Smoothed Boundary Distance Loss Function for Enhancing Character Extraction from High-Resolution
Scans of Historical Documents
Woo-Seok Lee1
Maaz Ahmed1
Kang-Sun Choi1,*
-
Korea University of Technology and Education, Cheon-an, Korea. {book0496, maaz9898,
ks.choi}@koreatech.ac.kr
Copyright © 2026 The Institute of Electronics and Information Engineers
Keywords
Loss function, Boundary distance, Denoising, Character segmentation, Historical documents
1. Introduction
Historical printed documents are valuable for understanding past societal and cultural
contexts, as well as the nature of ancient civilizations [1]. Recently, the field of extracting information from ancient documents through advanced
analysis techniques are growing. This involves not only examining the textual contents
but also assessing the technology used in metal type production via text part of metal
type estimation, and evaluating printing techniques through quality inspections.
Despite their importance, these documents often suffer from significant loss of information
due to their age [2]. Their poor preservation condition and age present challenges to researchers attempting
to retrieve accurate information [3]. To address these issues, advancements in machine learning and computer vision, especially
in character enhancement and segmentation, are being utilized [4]. Even many researchers developed advanced computer vision techniques, there is not
a reliable system for extracting precise information from these documents [5]. Despite the difficulty, accurate character segmentation is essential for effective
information extraction. Digital image processing can significantly improve the legibility
of these characters. A critical aspect of this improvement involves measuring the
distance between predicted and actual character boundaries [6]. Additionally, a denoising loss function is proposed to reduce noise around character
boundaries, ensuring precise segmentation with minimal errors [7].
One of the main challenges in text extraction from old Korean movable metal type documents
is the inconsistency in print quality, as shown in Fig. 1(a). Unlike Gutenberg's European pressing technique, Korean prints involved hand-pressing
procedure using wood sticks or cotton lumps. Due to the uneven pressure, it often
lead to unclear lettering. Uneven ink coverage on metal types results in noisy 'dots'
and 'holes' as shown in Fig. 1(a). Inconsistent hand pressure causes slight movements of types, and it makes blurred
prints. Ink bleed can also caused by the long-fiber pulps that were not removed during
the procedure of making paper, as seen in the lower box. This makes character segmentation
networks trained with conventional loss functions produce unsatisfactory results with
rough strokes, noisy dots, and holes, as illustrated in Fig. 1(b).
Fig. 1. Example of a low-quality printed document image. (a) Scanned image. (b) Character
extraction result obtained using a conventional segmentation network. (c) Ground truth
image.
To create a new dataset, modifying results obtained using pre-trained models is common.
Fig. 1(c) shows the ground truth (GT) label for Fig. 1(a). Due to the low print quality, generating consistent GT labels is challenging. Stroke
boundary ambiguity leads to rough and bumpy boundaries in the pretrained model predictions.
Fig. 2 shows part of the ground truth (GT) hand-refined by our researchers. When producing
a large amount of GT by hand, occasional human errors occur at the bit-scale. This
is shown as red in Fig. 2(d), and such low-quality GT disturb proper training of the networks.
Fig. 2. Example of hand-refined drawn GT by researchers. (a) Original image patch.
(b) Parts of image patch. (c) Parts of hand-refined GT. (d) Example of errors in the
hand-refined GT, highlighted in red.
This study focuses on the effectiveness of the boundary distance loss technique for
denoising, facilitating more efficient information retrieval from ancient texts [8]. The proposed Smoothed Boundary Distance (SBD) loss is designed to enhance the accuracy
of character extraction and reduce processing time for ancient Korean metal type printed
documents. Unlike many character segmentation studies that focused on low-noise environments
[9,
10], our method is designed to operate in challenging environment where both the input
image and the GT contain noise. Our goal is not merely to extract the printed part
as it is, but to produce results that are closer to the original form of the characters,
with smooth boundaries and without noise. The SBD loss measures the deviation between
the predicted character stroke boundaries and the GT's counterparts. Instead of calculating
distances by directly comparing corresponding pixels like brute-force approach, the
SBD loss utilizes the difference between boundary pixel values from Gaussian-smoothed
version of the GT for computational efficiency. Consequently, in an environment where
the GT contains errors, the proposed method shows superior stroke extraction results
compared to conventional methods and it reduces the roughness of stroke boundaries,
and leads the segmentation model to predict smoother stroke boundaries.
In Section 2, we review related works, followed by a detailed explanation of the proposed
Smoothed Boundary Distance loss in Section 3. In Section 4, we validate the performance
of the proposed method through experiments, and finally, in Section 5, we conclude
the paper.
