Handwriting Trajectory Recovery of Latin Characters with Deep

Learning: A Novel Exploring the Amount of Points per Character

and New Evaluation Method

Simone Bello Kaminski Aires

, Erikson Freitas de Morais

and Yu Han Lin

Department of Computing, Federal Technology University of Parana, Washington Subtil Chueire, Ponta Grossa, Brazil

Keywords: Deep Learning, Handwriting Trajectory Recovery, Handwriting Reconstruction.

Abstract: The research on handwriting trajectory recovery (HTR) has gained prominence in offline handwriting

recognition by utilizing online recognition resources to simulate writing patterns. Traditional approaches

commonly employ graph-based methods that skeletonize characters to trace their paths, while recent studies

have focused on deep learning techniques due to their superior generalization capabilities. However, despite

promising results, the absence of standardized evaluation metrics limits meaningful comparisons across

studies. This work presents a novel approach to recovering handwriting trajectories of Latin characters using

deep learning networks, coupled with a standardized evaluation framework. The proposed evaluation model

quantitatively and qualitatively assesses the recovery of stroke sequences and character geometry, providing

a consistent basis for comparison. Experimental results demonstrate the significant influence of the number

of coordinate points per character on deep learning performance, offering valuable insights into optimizing

both evaluation and recovery rates. This study provides a practical solution for enhancing HTR accuracy and

establishing a standardized evaluation methodology.

1 INTRODUCTION

Handwriting recognition involves transforming

handwritten graphical marks into digital signals,

enabling the interpretation of unique individual

writing styles (Plamondon and Srihari, 2000).

However, the variability in handwriting presents

significant challenges, particularly in generalizing

across different scripts and languages. Neural

networks have shown considerable potential in

addressing these challenges by learning to adapt to

diverse styles and input formats (Xiong, Dai, and

Meng, 2023; Gautam and Singh, 2022; Shaji, Shoba,

Jemimma, and Chester, 2023). Nevertheless, offline

handwriting recognition remains less accurate than

online recognition due to the lack of temporal and

dynamic information (Zhang, Bengio, and Liu, 2017).

To overcome this limitation, handwriting

trajectory recovery (HTR) systems have been

developed to reconstruct the temporal order of strokes

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from static images, providing dynamic information

that helps distinguish characters with similar

geometric forms (Noubigh and Kherallah, 2016).

Traditional HTR methods often rely on heuristic

approaches, such as graph-based skeletonization and

greedy algorithms, to approximate handwriting

trajectories (Dinh, Yang, Lee, Kim and Do, 2016).

Although these methods can be effective for simpler

cases, they lack the flexibility required to manage the

complexity and variability inherent in handwriting.

Deep learning techniques, including

Convolutional Neural Networks (CNNs) and Long

Short-Term Memory (LSTM) networks, have

significantly advanced the field of HTR by leveraging

their generalization capabilities to predict stroke

sequences from static handwriting images (Singh,

Rohilla and Sharma, 2024; Jayanna, Nagaraja,

Yadava, Deekshith, Seelam and Jamkhandi, 2024;

Lv, 2023; Qu, 2024). Recent studies have

demonstrated the successful integration of CNNs

with LSTMs to predict coordinate points, achieving

Aires, S. B. K., Freitas de Morais, E. and Lin, Y. H.

Handwriting Trajectory Recovery of Latin Characters with Deep Learning: A Novel Exploring the Amount of Points per Character and New Evaluation Method.

DOI: 10.5220/0013383100003912

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 20th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2025) - Volume 3: VISAPP, pages

855-862

ISBN: 978-989-758-728-3; ISSN: 2184-4321

855

promising results (Zhao, Yang, and Tao, 2019;

Zhang, Bengio and Liu, 2017; Wang, Sonogashira,

Hashimoto and Iiyama, 2019; Elbaati, Hamdi and

Alimi, 2019). However, the absence of standardized

evaluation methods is a limitation, as current research

relies on diverse proprietary metrics or statistical

coefficients with non-uniform thresholds (Kumar,

Bhowmick, Bhunia, Konwer, Banerjee, Roy and Pal,

2018; Zhao, Yang and Tao, 2019; Elbaati, Hamdi and

Alimi, 2019). This inconsistency hinders the

comparability of results across different HTR

systems.

