# Challenges and Applications of Automated Extraction of Socio-political
Events from Text (CASE 2021): Workshop and Shared Task Report

Ali Hürriyetoğlu
Koç University
Sarıyer, İstanbul, Turkey
<EMAIL_ADDRESS>
Hristo Tanev
European Commission
Ispra, Varese, Italy
<EMAIL_ADDRESS>
Vanni Zavarella
European Commission
Ispra, Varese, Italy
<EMAIL_ADDRESS>
Jakub Piskorski
Polish Academy of Sciences
Warsaw, Poland
<EMAIL_ADDRESS>
Reyyan Yeniterzi
Sabancı University
Tuzla, İstanbul, Turkey
<EMAIL_ADDRESS>
Erdem Yörük
Koç University
Sarıyer, İstanbul, Turkey
<EMAIL_ADDRESS>

###### Abstract

This workshop is the fourth issue of a series of workshops on automatic
extraction of socio-political events from news, organized by the Emerging
Market Welfare Project, with the support of the Joint Research Centre of the
European Commission and with contributions from many other prominent scholars
in this field. The purpose of this series of workshops is to foster research
and development of reliable, valid, robust, and practical solutions for
automatically detecting descriptions of socio-political events, such as
protests, riots, wars and armed conflicts, in text streams. This year workshop
contributors make use of the state-of-the-art NLP technologies, such as Deep
Learning, Word Embeddings and Transformers and cover a wide range of topics
from text classification to news bias detection. Around 40 teams have
registered and 15 teams contributed to three tasks that are i) multilingual
protest news detection, ii) fine-grained classification of socio-political
events, and iii) discovering Black Lives Matter protest events. The workshop
also highlights two keynote and four invited talks about various aspects of
creating event data sets and multi- and cross-lingual machine learning in few-
and zero-shot settings.

##  1 Introduction

Today, the unprecedented quantity of easily accessible data on social,
political, and economic processes offers ground-breaking potential in guiding
data-driven analysis in social and human sciences and in influencing policy-
making processes. The need for precise and high-quality information about a
wide variety of events ranging from political violence, environmental
catastrophes, and conflict to international economic and health crises has
rapidly escalated (Della Porta and Diani, 2015; Coleman et al., 2014).
Governments, multilateral organizations, and local and global NGOs present an
increasing demand for this data to prevent or resolve conflicts, provide
relief for those that are afflicted, or improve the lives of and protect
citizens in a variety of ways. For instance, Black Lives Matter protests
111http://protestmap.raceandpolicing.com, accessed on June 2, 2021., conflict
in Syria 222https://www.cartercenter.org/peace/conflict_resolution/syria-
conflict-resolution.html, accessed on June 2, 2021. and COVID-19 related
events
333https://en.wikipedia.org/wiki/Protests_over_responses_to_the_COVID-19_pandemic,
accessed on June 2, 2021. are only a few examples where we must understand,
analyze, and improve the real-life situations using such data.

A recent report from ReliefWeb 444https://reliefweb.int/report/world/trends-
armed-conflict-1946-2017, accessed on June 3, 2021. clearly demonstrates that
the number of wars and other armed conflicts is on an increasing trend. In
particular, the so-called internationalized conflicts are on a rise in the
last two decades. In this situation, it is important to provide solutions for
situation awareness, using various branches of artificial intelligence (AI),
natural language processing (NLP), machine learning (ML), and advanced
statistical methods.

In this clue, event detection and extraction plays an important role, because
of its capacity to detect conflict developments in news and social media and
to extract important information about them. Such information involves the
quantity and the profiles of the victims, the participating entities, the
conflict dynamics, its spatio-temporal characteristics, the weaponry used, as
well as infrastructural, technical and human impact. This information
extracted through various NLP methods can throw light on the intensity and the
trend development of each conflict, as it is reflected in the media. Event
detection has been used by political analysts to write their daily situation
reports for decision makers, to create long-term analyses, as well as for
conflict forecasting and prediction.

Automation offers scholars not only the opportunity to improve existing
practices, but also to vastly expand the scope of data that can be collected
and studied, thus potentially opening up new research frontiers within the
field of socio-political events, such as political violence and social
movements. Event information collection has long been a challenge for the NLP
community as it requires sophisticated methods in defining event ontologies,
creating language resources, and developing algorithmic approaches
(Pustejovsky et al., 2003; Tanev et al., 2008; Emanuela, 2018; Chen et al.,
2021). We believe that this workshop and the shared task contribute strongly
towards putting emphasis on this important technology, providing a gathering
point for scientists and developers in NLP, AI, conflict studies and related
areas.

Social and political scientists have been creating event databases such as
ACLED (Raleigh et al., 2010), EMBERS (Saraf and Ramakrishnan, 2016), GDELT
(Leetaru and Schrodt, 2013), ICEWS (O’Brien, 2010), MMAD (Weidmann and Rød,
2019), PHOENIX, POLDEM (Kriesi et al., 2019), SPEED (Nardulli et al., 2015),
TERRIER (Liang et al., 2018), and UCDP (Sundberg et al., 2012) for decades.
These projects and the new ones increasingly rely on machine learning (ML) and
NLP methods to deal better with the vast amount and variety of data in this
domain (Hürriyetoğlu et al., 2021). Nonetheless, automated approaches suffer
from major issues like bias, low generalizability, class imbalance, training
data limitations, ethical issues, and lack of recall quantification which
affect the quality of the results and their use drastically (Leins et al.,
2020; Bhatia et al., 2020; Chang et al., 2019; Yörük et al., 2021). Moreover,
the results of the automated systems for socio-political event information
collection may not be comparable to each other or not of sufficient quality
(Wang et al., 2016; Schrodt, 2020).