2. Related Work
2.1. Character Segmentation
The analysis of scholarly articles indicates that character segmentation is crucial
for evaluating ancient documents, especially those with significant information loss.
Researchers typically divide character segmentation into three main stages to achieve
the desired outcomes: text line segmentation, word segmentation, and character segmentation
[11]. For both horizontal and vertical scripts, line segmentation is essential. Most scholarly
articles have focused on the importance of character segmentation in Arabic, Thai,
Chinese, and Japanese scripts. However there are studies that focusing on the Korean
language.
Ancient Korean documents are seldom investigated compared to modern Korean language
documents due to the complexity of character formation and segmentation challenges
[7].
Kim et al. studied Chinese character segmentation, primarily using recognition-based
methods for segmenting handwritten Korean text [12]. To reduce evaluation errors, researchers emphasized character geometric features
and contextual information. In contrast, Mathieu et al. developed the image gradient
difference loss function to improve the quality of evaluation by calculating the gradient
difference at the boundaries [13]. Their results demonstrated more clear images with enhanced information sharing,
leading to better predictions for subsequent frames.
2.2. Gradient Difference Loss
Mathieu et al. worked on pixel-spaced video prediction by adopting an unsupervised
machine learning method by defining a new image gradient difference loss function
[13]. Different from total variation loss [14], the Gradient difference loss considers the difference between the gradient magnitude
of prediction image $\hat{Y}$ and GT image $Y$ for denoising. Let $\alpha$ be a hyperparameter
value that is greater than 1 and $(i, j)$ be the pixel position in the image. Then
$L_{GD}$ is defined as
2.3. Boundary Gradient Consistency Loss
Boundary gradient consistency loss is designed to ensure the consistency of character
boundary gradient vectors [15]. This function was developed specifically for smoothing the boundary lines of characters
printed using the Korean movable metal type. It involves comparing the gradient magnitude
of an anchor (center) pixel with the maximum gradient magnitude among its neighboring
pixels.
To tailor the range of neighboring pixels considered by an anchor pixel, resizing
parameter is defined. When the resolution of the input image is high, considering
only the nearest pixel may be ineffective. Although the loss function smoothens the
boundary, if the considered range is too small, the final result may appear unrefined.
To address this issue, a resizing parameter $s$ is introduced to expand the range
of consideration. Consequently, the anchor pixel accounts for a $s * s$ range of neighboring
pixels. $L_{BGC}^s$ is defined as
where $\hat{B}$ is set of boundary pixels from $\hat{Y}$ and $(i, j)$ is anchor pixel
in $\hat{Y}$. $N(i, j)$ is a set of neighboring pixels around anchor pixel $(i, j)$
and $|\nabla \hat{Y}_{k,l}^s|$ is magnitude of $(k,l)$. Then, maximum gradient magnitude
position $(i^*, j^*)$ is defined as
3. Proposed Method
Boundary distance measures how far the set of boundary pixels in prediction image
$\hat{Y}$ is from the set of boundary pixels in ground truth image $Y$, as illustrated
in Fig. 3 where $Y$ and $\hat{Y}$ are indicated in blue and green, respectively.
The SBD loss is proposed to smooth the boundaries of characters in the process of
extracting characters from scanned documents. To do this, the proposed loss function
calculates boundary distance using the Gaussian blurring on $Y$. This difference is
illustrated in Fig. 3. If the boundary line of the characters in $\hat{Y}$ is rough, the distance from
$\hat{Y}$ to $Y$ will be higher and the loss value will be larger. This method makes
the boundary line of $\hat{Y}$ be as smooth as $Y$. Unlike kernel distance [16], using Gaussian blur instead of Euclidean distance allows to use an optimal method
that does not use a brute-force approach when calculating the distance between an
arbitrary prediction pixel coordinate and the closest $Y$ pixel coordinate, and only
uses convolution instead of a loop. The architecture of this loss function is shown
in Algorithm 1, Fig. 4, and the expression is as follows:
Fig. 3. Boundary distance between GT and prediction. (a) A GT $Y$ and a prediction
$\hat{Y}$ are represented in blue and green, respectively. (b) Boundary distance between
GT and prediction.
Fig. 4. The process of the smoothed boundary distance loss calculation.