In this context, the present study introduces a

novel HTR approach leveraging deep learning,

specifically targeting Latin lowercase characters from

the IRONOFF dataset. Unlike existing methods, this

work proposes a standardized evaluation framework

to assess the accuracy of predicted trajectories,

enabling consistent and comparable analyses.

Furthermore, the study systematically examines the

impact of varying the number of coordinate points per

character on model performance, offering valuable

insights for optimizing trajectory recovery and

evaluation methodologies.

The remainder of this paper is organized as

follows: Section 2 reviews related work on HTR,

Section 3 details the methodology and experimental

setup, Section 4 discusses the proposed evaluation

framework, Section 5 presents results and analysis,

and Section 6 concludes and future directions.

2 RELATED WORKS

Handwriting trajectory recovery (HTR) methods can

be broadly categorized into two main approaches:

heuristic algorithms and artificial

intelligence/machine learning-based techniques.

Heuristic algorithms, such as skeletonization and

graph-based pathfinding, have been widely utilized to

approximate handwriting trajectories (Noubigh and

Kherallah, 2016; Nguyen and Blumenstein, 2010).

Prominent examples include the use of Euclidean

path optimization in undirected graphs (Nagoya and

Fujioka, 2011) and code chain algorithms to recover

trajectories from character skeletons (Sharma, 2013).

Subsequently, (Sharma, 2015) extended this

approach by integrating dynamic and static features,

significantly improving handwriting recognition

performance.

Genetic algorithms have also been employed to

optimize trajectory paths, as demonstrated by

(Elbaati, Kherallah, Ennaji and Alimi, 2009), who

restored stroke chronology for Arabic handwriting

recognition. More recently (Jin, Ran, Yuan, Lv,

Wang and Xiao, 2024) introduced the Bagging in

Hidden Semi-Markov Model (BHSMM) algorithm,

which partitions demonstration data into sub-datasets,

encodes them using Hidden Semi-Markov Models

(HSMM), and derives task-specific weights to

enhance trajectory accuracy and robustness.

Deep learning has emerged as a transformative

approach in HTR, leveraging convolutional neural

networks (CNNs) and recurrent neural networks

(RNNs) for feature extraction and sequence

prediction. In work present by (Zhao, Yang and Tao,

2019) are developed a dual-CNN architecture to

extract static and dynamic writing energies,

combining them to recover the drawing order.

Similarly (Wang, Sonogashira, Hashimoto and

Iiyama, 2019) utilized a hybrid strategy with CNNs

and graph-cut algorithms to refine stroke order in

Chinese characters. Both approaches highlight the

integration of deep learning with heuristic techniques

to enhance performance.

Fully deep learning-based methods have also been

explored (Kumar, Bhowmick, Bhunia, Konwer,

Banerjee, Roy and Pal, 2018) proposed a CNN-

LSTM framework to generalize dynamic feature

learning across scripts, while (Elbaati, Hamdi and

Alimi, 2019) utilized a VGG-16 combined with a

beta-LSTM for trajectory recovery. However, these

studies lack consistent evaluation metrics, relying on

statistical measures such as Dynamic Time Warping

(DTW) and Root Mean Square Error (RMSE), which

require arbitrary thresholds. Others, like (Kumar,

Bhowmick, Bhunia, Konwer, Banerjee, Roy and Pal,

2018), adopted parameters from (Rousseau, Anquetil

and Camillerapp, 2005), or bypassed these metrics

entirely by integrating predicted trajectories into

online recognizers (Elbaati, Hamdi and Alimi, 2019).

While these methods represent significant

advancements, the lack of a standardized evaluation

framework hinders comparability across studies. To

address this limitation, our approach proposes a

universal evaluation system capable of assessing both

the geometric accuracy of predicted characters and

the correctness of coordinate sequences. This

framework ensures applicability and enhances the

reliability and consistency of HTR evaluations.

3 METODOLOGY

This section outlines the process of converting offline

data into online trajectories, detailing the dataset,

preprocessing, neural network architecture, training

process, and evaluation methods. The proposed deep

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neural network was inspired by the architecture

proposed by (Kumar, Bhowmick, Bhunia, Konwer,

Banerjee, Roy and Pal, 2018). We use their HTR

system as a start point experiment to perform the

handwriting recovery and develop our own deep

learning network to recover the handwriting

characters trajectory to make a benchmark.

