) and the ordinate is thescale value, which represents sharpness perception. Each line corresponds to a blur level (blue ● 0, red ■1, green ▲2).
The mark (*) in Fig. 11 indicates significant differences with asignificance level of 5%. For non-blurred images, in (a) and (b),there is no significant difference among 0, 0_w10 and 0_w20; in(c) and (d), significant differences only appear between 0 and
0_w20. These results indicate that for sharp images, noise is noteffective. For blurred images, except 1 and 1_w10 in (b), there
are significant differences between 1 and 1_w10, 1_w10 and 1_w20,
2 and 2_w10, and 2_w10 and 2_w20.
To observe the differences among samples more clearly, we
present a magnified image of some samples in Fig. 12. Overall,the effect of the addition of noise is more evident in strongly
blurred images than in weakly blurred images. In particular, forthe flat, round rice cracker (a) and the square cookie (c), the original low-frequency and flat-textured images, sharpness increases
with an increase in noise level to the extent that the blurred images appear similar to the non-blurred images. On the other
hand, for the buckwheat cookie (d), the high-frequency image,the addition of noise was not as effective. For image (b), which has
many lines and a distinct texture but a low-frequency image, noise
had only a minor effect in contrast to the effects seen in (a) and (c).

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Bull. Soc. Photogr. Imag. Japan. Vol. 24 No. 2 (2014)

Fig. 12. Magnified images to observe differences among samples more clearly(a) Magnified 120% (b) Magnified 130% (c) Magnified 190% (d) Magnified 200%

It is possible that the addition of noise erased the lines on thesurface of the deep-fried rice cracker (b), resulting in a loss of
texture.

noise of memory texture. Because previous studies did not discuss
the individual differences, we will discuss the relationship between the individual differences in the perception of image sharpness and those in memory texture.

4. Conclusion
Acknowledgment
We found that the effect of noise in improving image sharpness
was frequency-dependent, i.e., its effects were more evident inblurred images than in sharp images, and in strongly rather thanweakly blurred images. The conclusion is consistent with resultsfrom previous studies. In addition, results obtained using blackand-white, single-frequency patterns were verified in color imagesof natural objects. Further, we obtained new information on theinfluence of texture, i.e., because the addition of noise can erase
edges, it may have no significant effect, even on low-frequency
images.
Further work is required to elucidate the mechanisms involved
in increasing sharpness through noise addition. According to thestudy on memory texture, there is a texture appropriate for eachobject—some textures can be divided into white noise or 1/f noise.
We hypothesized that adding noise to a blurred image causes the
subject to recall the texture of that object from memory; simultaneously, the subject perceives sharpness. We will test the hypothesis by adding white noise and 1/f noise to a variety of objects to
identify if noise that better improves sharpness matches with the

The authors wish to express their appreciation to Mr. Yuya
Nakao (Chiba University) for his assistance with the experiments.

References
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Description in Digital Print by Adding Noise,” J. Soc. Photogr. Sci.
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