Socio-political events are varied and nuanced. Both the political context and
the local language used may affect whether and how they are reported.
Therefore, all steps of information collection (event definition, language
resources, and manual or algorithmic steps) may need to be constantly updated.
This leads us to a series of challenging questions such as: Do events related
to minority groups are represented well? Are new types of events covered? Are
the event definitions and their operationalization comparable across systems?
We organize the workshop on Challenges and Applications of Automated
Extraction of Socio-political Events from Text (CASE 2021)
555https://emw.ku.edu.tr/case-2021/, accessed on June 9, 2021. and the shared
task Socio-political and Crisis Events Detection
666https://github.com/emerging-welfare/case-2021-shared-task, June 12, 2021.
to seek answers to these and related questions, to inspire innovative
technological and scientific solutions for tackling the aforementioned issues,
and to quantify the quality of the automated event extraction systems.
Moreover, the workshop aims to trigger a deeper understanding of the
performance of the computational tools used and the usability of the resulting
socio-political event datasets. The workshop is co-located with the Joint
Conference of the 59th Annual Meeting of the Association for Computational
Linguistics and the 11th International Joint Conference on Natural Language
Processing (ACL-IJCNLP 2021).

We invited contributions from researchers in computer science, NLP, ML, AI,
socio-political sciences, conflict analysis and forecasting, peace studies, as
well as computational social science scholars involved in the collection and
utilization of socio-political event data. Social and political scientists are
interested in reporting and discussing their approaches and observe what the
state-of-the-art text processing systems can achieve for their domain.
Computational scholars have the opportunity to illustrate the capacity of
their approaches in this domain and benefit from being challenged by real-
world use cases. Academic workshops specific to tackling event information in
general or for analyzing text in specific domains such as health, law,
finance, and biomedical sciences have significantly accelerated progress in
these topics and fields, respectively. However, there is not a comparable
effort for handling socio-political events. We hope to fill this gap and
contribute to social and political sciences in a similar spirit. We invite
work on all aspects of automated coding of socio-political events from mono-
or multi-lingual text sources. This includes (but is not limited to) the broad
topics below.

Data:

collecting and annotating data, identifying the qualities, bias and fairness
of the sources, handling ethics, misinformation, privacy, and fairness
concerns pertaining to event datasets, respecting copyright of the sources at
the creation, dissemination, and release phases of an event dataset;

Task:

defining, populating, and facilitating event schemas and ontologies,
extracting events in and beyond a sentence, detecting event coreference and
event-event relations such as subevents, main events, and causal relations,
investigating lexical, syntactic, and pragmatic aspects of event information
manifestation, determining socio-poltical events pertaining to societal issues
such as COVID-19 and BLM, detecting novel events;

Approaches:

developing rule-based, machine learning, hybrid, and human-in-the-loop
approaches for creating event datasets; and

Evaluation:

evaluating event datasets in light of reliability and validity metrics,
estimating what is missing in event datasets using internal and external
information, utilizing event datasets, releasing of new event datasets.

We provide summaries of the accepted papers, the shared task, keynotes, and
invited talks in the sections 2, 3, 4, and 5 respectively. Section 6 concludes
this report with main lessons derived from these efforts and interactions.

##  2 Accepted Papers

The workshop attracted 21 submissions. The competition was high and 7 of them
were accepted based on reviewer evaluations, which vary between 4 and 6 for
each paper.

Here are brief descriptions of all accepted papers, except from the ones
participating in the shared task, which are described in other papers in this
proceedings:

de Vroe et al. (2021) present an open domain, lexicon-based event extraction
system that captures various types of event modality. The definition of
“event” in this work is quite broad, i.e. every predicate construction is
taken into consideration. The authors use syntactic parsing to detect the
event modality, which is a very important phenomena when making distinction
between current, past and just probable events. The system explores
conditionality, counterfactuality, negation, and propositional attitude. The
achieved accuracy in the modality labelling task is 0.81 F1 that is measured
on a small corpus of 100 manually annotated predicates.

Raza (2021) explores the topic of detecting fake news, which is potentially
related to the trustability of the sources, from which events are extracted.
The main approach in this study is based on a modified version of a pre-
trained Bidirectional Encoder Representations from Transformers (BERT) with
the capability to receive as input news-related and side information. In
particular, each news item is represented by its title (main information) and
side information, such as temporal, news-related information, author and
source, as well as social contexts (related tweets) which give information
about users’ reactions on the news. The proposed model is quite promising,
considering it outperforms all other state-of-the-art methods. It achieves 96%
accuracy in deciding between fake and real news on a test set with fake and
real news nearly equally represented.