3.1 Dataset

For the handwriting trajectory recovery task in this

work, the dataset must have both on/off information.

The experiments of this work are carried on the online

data of Latin IRONOFF (Viard-Gaudin, Lallican,

Knerr and Binter, 2015), the images are the drawings

of online coordinates.

The IRONOFF database contains both on-line and

offline information for each character. It’s composed

by 4.086 isolated digits and 21.364 isolates

characters. Our experiments only use the single

strokes of those isolates characters, which constitutes

a quantity of 10.685 characters. Seven datasets with

different levels of granularity were created, varying

the number of points per character to 20, 30, 40, 50,

60, 70, and 100 points.

3.2 Pre-Process

As mentioned before, we only use the on-line data

from the database, more specifically, the (x, y)

coordinates. The pre-processing stage are done in

those coordinates, and is following by three main

step: resizing, normalization and data augmentation.

3.2.1 Resizing

The goal is to resize the characters to 64x64. First, the

region of interest is translated by shifting the main

character to the origin (0, 0). This is achieved by

subtracting the smallest coordinate value from all

coordinate values.

Afterward, the resizing is computed as follows.

Assuming C represents all the coordinates of a

character and C(xi,yi) is a single coordinate from C,

the scaling ratios for the x and y axes are rx=W/64r

and ry=H/64, where W and H are the highest

coordinate values along the x and y axes. The new

coordinates are then calculated using Equation 1.

(1)

With that, the coordinates will be within the

limit of 64x64.

3.2.2 Normalization

In this phase, we want to standardize the amount of

the coordinates (x, y) of all samples. By applying the

Bresenham Algorithm (Bresenham, 1965), we

generate new points by connecting two coordinates.

We do this to all the coordinate pairs, this will

create the skeleton of the character. Then, the points

are sampled uniformly over the complete skeleton

trajectory by 20, 30, 40, 50, 60 and 70 points (points

per character). This will produce seven different

databases, each one will feed their own deep neural

network, that are used in the experiments.

3.2.3 Data Augmentation

Deep learning neural networks require large datasets

to achieve effective generalization (LeCun, Bengio,

and Hinton, 2015). Data augmentation enhances

dataset size and quality by applying transformations

to images, improving the network's performance

(Shorten and Khoshgoftaar, 2019).

For handwriting trajectory recovery (HTR),

careful selection of augmentation algorithms is

crucial to avoid harming the learning process.

Techniques like random erasing are unsuitable due to

limited data points, while transformations such as

color adjustments or noise injection are irrelevant due

to pre-processed, binarized images. Slight rotations,

however, are effective for character recognition tasks,

as they introduce variability in the dataset by rotating

samples between 1° and 359° (Shorten and

Khoshgoftaar, 2019). For HTR, this involves rotating

data points within each sample to enhance learning.

In Figure 1, the coordinates are drawn for

visualize the effect of rotation. We apply the rotation

on an central axis in four different angles: 30◦, 15◦,

−15◦ and −30◦ (1). With the original sample at 0◦, we

expand the dataset in five times compared the original

data amount.

Figure 1: Illustration of Rotation Augmentation.

3.3 Deep Neural Network

The two main networks used in this work are the

combination of CNN and Encoder- Decoder LSTM,

with a fully connected network with one layer and

two output. The offline images is the input of the

CNN, which have has main task extract the high level

Handwriting Trajectory Recovery of Latin Characters with Deep Learning: A Novel Exploring the Amount of Points per Character and New

Evaluation Method

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features of the characters. The set of features

extracted from the CNN are the high-level

representation of the trajectory of the character, that

are the input of the encoder-decoder LSTM network.

The encoder-decoder LSTM network will interpret

and translate the features in a dependency string,

which are the input of a fully connected layer, that

will produce the (x, y) coordinates (Figure 2).

In Figure 2, are presented the coordinates

prediction are done by a set of iterations. For each

iteration, a new coordinate is predicted and queued

behind the coordinates that are already has been

predicted. At the beginning, the set of coordinates are

empty. The second iteration already have the

coordinate of the first iteration, so the Decoder LSTM

will know that he has to predict the next coordinate

following.

