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Journal of Vision (2018) 18(1):1, 1–13 1
Comparing the minimum spatial-frequency content for
recognizing Chinese and alphabet characters
Department of Biomedical Engineering,
University of Minnesota, Minneapolis, MN, USA
Present address: Athinoula A. Martinos Center for
Biomedical Imaging, Department of Radiology,
Massachusetts General Hospital and Harvard Medical
Hui Wang School, Charlestown, MA, USA $
Department of Psychology University of Minnesota,
Gordon E. Legge Minneapolis, MN, USA $
Visual blur is a common problem that causes difficulty in Introduction
pattern recognition for normally sighted people under
degraded viewing conditions (e.g., near the acuity limit,
when defocused, or in fog) and also for people with Character recognition is a prerequisite for reading
impaired vision. For reliable identification, the spatial and is typically a fast and accurate visual process. It
frequency content of an object needs to extend up to or becomes difficult under degraded visual conditions,
exceed a minimum value in units of cycles per object, suchasreadingsmallsymbolsatalongdistanceorwith
referred to as the critical spatial frequency. In this study, optical defocus, and is especially difficult in patients
we investigated the critical spatial frequency for with severe low vision. The spatial-frequency properties
alphabet and Chinese characters, and examined the of letter recognition have been widely explored.
effect of pattern complexity. The stimuli were divided Previous studies show that the visual system utilizes a
into seven categories based on their perimetric spatial frequency of 1–3 cycles per letter (CPL) for
complexity, including the lowercase and uppercase
alphabet letters, and five groups of Chinese characters. reliable identification (Alexander, Xie, & Derlacki,
Wefound that the critical spatial frequency significantly 1994; Chung, Legge, & Tjan, 2002; Ginsburg, 1978;
increased with complexity, from 1.01 cycles per Gold, Bennett, & Sekuler, 1999; Legge, Pelli, Rubin, &
character for the simplest group to 2.00 cycles per Schleske, 1985; Parish & Sperling, 1991; Solomon &
character for the most complex group of Chinese Pelli, 1994), with the optimal spatial frequency de-
characters. A second goal of the study was to test a pending somewhat on the angular size of letters (Majaj,
space-bandwidth invariance hypothesis that would Pelli, Kurshan, & Palomares, 2002). Kwon and Legge
represent a tradeoff between the critical spatial (2011) reported that accurate letter identification is
frequency and the number of adjacent patterns that can possible with letters containing spatial frequencies only
be recognized at one time. We tested this hypothesis by upto0.9CPL.Theseauthorsappliedlowpassfiltersto
comparing the critical spatial frequencies in cycles per images of letters and faces and obtained psychometric
character from the current study and visual-span sizes in functions showing recognition performance (percent
number of characters (measured by Wang, He, & Legge, correct) as a function of the cutoff frequency of the
2014) for sets of characters with different complexities. filters. They referred to the minimal spatial-frequency
For the character size (1.28) we used in the study, we requirement for pattern recognition (with 80% accura-
found an invariant product of approximately 10 cycles, cy) as the critical spatial frequency.
which may represent a capacity limitation on visual Chinese characters differ from alphabetic characters
pattern recognition.
in having a wider range of pattern complexities.
Studying Chinese character recognition may elucidate
the connection between pattern recognition and pattern
complexity. The goal of our study was to determine the
critical-frequency requirements for Chinese characters,
and to examine the effect of pattern complexity.
Citation: Wang, H. & Legge, G. E. (2018). Comparing the minimum spatial-frequency content for recognizing Chinese and
alphabet characters. Journal of Vision, 18(1):1, 1–13, https://doi.org/10.1167/18.1.1.
https://doi.org/10.1167/18.1.1 Received April 11, 2017; published January 2, 2018 ISSN 1534-7362 Copyright 2018 The Authors
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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Journal of Vision (2018) 18(1):1, 1–13 Wang & Legge 2
Critical cutoff frequencies can be expressed in both complexity increases (Wang et al., 2014). If critical
retinal spatial frequency (cycles per degree) or image- frequencies are found to increase with complexity, it is
based spatial-frequency (cycles per character; CPC). In possible that the product of critical frequency and
this paper, we will usually refer to spatial frequencies visual-span size may be constant, representing a form
(including cutoff frequencies) in cycles per character. of capacity limitation on visual pattern recognition. In
Anexception will be our consideration of the effects of the context of this paper, we refer to the bandwidth of
the contrast sensitivity function (CSF) in the Discus- the low-pass filter as the range from zero to the critical
sion. frequency. For simplicity, we used the term bandwidth
Previous studies have shown that the acuity limit for instead of the critical frequency in our hypothesis.