Caselli et al. (2021) explore how efficiently a retrained BERT model detects
protest events. Authors present the PROTEST-ER system, which uses a retrained
BERT model for protest event extraction. They use annotated event data from
the protest event detection task following the 2019 CLEF ProtestNews Lab
(Hürriyetoğlu et al., 2019a, b). A worth-to-mention finding of this work is
that PROTEST-ER outperforms a corresponding generic BERT with 8.1 points.

Ramrakhiyani et al. (2021) describe a deep learning approach for detecting
incidents from industrial reports. Incidents in industries have huge social
and political impacts. However, automated analysis of repositories of incident
reports has remained a challenge. Due to absence of event annotated datasets
for industrial incidents authors employ a transfer learning based approach. A
detailed analysis is provided on how amount of data utilized affect pre-
training and why pre-training improves the performance. Data is gathered from
aviation and construction incident reports. Different deep learning methods
are evaluated for the task, including BiLSTM and transfer learning. Transfer
learning consistently outperforms the baseline and achieves F1 measure of
0.81.

Radford (2021) presents a study on geocoding and a new data set. Geocoding is
an important sub-task of event detection, in which the goal is to find the
geographic coordinates associated with event descriptions. The paper presents
an “end-to-end probabilistic model” for geocoding from text data. A novel data
set has been created for evaluating the performance of geocoding systems. The
output of the new model is compared with a state-of-the-art model, called
Mordecai. The comparison clearly shows an improvement provided by the proposed
model.

Scharf et al. (2021) report on a study on the political bias in Hong Kong
published news reporting about protest events. The paper reports on lexical
differences between home and Western news sources about protests happening in
Hong Kong in the period 1998-2020. Experiments on topic modeling, sentiment
analysis, lexical distribution and comparative lexical analysis between
Western- and Hong Kong-based sources reveal a bias in the reporting from the
Hong Kong press. The evaluation reveals that during the Anti-Extradition Law
Amendment Bill Movement reports from Hong Kong made fewer references to police
violence compared to the Western media. The study also reveals that the
lexical contexts of salient keywords changed in Hong Kong sources when the
Movement emerged.

Kar et al. (2021) describe an algorithm for event argument detection and
aggregation. The paper reports on document level aggregation of the following
argument types: Time, Place, Casualties, After-Effect, Reason, and
Participant. The ArgFuse algorithm is based on a BERT based active learning
classifier, which identifies whether a pair of event arguments is redundant,
and a Biased Text Rank argument ordering function. Authors report F1 measure
of 0.61, which beats all the other 5 baseline algorithms with which the
ArgFuse performance is compared.

##  3 Shared Task: Socio-political and Crisis Events Detection

The work on event database creation comprises of three steps that are
collecting events, classifying them, and measuring utility of the system
output, which is an event database, against ground-truth. Each of these steps
contains pitfalls and subject to limitations. For instance, the data source
utilized maybe biased or a ground-truth may not be available. Although
aforementioned issues in socio-political and crisis event studies have been
studied by numerous scholars for decades to date, there are still no answers
or solutions to them Wang et al. (2016); Lorenzini et al. (2016); Schrodt
(2020); Raleigh (2020); Eck (2021); Boschee (2021). Therefore, we aim at
contributing to the understanding and resolution of event database creation
via quantifying performance of the state-of-the-art text processing systems in
the shared task Socio-political and Crisis Events Detection. 777
https://github.com/emerging-welfare/case-2021-shared-task, accessed on June 9,
2021.

The shared task consists of three tasks that are on collection (Task 1),
classification (Task 2) (Haneczok et al., 2021), and evaluation (Task 3) of
event databases. Shared task and submission details are reported in the
overview papers of the tasks (Hürriyetoğlu et al., 2021; Haneczok et al.,
2021; Giorgi et al., 2021) and the system description papers in this
proceedings respectively. We provide a summary of the tasks and the findings
in the following subsections.

###  3.1 Task 1: Multilingual protest news detection

The task is designed to be both multilingual (having both training and test
data in English, Portuguese, and Spanish) and cross-lingual (having data in
Hindi only for test). There are four subtasks that are document classification
(subtask 1), sentence classification (subtask 2), event sentence
classification (subtask 3), and event extraction (subtask 4). Event
information is at the center of all of the subtasks, i.e. documents and
sentences are classified as containing event information in subtasks 1 and 2,
sentences that are about the same event are identified in subtask 3, and event
trigger and its arguments are extracted in subtask 4.

13 teams have submitted 238 submissions for the evaluation scenarios specified
with subtask and language combinations. The best submissions utilized deep
learning approaches that combine the training data in various languages,
utilize large models, further re-train the models, and create ensemble models
(Awasthy et al., 2021; Hettiarachchi et al., 2021; Re et al., 2021; Hu and
Stoehr, 2021; Tan et al., 2021). Although training data was limited in
Portuguese and Spanish and not available in Hindi, the best performing
participants managed to deliver predictions that are between 77.27 and 93.03
F1-macro in subtasks 1, 2, and 3 for all languages. The performance of the
best system for subtask 4 for all languages was between 66.20 and 78.11 for
all languages and 4-5 F1-macro points ahead of all other teams in all
languages.