Figure 2: CNN and Encoder-Decoder LSTM.

The numbers of iterations are the number of points

of the dataset. The main reason to normalize the

dataset to a fixed number of points is to increase the

learning process. If the network has to learn different

number of points from each sample, different weights

of the Decoder LSTM network will needed to be

refreshed; if the amount of points are the same, the

same weights for all samples are used.

We use the L1 distance to compute the fitness of

the network as follows:

(2)

In Equation 2, where 𝑧

𝑡

⃗

is the predicted

coordinate, 𝑍

𝑡

⃗

is the ground-truth coordinate and n

the amount of points of each sample.

3.3.1 Networks Parameters

We explore some variations of (Kumar, Bhowmick,

Bhunia, Konwer, Banerjee, Roy and Pal, 2018)

network by adding layers in both CNN and Encoder-

Decoder LSTM. We reach results that better fit for the

HTR problem on latin characters.

The network proposed by (Kumar, Bhowmick,

Bhunia, Konwer, Banerjee, Roy and Pal, 2018) have

six convolutional layers (CL) and two bidirectional

layers in each Encoder-Decoder LSTM, we call

netBh. Four additional configurations are tested in the

experiments. We call them net-v1, net-v2, net-v3 and

net-v4, respectively.

• netBh: 6 CL and 2 LSTM layers.

• net-v0: 6 CL and 3 LSTM layers.

• net-v1: 8 CL and 3 LSTM layers.

• net-v2: 12 CL and 3 LSTM layers.

• net-v3: 16 CL and 3 LSTM layers.

These architectures were tailored to determine the

effectiveness of deeper networks in processing

datasets with higher point densities per character.

3.3.2 Implementation Details

All the experiments are conducted on a serve with

Nvidia Ge-Force GTX Titan 6GB, i7-3770K CPU

and 8GB of memory. All coding with Python and the

Tensorflow framework.

The networks are trained with 200 epoch with

cross-validation. Samples are divided in 70%

training, 15% validation and 15% for test. The time

of training is directly proportional to the amount of

points of the dataset.

3.4 Evaluation Method

Evaluation methods in the literature often use

statistical metrics such as DTW, RMSE, and Pearson

Correlation to measure the similarity between

predicted coordinates and ground truth. While these

metrics indicate geometric similarity, they rely on

arbitrary thresholds that affect final accuracy, leading

to inconsistent results. Some metrics also include

stroke direction evaluation, but they lack

standardization.

The evaluation method described by (Kumar,

Bhowmick, Bhunia, Konwer, Banerjee, Roy and Pal,

2018) is less inconstant than those mentioned before.

By formalizing the first evaluation proposed by

(Rousseau, Anquetil and Camillerapp, 2005), the

metric can compute the accuracy by:

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• Starting Point (SP): Evaluates whether the

starting point of the sequence is correctly

predicted.

• Junction Points (JP): Measures accuracy in

determining the entry and exit paths at junction

points.

• Complete Trajectory (CT): Verifies if the entire

trajectory, including the starting point, is

correctly predicted.

Before applying those metrics, (Kumar,

Bhowmick, Bhunia, Konwer, Banerjee, Roy and Pal,

2018) also translate the output coordinate points of

the network to the nearest point on the ground truth

skeleton as a post processing step. In the research for

a standard evaluation measure, we could deduce that

the last one has a better potential to reflect the better

accuracy for the predicted results. However, in a

qualitative analysis, the experiments show the

inconsistency of the metric by assigns false positives

and false negatives to the predicted coordinate

sequence. The reason of these factors will be

described below.

Figure 3: Trajectory of the ’e’ character.

In Figure 3, the predicted trajectory (blue) has

been a little bit deviate from the ground-truth (green).

First of all, the post processing step is inaccurate. We

can see the case illustrated at Figure 3. The translation

step translates the crossing coordinates (indicated in

red) wrongly. We can see that the third coordinate are

not translated to the correct place, and it will be

considered a wrong prediction by the evaluation

method. But the prediction are not wrong, it just a

little bit deviated. This is a case of false negative and

occurs with various predicted samples.