Algorithm 1: The smoothed boundary distance loss.
where $B$ is the boundary of image obtained using morphological operations. $(\cdot)
\ominus S$ and $\odot$ are erosion with $3 * 3$ erosion kernel matrix $S$ and element-wise
production, respectively. $G_\sigma(\cdot)$ is Gaussian smoothing function. $|B|$
is the cardinality of set $B$, that is, the number of boundary pixels. First, the
boundary lines of $\hat{Y}$ and $Y$ images, $\hat{B}$ and $B$ are obtained using the
erosion method. Next, we blur $Y$ using $G_\sigma(\cdot)$ to get $G$, and then perform
element-wise production to get the values of $\hat{B}$ and $B$ in $G$, finally calculate
their average with $|\cdot|$. The values of $V$ always have the same value in binary
image. However, since $\hat{B}$ is different between $B$, $\hat{V}$ has different
values. By examining the values at $\hat{V}$, we can simply determine the distance
between $Y$ and $\hat{Y}$. Therefore, we get the final loss value by taking the difference
between the average of the values of $V$ and $\hat{V}$ in $G$.
If the $\sigma$ in $G_\sigma(\cdot)$ is too small compared to the width of the object,
the value of the corresponding pixel in $G_\sigma(Y)$ becomes nearly zero even at
a slight distance from the character boundary. This results in excessively large distances
between the pixels, represented as “diff” in Fig. 5, when calculating the distance between the input boundary and the GT boundary. Consequently,
many distance values may be fixed at their maximum, making the loss function less
sensitive to variations in distance. Additionally, the blur is applied too weakly
to the input image, failing to sufficiently smooth the bumpy character boundaries.
On the other hand, if the $\sigma$ is too large, the pixel distances become too small,
and it makes the loss function less sensitive to variations in distance. Moreover,
the excessive blur prevents proper extraction of information from the original image.
Fig. 5 explains how to calculate the Gaussian distance. To simplify the explanation, we
slice a line of the character image and describe it as one-dimensional data. The value
in $\hat{V}$ moves farther from $\hat{Y}$ as the distance between $Y$ and $\hat{Y}$
increases. This difference is ”diff”, represented by the red arrows. The closer $Y$
is to $\hat{Y}$, the more sensitive the value of the distance difference is, since
the Gaussian blur also acts as a weight. This feature makes the loss function sensitive
to small differences between $Y$ and $\hat{Y}$, leading to precise results. Also,
if the distance between $Y$ and $\hat{Y}$ is large, the effect of outlier noise can
be ignored by fixing the value of loss to the maximum value. This method can guide
the boundaries of the extracted letters to be smooth while removing noise far from
the letters. Since SBD loss focuses on the outline of the stroke, using SBD loss alone
will result in poor stroke extraction performance. Therefore, we use SBD loss in combination
with other loss function.
Fig. 5. Algorithm overview of the proposed smoothed boundary distance loss.
4. Experimental Results
4.1. Dataset
We scanned old Korean documents to create a dataset. The majority of these documents
were scanned at a resolution of 600 dpi, while a subset was scanned at 300 dpi. Following
the scanning process, we binarized the images to serve as GT. To augment our dataset,
we extracted patches of size 1024x1024 pixels from the scanned images. Through this
process of data augmentation, we generated a total of 13,500 patches, which comprise
our dataset. These patches are divided into a training set of 12,150 patches and a
validation set of 1,350 patches.
4.2. Evaluation of Hyperparameter
To evaluate the effectiveness of the proposed loss function, we trained the TransUNet
[17] network for 40 epochs by Python. We conducted experiments with various $\sigma$ values
to determine the optimal parameter $\sigma$ used in $L_{SBD}^\sigma$.
The widths of the characters in our dataset vary significantly, ranging from 5 to
40 pixels, even in 600 dpi resolution data. Additionally, the width of the characters
differs from book to book. Due to this wide variation, we could not be certain that
the resolution of the image and the character width were proportional. Therefore,
without considering the resolution of the input images, the initial $\sigma$ was determined
approximately, and the optimal value was then searched through experimentation. Table 1 presents the results of $L_D + L_{SBD}^\sigma$ after 40 training epochs using different
sigma values. Our experiments showed that a $\sigma$ of 20 yielded the best performance.
Table 1. Character extraction model's performance comparison of the proposed SBD loss
in terms of dice coefficient with different $\sigma$'s.
|
$\sigma$
|
Dice score
|
|
10
|
0.9650
|
|
15
|
0.9638
|
|
20
|
0.9671
|
|
25
|
0.9649
|
|
30
|
0.9657
|
In this part, we extend our investigation to evaluate the effectiveness of the proposed
loss functions in handling character segmentation in input images with significant
noise, particularly those with poor print quality. This assessment aims to determine
whether the proposed loss function facilitates clear and consistent character extraction
under challenging conditions. Evaluating the performance on all validation sets is
not appropriate, as it is challenging to verify the effectiveness of SBD loss in handling
noisy input images. Therefore, we find a few cases with bad print quality in the validation
set and conduct further experiments. We selected 7 low-quality validation images that
from old printed document and denoised them with combination of dice loss [18] ($L_D$) and $L_{BGD}$ to get high dice score set (clearly extracted result).