###  3.2 Task 2: Fine-grained Event Classification in News-like Text Snippets

Task 2 aims at evaluating conventional and generalized zero-shot learning
event classification approaches to classify short text snippets reporting
socio-political and crisis events. The task is divided into three subtasks:
(a) classification of text snippets reporting socio-political events, using 25
events classes from the Armed Conflict Location and Event Data Project (ACLED)
event taxonomyRaleigh et al. (2010), for which vast amount of training data
exists, although exhibiting slightly different structure and style vis-a-vis
test data, (b) enhancement to a generalized zero-shot learning problem, where
3 additional event types were introduced in advance, but without any training
data (‘unseen’ classes), and (c) further extension, which introduced 2
additional event types, announced shortly prior to the evaluation phase. Task
2 focuses on classification of events in English texts and the event
definitions of events in this task are not fully compatible with those in Task
1.

8 teams registered, out of which 4 returned system responses, for Task 2. Best
performing systems for the subtask 1, 2 and 3 achieved 83.9%, 79.7% and 77.1%
weighted $F_{1}$ scores respectively. Most of the solutions submitted are
built on top of fine-tuned Transformer-based models like Bert and RoBERTa.
Given the specific set up of this task, i.e., the training data being some-
what different from the test data and inclusion of some unseen classes the top
results obtained can be considered good, however, there is place for
improvement.

###  3.3 Task 3: Discovering Black Lives Matter events in United States

Task 3 is only an evaluation task where the participants of Task 1 have the
possibility to evaluate their systems on reproducing a manually curated Black
Lives Matter (BLM) related protest event list. Participants use document
collections, provided by the organizers and different from the documents from
where Gold Standard has been extracted, to extract place and date of the BLM
events in these collections. The event definition applied for determining
these events is the same as the one facilitated for task 1. Participants may
utilize any other data source to improve performance of their submissions. The
goal of the task is to achieve as high correlation as possible with the events
from the Gold Standard, as computed by aggregating events on a regular cell
geographical grid..

5 teams that performed the best in Task 1 were invited to participate in this
task. In general all participating systems showed low levels of correlation
with the Gold standard data, including the baseline system. The low recall at
this year’s shared task is most probably due to the low coverage of the test
corpus, which participating systems have used, and its poor overlapping with
manually collected Gold Standard Data. Two systems showed a relatively good
performance: NoConflict Hu and Stoehr (2021) and EventMiner Hettiarachchi et
al. (2021). The main lesson from this task is that Gold Standard data and test
data should be checked for consistency and correlation. Moreover, this
evaluation task highlighted some of the current limits on the usability of
automatically extracted event datasets for modelling socio-political
processes, such as fine-grained geocoding of events.

##  4 Keynotes

Kristine Eck and Elizabeth Boschee will deliver the keynote talks. Eck (2021)
addresses the responsibility of the scholars that create event datasets to
define and apply what is right, suggests data sources alternative to news data
that may report event information inconsistently, and emphasizes the need for
interdisciplinary collaboration for creating data sets that advance conflict
studies. Boschee et al. (2013); Boschee (2021) share the concerns addressed by
Prof. Eck and presents a detailed study that compares various approaches for
utilizing multilingual data in a cross-lingual zero-shot setting to improve
quality of the event datasets.

##  5 Invited Talks

The workshop contains an invited talks session as well. The authors of the
papers published in Findings of ACL and related to workshop theme are invited
to present their work in this session. The papers are

Zhou et al. (2021)

propose an event-driven trading strategy that predicts stock movements by
detecting corporate events from news articles;

Halterman et al. (2021)

introduce the IndiaPoliceEvents Corpus—all 21,391 sentences from 1,257 Times
of India articles about events in the state of Gujarat during March 2002;

Halterman and Radford (2021)

show utility of “upsampling” coarse document labels to fine-grained labels or
spans for protest size detection; and

Tsarapatsanis and Aletras (2021)

discuss the importance of academic freedom, the diversity of legal and ethical
norms, and the threat of moralism in the computational law field.

##  6 Conclusion

This workshop is the fourth event from a series of workshops on automatic
extraction of socio-political events from news, organized by the Emerging
Market Welfare Project, with the support of the Joint Research Centre of the
European Commission, with contributions from many other prominent scholars in
this field. The purpose of this series of workshops is to foster research and
development in the area of event extraction of socio-political events.

The topics cover a wide range of applications and technologies: event
detection via text classification, detection of news bias, fake news
detection, modality analysis through syntactic parsing, event argument
extraction and aggregation, a new geo-coding algorithm and the creation of a
new geocoding dataset. Most of the papers are dedicated to protest events, one
paper is about industrial reports, and one paper discusses generic events, not
related to the socio-political topic.

The papers in this issue of the workshop make use of state-of-the-art NLP
technologies, such as Deep Learning, Word Embeddings and Transformers. Most of
the papers use the BERT model: some use the pre-trained existing models,
others train domain-specific ones, and one of the paper introduces a modified
version of BERT. Most papers use BERT embeddings as features in their models
and one paper discusses an algorithm, which uses a full syntactic parser.
Sentiment analysis is used in one paper, which studies the political bias of
the news.