recognizing Chinese characters with more strokes The study of character recognition has important
requires larger size (Cai, Chi, & You, 2001; Chi, Cai, & practical implications for reading performance. It is
You, 2003; Huang & Hsu, 2005). Chinese characters known that a critical frequency is required for
with more strokes also have higher contrast thresholds uncompromised reading speed in alphabet reading
(Yen & Liu, 1972) and longer response times (Yu & (Kwon&Legge,2012).Therefore,studying the spatial-
Cao, 1992). However, reports on the spatial frequency frequency requirements for Chinese characters may be
properties of Chinese character recognition are scarce. relevant to Chinese reading under low-resolution
Chen, Yeh, and Lin (2001) adopted the critical-band– conditions including low vision. It may also have
maskingparadigmusedbySolomonandPelli(1994)to practical applications in designing reading material for
investigate the best central frequencies for Chinese difficult viewing conditions.
characters. They tested Chinese characters with 3 to 21
strokes, and reported an average spatial frequency of
approximately 8 CPC. The study however, did not take Methods
the variation of complexities into account, and did not
investigate the minimal spatial-frequency requirements
for Chinese character recognition. Subjects
In this study, we explored the critical spatial-
frequency requirements for alphabet and Chinese Six college students (three men, three women) with
characters, and examined the effect of complexity on normal or corrected-to-normal vision participated in
these requirements. As the more complex characters the experiments. They were all native Chinese speakers,
have broader spatial-frequency spectra than the simple originally educated in the simplified Chinese script
characters, they may require higher spatial frequency system, and all had more than 10 years education in
for character recognition. We divided alphabet char- English. The subjects signed an Internal Review Board
acters and Chinese characters into categories, based on (IRB) approved consent form before the experiments.
ranges of complexity values, using the perimetric
complexity metric (Arnoult & Attneave, 1956; Pelli,
Burns, Farell, & Moore-Page, 2006). The perimetric Stimulus sets
complexity of a symbol is defined as its perimeter
squared divided by its ink area. We showed The stimulus characters were lowercase (LL) and
previously (Wang et al., 2014) that the perimetric uppercase (UL) alphabet letters in the Arial font, and
complexity metric has high correlation with other simplified Chinese characters in the Heiti font in which
complexity metrics, such as the number of strokes, the all the strokes have the same width.
stroke frequency (Majaj et al., 2002; Zhang, Zhang, The 700 most frequently used Chinese characters
Xue, Liu, & Yu, 2007) and the skeleton method (State Language Work Committee, 1992) were divided
(Bernard & Chung, 2011). For each complexity into five nonoverlapping groups based on their
category, we measured recognition performance for perimetric complexity values (Pelli et al., 2006).
sets of 26 characters as a function of the cutoff Twenty-six characters whose complexity values were
frequency of low-pass filters. close to the mean of the group were selected to form
Asecond goal of this study was to test an empirical five sets of symbols (C1–C5). Characters with very high
hypothesis of a tradeoff between the critical frequency or low similarity were excluded from the stimulus sets.
for character recognition and the visual span for Ameasure of similarity for the characters in each set
character recognition; we term this the space-band- was computed using a normalized Euclidean distance
width invariance hypothesis. The visual span is the method (Wang et al., 2014).
number of characters that can be recognized without To determine whether subjects familiarity with the
moving the eyes. We have examined the size of the characters affected their performance, we included a
visual span for alphabet letters and Chinese characters, groupofChinesecharacterswithlowerusagefrequency
and discovered that the visual span size decreases as in text but comparable in complexity with characters in
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Journal of Vision (2018) 18(1):1, 1–13 Wang & Legge 3
f ¼ 1 ð1Þ
1þ r 2n
c
where r is the radius of the components in the
frequency domain, c is the radius of the cutoff
frequency, and n is the order of the filter. Figure 2A
demonstrates the response function of the low-pass
filter in the spatial-frequency domain.
To test the recognition accuracy as a function of
blurring levels, six cutoff frequencies were selected for
each stimulus set while character size remained
constant. A demonstration of the characters with and
without low-pass filtering is shown in Figure 2. The sets
of filter cutoffs used for the eight complexity groups
were chosen based on recognition performance in pilot
Figure 1. Representative characters from the eight stimulus sets runs. We ensured that the cutoffs were selected so that
(LL, UL, C1–C5, and C30). The complexity gradually increases in recognition accuracy spanned a wide range, and the
the first seven rows (from LL to C5). The bottom row (C30) psychometric function exhibited a clear transition from
shows a group with comparable complexity to C3, but lower low to high performance accuracy. The cutoffs used for
familiarity. each stimulus set are summarized in Table 2.