And we denoised again with combination of $L_D$ and cross-entropy loss [19] ($L_{CE}$) to get low dice score set (badly extracted result). This resulted in 2
groups with good and bad denoising outcomes that have 7 images. The dice score of
Gaussian blur with $\sigma$ that ranging from 2 to 45 is plotted in Fig. 6, where the kernel size is $4 * \sigma + 1$. The blue line shows experimental results
of bad denoising group and the yellow line shows results of good denoising group.
With higher noise, the loss value should be larger. Larger differences between the
two lines means propose method can distinguish good and bad image. $\sigma$ between
20-30 performed best for this distinction. This experiment suggested appropriate hyperparameter
for the proposed loss function. After this section, we had set $\sigma$ to 20.
Fig. 6. Good and bad denoising results based on sigma.
4.3. Performance Comparing
We trained the TransUNet using a variety of loss functions, including those derived
from related works. Specifically, we compared the dice coefficient loss ($L_D$), cross-entropy
loss ($L_{CE}$), gradient difference loss ($L_{GD}$), gradient consistency loss ($L_{GC}$),
and our proposed SBD loss in terms of the dice score and standard deviation. The models,
each trained with a different loss function, were used to perform character extraction
on the validation set.
In the experiments, we combined different loss functions. Since $L_{GD}$ and $L_{GC}$
are not differentiable, backpropagation cannot be performed, making it impossible
to use them alone. Therefore, they were combined with other loss functions. When creating
these combinations, we referred to the combo loss [20] ($L_D+L_{CE}$) and incorporated dice loss as a component.
The values presented in Table 2 represent the average dice score and average F1 score across all predicted images.
The standard deviation was calculated based on each scores. A low standard deviation
across all validation images indicates a reliable performance by the loss function.
As depicted in Table 2, the combination of $L_D+L_{SBD}^\sigma$ achieved the highest dice score and the
lowest standard deviation, indicating that the proposed loss function facilitates
clear and consistent character extraction.
Table 2. Character extraction model's performance comparison of the proposed SBD loss
in terms of dice coefficient and F1 score with different $\sigma$'s.
|
Loss functions
|
Dice score
|
Dice STD
|
F1 Score
|
F1 STD
|
|
$L_D$
|
0.9653
|
0.0248
|
0.9976
|
0.0133
|
|
$L_D+L_{CE}$
|
0.9662
|
0.0303
|
0.9942
|
0.0254
|
|
$L_D+L_{GD}$
|
0.9626
|
0.0262
|
0.9975
|
0.0157
|
|
$L_D+L_{GC}$
|
0.9556
|
0.0235
|
0.9965
|
0.0136
|
|
$L_D+L_{SBD}^\sigma$
|
0.9671
|
0.0219
|
0.9976
|
0.0108
|
To discern the attributes of the SBD loss, we conducted a comparative analysis with
the $L_{CD}$ loss. The results of these supplementary experiments are presented in
Table 3.
Table 3. Result comparison between $L_D + L_{CE}$ and $L_D + L_{SBD}$. AVG is average
and STD is standard division. AVG and STD are abbreviations for average and standard
deviation, respectively.
|
|
Number of data
|
Total set
|
Bad set
|
Worst data
|
|
1,350
|
105
|
32
|
|
AVG
|
$L_D+L_{CE}$
|
0.9662
|
0.9486
|
0.9268
|
|
$L_D+L_{SBD}^\sigma$
|
0.9671
|
0.9512
|
0.9410
|
|
STD
|
$L_D+L_{CE}$
|
0.0286
|
0.0852
|
0.1521
|
|
$L_D+L_{SBD}^\sigma$
|
0.0219
|
0.0517
|
0.0916
|
In this table, 'AVG' refers to the average dice score, and 'STD' indicates the standard
deviation of the dice scores.
From a total of 1,350 validation set images, we curated a “bad set” comprising 105
images with subpar printing quality. Within this subset, we further identified the
“worst set” of 32 images, representing the most severely affected by poor print quality.
The experimental outcomes demonstrated that SBD loss consistently yielded higher dice
scores and lower standard deviations across all sets. Notably, the sets composed exclusively
of low-quality images exhibited substantial improvements, highlighting the superior
performance of SBD loss over $L_{CE}$ loss in processing images of inferior quality.