The shared task results shed light on critical aspects of the automated socio-
political extraction and evaluation methodology. 888Detailed results are
summarized in the overview papers (Hürriyetoğlu et al., 2021; Haneczok et al.,
2021), and evaluation (Task 3) (Giorgi et al., 2021) of event databases.
Moreover, system description papers provide full details

## Acknowledgments

The authors from Koc University were funded by the European Research Council
(ERC) Starting Grant 714868 awarded to Dr. Erdem Yörük for his project
Emerging Welfare.

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# Content-Aware Quantization Index Modulation: Leveraging Data Statistics for
Enhanced Image Watermarking

Junlong Mao, Huiyi Tang, Shanxiang Lyu, Zhengchun Zhou, Xiaochun Cao  Junlong
Mao, Huiyi Tang and Shanxiang Lyu are with the College of Cyber
Security/College of Information Science and Technology, Jinan University,
Guangzhou 510632, China (Emails<EMAIL_ADDRESS><EMAIL_ADDRESS>lsx07@jnu.edu.cn). Zhengchun Zhou is with the
School of Mathematics and the Key Laboratory of Information Coding and
Wireless Communications, Southwest Jiaotong University, Chengdu 611756, China
(E-mail: zzc@swjtu.edu.cn). Xiaochun Cao is with the School of Cyber Science
and Technology, Sun Yat-sen University, Shenzhen Campus, Shenzhen 518107,
China (E-mail: caoxiaochun@mail.sysu.edu.cn). This work has been submitted in
part to 2023 IEEE Global Communications Conference (GLOBECOM) for possible
presentation.

###### Abstract

Image watermarking techniques have continuously evolved to address new
challenges and incorporate advanced features. The advent of data-driven
approaches has enabled the processing and analysis of large volumes of data,
extracting valuable insights and patterns. In this paper, we propose two
content-aware quantization index modulation (QIM) algorithms: Content-Aware
QIM (CA-QIM) and Content-Aware Minimum Distortion QIM (CAMD-QIM). These
algorithms aim to improve the embedding distortion of QIM-based watermarking
schemes by considering the statistics of the cover signal vectors and
messages. CA-QIM introduces a canonical labeling approach, where the closest
coset to each cover vector is determined during the embedding process. An
adjacency matrix is constructed to capture the relationships between the cover
vectors and messages. CAMD-QIM extends the concept of minimum distortion (MD)
principle to content-aware QIM. Instead of quantizing the carriers to lattice
points, CAMD-QIM quantizes them to close points in the correct decoding
region. Canonical labeling is also employed in CAMD-QIM to enhance its
performance. Simulation results demonstrate the effectiveness of CA-QIM and
CAMD-QIM in reducing embedding distortion compared to traditional QIM. The
combination of canonical labeling and the minimum distortion principle proves
to be powerful, minimizing the need for changes to most cover
vectors/carriers. These content-aware QIM algorithms provide improved
performance and robustness for watermarking applications.

###### Index Terms:

watermarking, quantization index modulation (QIM), data-driven, minimum
distortion

##  I Introduction

Digital watermarking is a technique used to embed information or digital
markers into digital media, such as images, videos, audio files, or documents,
without significantly altering the perceptual quality of the content [1, 2].
This embedded information, known as a watermark, serves various purposes,
including copyright protection, content authentication, and data integrity
verification. It plays a crucial role in protecting the rights and integrity
of digital media in an increasingly digital and interconnected world [3, 4,
5].

Quantization index modulation (QIM) [6] is a popular data hiding paradigm due
to its considerable performance advantages over spread spectrum techniques. It
excels in terms of information hiding capacity, perceptual transparency,
robustness, and tamper resistance. QIM has been tailored to meet the demands
of many applications. Some examples include angle QIM (AQIM) [7] and
difference angle QIM (DAQIM) [8] for resisting gain attacks, dither-free QIM
[9] to reduce the amount of synchronization information, $E_{8}$ lattice-based
QIM [10] for enjoying the trade-off between computational complexity and
robustness performance, the Tucker decomposition-based QIM [11] for robust
image watermarking, and minimum distortion QIM (MD-QIM) [12] by moving the
data point to the boundary of Voronoi regions to achieve smaller distortions.

Digital watermarking techniques have continuously evolved to meet the emerging
challenges and threats in the field. One notable trend is the emergence of
data-driven watermarking methods, which leverage advanced technologies such as
machine learning and blockchain algorithms to generate and embed watermarks
that are specifically tailored to the unique characteristics of the media
content [13, 14]. These data-driven approaches have shown promise in enhancing
the robustness and imperceptibility of watermarking algorithms. Advancements
in technology have played a significant role in the development of robust and
imperceptible watermarking algorithms. Researchers have explored various
techniques and methodologies to improve the performance of watermarking
systems. Robustness refers to the ability of a watermark to withstand attacks
and intentional modifications, while imperceptibility refers to the extent to
which the embedded watermark is perceptually invisible to human observers.

Several approaches have been proposed to enhance the robustness and
imperceptibility of watermarking algorithms. Hybrid methods that combine
multiple watermarking techniques, such as transform-based methods and spread
spectrum techniques, have demonstrated improved performance in terms of both
robustness and imperceptibility [15, 16]. These hybrid approaches leverage the
strengths of different techniques to achieve a balance between robustness and
imperceptibility. Furthermore, comprehensive surveys and studies have been
conducted to analyze the effectiveness of existing watermarking algorithms and
identify areas for improvement [17]. These studies provide valuable insights
into the strengths and limitations of different approaches and offer
guidelines for developing more robust and imperceptible watermarking
techniques.