the group C3. We did this by identifying the next 700
most frequent Chinese characters and divided them Image display
into five complexity groups as well, based on the same
complexity metric. Twenty-six characters were selected The stimuli were displayed on a 19 in. CRT monitor
to comprise a comparison group (C30), which had (refresh rate: 75 Hz, resolution: 1280 3 960). The
comparable complexity with C3 but lower frequency luminance of the blurred images on the screen was
and presumably lower familiarity. The pattern com- mapped onto 256 gray levels. The background of the
plexity in the 1,400 most frequently used characters image was set to the gray level 127, corresponding to a
2
covers most of the complexity range across all meanluminance of 40 cd/m . Luminance of the display
simplified Chinese characters. Remaining characters monitor was made linear using an 8-bit lookup table in
with even higher complexities are rarely used in conjunction with photometric readings from a Konica
ordinary reading. Five representative characters from Minolta CS-100 Chroma Meter (Konica Minolta
each stimulus set are shown in Figure 1. Statistics of the Sensing Americas, Inc., Ramsey, NJ). The image
perimetric complexity values for each stimulus set are luminance values were mapped onto the values stored
given in Table 1. in the lookup table for the display. The character image
was displayed at the center of the screen. The stimulus
symbol was created and controlled using MATLAB
Low-pass filtering (MathWorks, Natick, MA) and Psychophysics Tool-
box extensions (Brainard, 1997; Pelli, 1997; Kleiner et
al., 2007), running on a Mac Pro computer (Apple,
Ablack character was generated on a gray back- Cupertino, CA).
ground and stored as a grayscale image. The size of the
image was 2503250 pixels, and the size of the
characters (height of Chinese characters and x-height of Procedure
alphabet letters) subtended 1.28 visual angle at a
viewing distance of 40 cm. The image was blurred Each subject participated in three test sessions on
through a third order Butterworth low-pass filter (f) three days. One session consisted of eight blocks: seven
given by the following equation: blocks with varied complexity levels (LL, UL, C1–C5),
Group LL UL C1 C2 C3 C4 C5 C30
Complexity mean (SD) 48.6 (11.7) 66.5 (17.9) 98.0 (6.3) 136.9 (2.3) 176.6 (4.3) 216.2 (5.0) 280.1 (33.7) 182.0 (5.2)
Table 1. Perimetric complexity measures for the stimulus sets. Note: LL, lowercase letter; UL, uppercase letter; C1–C5, five sets of
Chinese characters from the simplest to the most complex; C30, Chinese character group of comparable complexity with C3 but less
familiarity.
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Journal of Vision (2018) 18(1):1, 1–13 Wang & Legge 4
Figure 2. (A) The response function of the third-order Butterworth filter in the spatial frequency domain.The arrow indicates a cutoff
frequency of 1.5 cycles per character (CPC) for a 18 letter size. The filter’s cutoff is defined as the frequency at half amplitude. (B)
Demonstration of low-pass filtered Chinese characters from the five complexity categories. The right column shows the unfiltered
character.
and one block with complexity equivalent to C3 but center of the screen. In each trial, a character was
lower character familiarity (C30). In each block, there presented for 200 ms at fixation. After that, the display
were 25 trials for each of six cutoffs forming a total of 2,
became uniform at the background level of 40 cd/m
150 trials. The stimulus symbol was randomly selected and the subject was asked to report the character. The
from the 26-character set, and the order of the cutoff experimenter recorded the responses, and the subject
frequencies presented was shuffled. The resulting clicked the mouse to start the next trial. A reference
psychometric functions for a given complexity category page was available, showing the 26 symbols in the
were therefore based on 450 trials (six cutoff frequen- current category, if the subject had trouble recalling the
cies and 75 trials per cutoff frequency). The orders of characters in the set. Subjects rarely responded with
the blocks were counterbalanced between sessions and characters outside of the stimulus category (,1% of
subjects. trials.) The 26 unfiltered characters were tested at the
The subject was shown the 26 unfiltered symbols on end of every block in order to evaluate the baseline
a hard copy page before the start of a block and urged performance for recognition. Performance on the
to restrict responses to the stimulus set. During test unfiltered stimuli was at the ceiling value of 100%.
trials, the subject was directed to fixate on a cross at the Achin rest was used during the test to reduce head
movements and to maintain the viewing distance.
Practice trials, including all the stimulus sets and the
Group f1 f2 f3 f4 f5 f6 filter cutoffs, were provided at the beginning of the test.
LL 0.78 1.02 1.27 1.49 1.80 2.16
UL 0.78 1.02 1.27 1.49 1.80 2.16 Data analysis
C1 0.78 1.02 1.27 1.49 1.80 2.16
C2 0.92 1.18 1.42 1.63 1.94 2.34 The character recognition accuracy was plotted
C3/C30 1.08 1.32 1.57 1.79 2.1 2.52 against the cutoff frequencies for each stimulus set.
C4 1.24 1.44 1.73 1.94 2.28 2.66 Cumulative Gaussian functions (Wichmann & Hill,
C5 1.30 1.54 1.87 2.09 2.46 2.82 2001)wereusedtofittheplotswiththeleast-square
Table 2. Butterworth filter cutoff frequencies (in cycles per criterion. The critical spatial frequency was estimated
character; CPC) used for recognition tests with the seven from the psychometric function, and defined as the
complexity categories. Note: LL, lowercase letter; UL, uppercase cutoff frequency yielding 80% correct responses. It is
letter; C1–C5, five sets of Chinese characters from the simplest noted that the guessing level of the psychometric
to the most complex; C30, Chinese character group of functionsis1/26¼3.85% for all the groups, because
comparable complexity with C3 but less familiarity. there are 26 stimuli in each complexity set. Figure 3
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