While the experimental results in Table 3 indicate that the proposed SBD loss performs better than other losses, the differences
are not substantial. Therefore, a qualitative evaluation was conducted to visually
assess the results, with some examples presented in Fig. 7.
In Fig. 7(a) to Fig. 7(d) compare the performance of $L_D+L_{CE}$ and $L_D+L_{SBD}^\sigma$. The leftmost image
is the input image, the second image is the GT, and the third and fourth images show
the results of the networks trained with $L_D+L_{CE}$ and $L_D+L_{SBD}^\sigma$, respectively.
Except for Fig. 7(a), where both methods produced good results, the remaining examples demonstrate the
superior performance of the SBD loss. For instance, in Fig. 7(b), $L_D+L_{CE}$ failed to fully fill the interior of the faintly printed character
and left small dot noise in the ‘灬’ part of the ‘為’ character. However, $L_D+L_{SBD}^\sigma$
handled these areas more effectively. In Fig. 7(c), $L_D+L_{SBD}^\sigma$ performed relatively better at removing the ink bleed caused
by the long-fiber pulps of the paper, as described in the introduction, compared to
$L_D+L_{CE}$. In Fig. 7(d), although both methods failed to completely fill the hole noise inside the ‘大’ character,
the proposed method did a better job of removing the outline traces to the right of
the ‘大’ character.
Fig. 7. Comparison of stroke extraction results with respect to various noises. Each
sub-figure shows the input image, the GT, and the results of models using $L_D + L_{CE}$
and the proposed loss ($L_D + L_{SBD}$) from left to right. (a) Example of a well
printed image. (b) Example of a weakly printed image with many hole and dot noises.
(c) Example of an image where the ink was smeared along paper fibers. (d) Example
of an image including the outline of the typesetting frame. If the image is clean
and the strokes are well printed, both the models predict characters well. For the
images with various noises, however, the conventional model fails to segment strokes
correctly and produces erroneous detection, while the proposed model effectively reduces
such noises and produces satisfying results.
5. Conclusion
In this paper, we proposed the smoothed boundary distance loss function, a significant
advancement for enhancing character segmentation in high-resolution scans of old Korean
printed documents. Our method diverges from traditional metrics by incorporating Gaussian
blur, which effectively smoothens character boundaries and reduces noise and outliers,
markedly improving segmentation clarity and accuracy. Although the SBD loss has the
limitation that it cannot actively respond to variations in the resolution of input
images, requiring the hyperparameter to be fitted through experimentation, it significantly
enhances the clarity and accuracy of character segmentation. Our experimental results
demonstrate the superiority of our proposed loss function, especially in comparison
with existing methods. The application of the smoothed boundary distance loss yielded
higher dice scores with low-quality input image, signifying a notable improvement
in character segmentation accuracy.
The Smoothed Boundary Distance loss function, optimized for character segmentation
in old document datasets where both the input data and GT contain noise, is expected
to make a substantial contribution to the quantitative analysis of character features
in the field of bibliography. This method proposes new possibilities for document
digitization and preservation research, making it a valuable tool for historical and
linguistic studies.
Acknowledgement
This research was supported by the Basic Science Research Program through the National
Research Foundation of Korea (NRF) funded by the Ministry of Education (RS-2025-24683900).
This work was supported by the BK-21 FOUR program through the National Research Foundation
of Korea (NRF) under the Ministry of Education.
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Woo-Seok Lee eceived the M.S. degree in electrical engineering from Korea University
of Technology and Education, in 2025. His research interests include loss function
and segmentation for reconstruction of historical documents.
Maaz Ahmed received the M.S. degree in electrical engineering from Korea University
of Technology and Education, in 2024. His research interests include 3D reconstruction,
pose estimation.
Kang-Sun Choi received his Ph.D. degree in nonlinear filter design in 2003, an M.S.
degree in 1999, and a B.S. degree in 1997 in electronic engineering from Korea University.
In 2011, he joined the School of Electrical, Electronics & Communication Engineering
at Korea University of Technology and Education, where he is currently a professor.
In 2017, he was a visiting scholar at the University of California, Los Angeles. From
2008 to 2010, he was a research professor in the Department of Electronic Engineering
at Korea University. From 2005 to 2008, he worked in Samsung Electronics, Korea, as
a senior software engineer. From 2003 to 2005, he was a visiting scholar at the University
of Southern California. His research interests are in the areas of deep learning-based
semantic segmentation, multimodal sensor calibration, human-robot interaction, and
culture technology. He is a recipient of an IEEE International Conference on Consumer
Electronics Special Merit Award (2012).