However, despite the progress made in robust and imperceptible watermarking
algorithms, there remains a need for further exploration of how data can be
effectively exploited to enhance QIM and its variants for image watermarking.
While data-driven watermarking techniques have shown promise in other domains,
their application and effectiveness in the context of QIM-based watermarking
are still relatively unexplored.

In this work, instead of relying on machine learning or blockchain, we propose
a data-driven watermarking scheme by leveraging the statistics of data. Our
goal is to enhance QIM or its variants by capturing the actual statistics of
the data to be embedded. We employ lattices as a fundamental tool for
theoretical analysis.

The contributions and highlights of this paper are as follows:

  * •

We introduce two novel approaches for image watermarking: Content-Aware QIM
(CA-QIM) and Minimum-Distortion Content-Aware QIM (CAMD-QIM). These methods
aim to achieve small-distortion watermarking while leveraging the statistical
characteristics of the input messages and carriers. The core concept of our
proposed approaches is to adaptively adjust the codebooks used for
quantization in QIM based on the statistical properties of the input data. By
doing so, we can effectively reduce the embedding distortion while maintaining
robustness and applicability across different types of host signals and
lattice bases.

  * •

Exploiting tools from lattices and probability theory, we derive the mean
square error (MSE) formulas of CA-QIM and CAMD-QIM. The derived results
demonstrate that CA-QIM outperforms original QIM, while CAMD-QIM outperforms
MD-QIM. We also derive the upper bound of the symbol error rate (SER) in
additive white Gaussian noise (AWGN) channels. Our approach does not rely on
the specific distribution of the host signals, thus showing positive effects
on MSE, which is consistent with the simulation results.

  * •

Numerical simulations justify the excellent performance of the proposed CA-QIM
and CAMD-QIM. We adopt the discrete cosine transform (DCT) as the transformed
domain for image processing. By embedding watermarks into the DCT domain, both
of the proposed methods excel in terms of imperceptibility, embedding
capacity, and SER. The simulation results demonstrate the merits of CA-QIM and
CAMD-QIM, both of which outperform their counterparts.

This paper is organized as follows. Section II introduces the preliminaries of
lattices and quantization index modulation. Section III presents the proposed
CA-QIM and CAMD-QIM. In Sections IV, we analyze the distortion and SER of the
two methods. Section V shows the simulation results. Conclusions are drawn in
the final section.

##  II Preliminaries

This section provides a brief overview of the fundamental concepts and
parameters related to lattices [18, 19] and Quantization Index Modulation
(QIM) [6, 9].

###  II-A Lattices

An $N$-dimensional lattice $\Lambda$ in $\mathbb{R}^{N}$ is defined as a
discrete additive subgroup
$\Lambda=\left\\{\mathbf{Gz}|\mathbf{z}\in\mathbb{Z}^{N}\right\\}$, where
$\mathbf{G}$ represents a set of $N$ linearly independent basic vectors
$\mathbf{g}_{1},\ldots,\mathbf{g}_{N}$ in $\mathbb{R}^{N}$. Figure 1
illustrates a three-dimensional lattice. The nearest neighbor quantizer
$Q_{\Lambda}(\cdot)$ is defined as the function that maps a point $\mathbf{x}$
to its nearest lattice point:

$Q_{\Lambda}(\mathbf{x})=\mathop{\arg\min}_{\mathbf{\lambda}\in\Lambda}\left|\mathbf{x}-\mathbf{\lambda}\right|.$
(1)

The Voronoi cell $\mathcal{V}_{\lambda}$ of a lattice point
$\lambda\in\Lambda$ is the set of points which are closer to $\lambda$ than
any other lattice points:

$\mathcal{V}_{\lambda}=\\{\mathbf{x}:Q_{\Lambda}(\mathbf{x})=\lambda\\},$ (2)

and the fundamental Voronoi cell is the set of points which are quantized to
the origin:

$\mathcal{V}_{\Lambda}=\\{\mathbf{x}:Q_{\Lambda}(\mathbf{x})=\mathbf{0}\\}.$
(3)

The volume of the Voronoi cell is defined by

$\rm{Vol}(\mathcal{V}_{\Lambda})=\int_{\mathcal{V}_{\Lambda}}d\mathbf{x}=|\rm{det}\mathbf{G}|.$
(4)

The normalized second moment of a lattice $\Lambda$ is defined by

$G(\Lambda)=\frac{1}{{\rm{Vol}}(\mathcal{V}_{\Lambda})^{\frac{2}{N}}}\times\frac{\int_{\mathbf{x}\in\mathcal{V}_{\Lambda}}||\mathbf{x}||^{2}\mathrm{d}\mathbf{x}}{N\rm{Vol}(\mathcal{V}_{\Lambda})}.$
(5)

Lattices naturally offer an elegant and efficient way to pack the spheres in
the Euclidean space. The packing spheres which do not intersect and the
packing radius of a lattice is the inner radius of the Voronoi Cell
$\mathcal{V}_{0}$. The packing radius $r_{pack(\Lambda)}$ is given by

$r_{pack(\Lambda)}=\frac{1}{2}{\mathrm{d}}_{\min}(\Lambda),$ (6)

where $\mathrm{d}_{\min}(\Lambda)$ is the minimum distance between any two
lattice points:

$\mathrm{d}_{\min}(\Lambda)\triangleq\mathop{\min}_{\lambda\in\Lambda,\lambda\neq
0}\|\lambda\|.$ (7)

Figure 1: A three-dimensional lattice.