Figure 4: Trajectory of the ’p’ character.

In the learning process, the network received a

specific coordinate order to learn. The test sample are

the same character, but the coordinate points are

ordered in the opposite order. The network can

predict what he learned and can estimate the

geometric form of the character. The coordinate

points sequence are inverse, but it is still a right

prediction. The example is show at Figure 4.

Translating the predicted points to the nearest

ground-truth coordinates can severely distort the

geometric shape of the predicted trajectory, leading to

an incorrect relationship between the prediction and

ground truth, as shown in Figure 5. This results in a

false positive, where the evaluation method classifies

the prediction as correct due to the correct stroke

direction, even though the geometric shape of the

character is inaccurate.

Figure 5: Trajectory of the ’r’ character.

By analysis the samples, the need of a precise

evaluation method to evaluate HTR deep learning

systems was noted. The last method mentioned

compute 15% samples of the test dataset incorrectly

(false positives and negatives), so the final accuracy

of the network are not accurate enough. The next

section, we will present a new evaluation method that

overcome the current scenario of the reliability lack

from HTR evaluation accuracy.

3.5 Proposed Evaluation Method

In this section, we present our proposed evaluation

method to evaluate the HTR deep learning systems.

To compute the evaluation of a HTR system, the

predicted online points have to be compared with the

online ground truth. Since the deep learning networks

prediction are slightly deviated from the ground-truth,

the comparison with them become a not simple task.

Our method can overcome this situation by using a

kernel to combine the predicted coordinate with the

ground-truth skeleton and output the correct result.

The evaluation process is described below.

The ground-truth skeleton is divided into N

segments, where the choice of N significantly impacts

the character's geometric representation. A high N

Handwriting Trajectory Recovery of Latin Characters with Deep Learning: A Novel Exploring the Amount of Points per Character and New

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value minimizes the impact of removing a single

segment, preserving the character's shape, while a

low N value causes greater deformation, potentially

rendering the character unrecognizable. Therefore, N

directly affects the final accuracy. Experiments reveal

that the higher the points per character (p/c), the

higher the N value required. A ratio between p/c and

N is established using a defined computation method,

as outlined in the Equation 3.

(3)

In Equation 3, N is the number of segments a

character will be divided into, and p/c denotes the

number of points per character. The floor function is

applied to convert the result into the largest integer

less than or equal to the computed value.

Once segmentation is complete, the character's

geometric form is evaluated by checking if the

predicted coordinates align with the ground-truth

coordinates. This is done using a kernel-based

technique, where the kernel slides along the ground-

truth skeleton to verify the presence of predicted

points in each segment. While Zhao, Yang, and Tao

(2019) use kernels referred to as top-1, top-5, and top-

10, this work employs a 5x5 kernel, equivalent to top-

25, to accommodate the larger image sizes used here.

The process, illustrated in Figure 6, ensures a

comprehensive evaluation of predicted trajectories.

In Figure 6, the white dots represent the predicted

coordinate points outputted by the deep neural

network. Each segment is colored by better

visualization. If the kernel found a predicted point,

the segment that the kernel is following is considered

predicted. If one of the segments of the character are

not predicted (in other words, no predicted points

were found in the sliding kernel covered area), means

that the network failed to predict the character.

Figure 6: 5x5 Kernel sliding the skeleton ground-truth.

The evaluation process ensures that predicted

points cover all segments of the original skeleton. If a

predicted point overlaps with two segments, it is

assigned to the segment that lacks a predicted point.

Once all segments are covered, the predicted points

are evaluated for their order.

As shown in Figure 7, segments are evaluated for

correct ordering by checking if at least one predicted

point from each segment aligns with the segment’s

sequence order. If such a combination exists, the

prediction order is considered correct. Multiple

combinations of predicted points and segments may

be valid.

Figure 7: Segments ordering.

In Figure 7, white dots represent predicted

coordinate points, and arrows illustrate an example of

correct ordering identified by the method. A

prediction is considered correct if it covers the

geometric shape of all segments from the ground-

truth skeleton and preserves the correct order of these

segments. This approach resolves the false positives

and false negatives identified in earlier methods.