Two $N$-dimensional lattices (${\Lambda}_{c},{\Lambda}_{f}$) is nested if
${\Lambda}_{c}\subset{\Lambda}_{f}$. $\Lambda_{f}$ is called the fine lattice,
and $\Lambda_{c}$ is called the coarse lattice. Their generator matrices are
denoted by $\mathbf{G}_{f}$ and $\mathbf{G}_{c}$, satisfying

$\mathbf{G}_{c}=\mathbf{G}_{f}\cdot\mathbf{J},$ (8)

where the sub-sampling matrix $\mathbf{J}$ is an $n\times n$ integer matrix.
The fine lattice $\Lambda_{f}$ can be decomposed as the union of
$|\Lambda_{f}/\Lambda_{c}|$ cosets of the coarse lattice $\Lambda_{c}$:

$\Lambda_{f}=\bigcup\limits_{{\mathbf{d}}_{i}\in\Lambda_{f}{/}\Lambda_{c}}(\Lambda_{c}+{\mathbf{d}}_{i}),$
(9)

where each coset $\Lambda_{c}+{\mathbf{d}}_{i}$ is a translated coarse lattice
and ${\mathbf{d}}_{i}$ is called the coset representative of
$\Lambda_{c}+{\mathbf{d}}_{i}$. If
$\mathbf{\Lambda}_{c}=\alpha\cdot\mathbf{\Lambda_{f}}$, then
$|{\rm{det}}\mathbf{J}|={\alpha^{N}}$ and ${\Lambda}_{c},{\Lambda}_{f}$ are
called self-nested.

###  II-B Quantization Index Modulation (QIM) based Watermarking

The QIM watermarking technique involves quantizing the cover signals into
different lattice cosets, where each coset corresponds to a unique message.
The process consists of two main phases: embedding and detection.

In the embedding phase, the following steps are performed:

i. [Lattice construction] A pair of nested lattices $\Lambda_{f}$ and
$\Lambda_{c}\subset\Lambda_{f}$ are considered, with their generators
$\mathbf{G}_{f}$ and $\mathbf{G}_{c}$ related as specified in (8).

ii. [Labeling] The message space $\mathcal{M}$ is defined as
$\mathcal{M}=\mathbb{Z}^{N}_{\alpha}=\\{0,\cdots,\alpha-1\\}^{N}$. Given a
host signal vector $\mathbf{s}$, to hide an information vector
$\mathbf{m}_{i}\in\mathcal{M}$ within $\mathbf{s}$, a process called labeling
is employed. One possible labeling solution is given by:

$\mathbf{d}_{i}=\mathcal{L}(\mathbf{m}_{i})\triangleq\mathbf{G}_{f}\cdot\phi(\mathbf{m}_{i}),$
(10)

where $\phi:\mathbb{Z}^{N}_{\alpha}\rightarrow\mathbb{R}^{N}$ is a natural
mapping function.

iii. [Quantization] The QIM encoder quantizes the host signal $\mathbf{s}$ to
the nearest lattice point in $\Lambda_{i}$ using the following equation:

$\mathbf{s}_{w}=Q_{\Lambda_{i}}(\mathbf{s})=Q_{\Lambda_{c}}(\mathbf{s}-\mathbf{d}_{i})+\mathbf{d}_{i}.$
(11)

The index $i$ in $\Lambda_{i}$ indicates that the coset $\Lambda_{i}$
corresponds to the message $\mathbf{m}_{i}$, i.e., it is used to transmit the
message $\mathbf{m}_{i}$. The payload of the embedding process is
$\alpha^{N}$, resulting in a code rate per dimension of $R=\log\alpha$.

In the detection phase, the embedded watermark is extracted from the
watermarked content to determine its presence and integrity. This allows
authorized parties to verify the authenticity of the media and detect any
unauthorized use or tampering. The detection algorithm of QIM can be described
as follows: Assuming the received signal vector is
$\mathbf{y}=\mathbf{x}+\mathbf{n}$, where $\mathbf{n}$ represents perturbation
noise, the QIM technique performs the following de-quantization step to
extract a coset representative:

$j=\mathop{\arg\min}_{i\in\left\\{1,2,\ldots,\alpha^{N}\right\\}}\mathrm{dist}(\mathbf{y},\Lambda_{i}),$
(12)

where
$\mathrm{dist}(\mathbf{y},\Lambda_{i})\triangleq\mathop{\min}_{\lambda\in\Lambda_{i}}\|\mathbf{y}-\lambda\|$.
If the noise is sufficiently small such that $Q_{\Lambda_{f}}(\mathbf{n})=0$,
then the embedded message $\hat{\mathbf{m}}$ obtained from delabeling is
correct. The estimated message is given by:

$\hat{\mathbf{m}}=\mathbf{G}_{f}^{-1}\cdot{\mathbf{d}_{j}}\ \mathrm{mod}\
\alpha.$ (13)

##  III The Proposed Method

In this section, we present the proposed method called Content-Aware
Quantization Index Modulation (CA-QIM), which improves upon the labeling step
of conventional QIM techniques by considering the statistics of the cover
signal vector and the messages.