4 RESULTS

We evaluate our system by using the existing

evaluation method (Complete Trajectory - CT) and

the proposed evaluation method. The metrics are

applied in all the data sets generated by the pre-

processing step. Table 1 and 2 show the accuracy of

the outputs from the network configuration of

(Kumar, Bhowmick, Bhunia, Konwer, Banerjee, Roy

and Pal, 2018) in all seven data sets.

Table 1: Accuracy from evaluation methods – part 1.

20p/c

30p/c

40p/c

Evaluation CT

84,6%

79,2%

71,9%

Proposed

91,4%

91,6%

7,8%

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Table 2: Accuracy from evaluation methods – part 2.

50p/c

60p/c

70p/c

100p/c

Evaluation

67,8%

56,1%

49,3%

32,0%

Proposed

86,0%

83,7%

79,5%

39,7%

The proposed evaluation can correct the false

positives and false negatives generated by the CT

method. The results show that the predictions are

quite better with our evaluation method. Six of seven

data sets show a very significant amount of

improvement. In the CT evaluation, the 20p/c and

70p/c have a difference of 36 points percentage, while

our evaluation method have only 12 points. Such

difference means that the CT evaluation doesn’t

compute with efficiency the predicted coordinates

with more points per character.

The Table 3 and Table 4 show all the network

developed in this work in all data sets in the two

evaluation methods.

Table 3: Accuracy from evaluation methods off all

networks – part 1.

Dat Set

net-v1

net-2

20p/c

85,29% - 90,75%

85,17% - 95,31%

30p/c

79,20% - 94,34%

81,18% - 95,14%

40p/c

74,33% - 92,51%

72,27% - 91,06%

50p/c

68,02% - 88,56%

66,42% - 87,97%

60p/c

60,84% - 86,59%

54,84% - 85,95%

70p/c

46,02% - 83,02%

55,04% - 86,93%

100p/c

29,87% - 44,82%

39,55% - 45,13%

Table 4: Accuracy from evaluation methods off all

networks – part 2.

Dat Set

net-v3

net-v4

20p/c

85,01% - 90,79%

81,89% - 85,17%

30p/c

79,23% - 92,39%

76,00% - 76,97%

40p/c

73,05% - 89,86%

67,81% - 76,42%

50p/c

64,11% - 86,46%

57,92% - 65,75%

60p/c

56,19% - 81,01%

51,57% - 59,24%

70p/c

48,37% - 78,27%

44,68% - 50,36%

100p/c

25,70% - 45,45%

25,28% - 23,29%

Is noticeable the accuracy difference between the

evaluations. We have improve the accuracy

considerably for the 70p/c data set in the net-v1, net-

v2 and net-v3 networks. Besides that, we show that

by resizing the amount of points per character and by

providing the network the right number of layers of

the network, the HTR can achieve better results, as

shown the result by 20p/c on net-v2 network.

5 CONCLUSION

The paper introduces a new evaluation method for

HTR systems that are more accurate comparing the

existing method. The proposed method utilizes the

kernel sliding system that can check if the predicted

points estimate the geometric form of the original

character, and the segmentation system simplifies the

evaluation of trajectory order sequence. The

experiments on the IRONOFF database also shown

that by normalizing and resizing the amount of points

per character can facilitate the network learning. Our

better results lay on the net-v2 on 20p/c, which

achieve 95,31% of accuracy.

Our great achieve it’s we provide a huge

improvement in the accuracy by proposing a more

efficient evaluation system, and a system to improve

the learning rate of the network, which is a important

and very challenge topic. Our network and evaluation

method effectively recover the trajectory of

handwriting from offline images of Latim characters.

In conclusion, Handwriting Trajectory Recovery

(HTR) is a key advancement in handwriting

recognition, transforming static images into dynamic

temporal data. Its versatility spans handwriting

recognition, robotic writing, historical manuscript

preservation, accessibility, and forensic analysis. By

recovering stroke sequences and geometric

structures, HTR enhances accuracy and enables

applications in multilingual systems and digital

design. Continued improvements in HTR methods

and evaluation will further expand its impact,

addressing complex handwriting challenges with

greater precision and adaptability.

ACKNOWLEDGEMENTS

The research leading to these results has received

support from the CAPES, Araucaria Foundation and

UTFPR-PG.

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