###  III-A CA-QIM

The CA-QIM method starts by finding the closest coset $\Lambda_{i}$ to each
actual cover vector $\mathbf{s}_{k}$ using a similar process as the de-
watermarking function:

$\mathrm{Neighbor}(\mathbf{s}_{k})=\mathop{\arg\min}_{i\in\left\\{1,2,\ldots,\alpha^{N}\right\\}}\text{dist}(\mathbf{y},\Lambda_{i}).$
(14)

To incorporate the cover vector statistics and messages into the labeling
process, an adjacency matrix $\mathbf{W}$ is constructed. The elements of
$\mathbf{W}$ are initially set to zero. The matrix is updated by examining all
pairs of $\mathbf{m}_{i}$ and $\mathbf{s}_{k}$. If
$\mathrm{Neighbor}(\mathbf{s}_{k})=j$ when embedding the information vector
$\mathbf{m}_{i}$, then the corresponding element is incremented as follows:

$w_{j,i}\rightarrow w_{j,i}+1.$ (15)

Here, $w_{j,i}$ represents the element at row $j$ and column $i$ of
$\mathbf{W}$. The resulting $\mathbf{W}$ is a square matrix with dimensions
$\alpha^{N}\times\alpha^{N}$.

In CA-QIM, the labeling step employs a canonical labeling approach that solves
a maximum-weight matching problem. The problem can be formulated as follows:

Problem: In a complete bipartite graph identified by the adjacency matrix

$\mathbf{W}=\begin{bmatrix}\mathit{w}_{0,0}&\mathit{w}_{0,1}&\cdots&\mathit{w}_{0,\alpha^{N}-1}\\\
\mathit{w}_{1,0}&\mathit{w}_{1,1}&\cdots&\mathit{w}_{1,\alpha^{N}-1}\\\
\vdots&\vdots&\ddots&\vdots\\\
\mathit{w}_{\alpha^{N}-1,0}&\mathit{w}_{\alpha^{N}-1,1}&\cdots&\mathit{w}_{\alpha^{N}-1,\alpha^{N}-1}\\\
\end{bmatrix},$

find the matching
$({\gamma_{0},0}),({\gamma_{1},1}),\ldots,(\gamma_{(\alpha^{N}-1)},{\alpha^{N}-1})$
such that the sum of weights

$w_{\gamma_{0},0}+w_{\gamma_{1},1}+\cdots
w_{\gamma_{(\alpha^{N}-1)},\alpha^{N}-1}$ (16)

is maximized with the constraint
$\gamma_{0}\neq\gamma_{1}\neq\ldots\neq\gamma_{(\alpha^{N}-1)}$.

The problem can be solved using the following procedure:

  1. 1.

Invert the sign of each element in $\mathbf{W}$.

  2. 2.

Subtract the minimum value from each row and column of the resulting matrix.

  3. 3.

Draw the minimum number of horizontal and vertical lines needed to cover all
zeros in the matrix. If $\alpha^{N}$ lines are drawn, an optimal match can be
found among the zeros from different rows and columns. Proceed to step 5. If
fewer than $\alpha^{N}$ lines are drawn, proceed to step 4.

  4. 4.

Find the smallest uncovered element and subtract it from all uncovered
elements. Add this value to all elements that are covered twice. Repeat from
step 3.

Based on the optimal matching
$({\gamma_{0},0}),({\gamma_{1},1}),\ldots,(\gamma_{(\alpha^{N}-1)},{\alpha^{N}-1})$,
the quantization function of CA-QIM is defined as:

$\mathbf{s}_{w}=Q_{\Lambda_{\gamma_{i}}}(\mathbf{s})$ (17)

for the message $\mathbf{m}_{i}$.

At the receiver’s side, the estimated message is obtained by finding the coset
representative index $\gamma_{j}$ that minimizes the distance between the
received signal vector $\mathbf{y}$ and each coset $\Lambda_{i}$:

$\gamma_{j}=\mathop{\arg\min}_{i\in\left\\{1,2,\ldots,\alpha^{N}\right\\}}\text{dist}(\mathbf{y},\Lambda_{i}).$
(18)

Finally, the estimated message is given by:

$\hat{\mathbf{m}}=\mathbf{G}_{f}^{-1}{\mathbf{d}_{j}}\ \mathrm{mod}\ \alpha.$
(19)

The CA-QIM method improves the conventional QIM technique by considering the
cover vector statistics and messages during the labeling process, resulting in
enhanced embedding performance. Two examples are given below to demonstrate
the rationale of CA-QIM.

(a)

(b)

Figure 2: The labeling schemes of QIM and CA-QIM. (a) QIM. (b) CA-QIM.

_Example 1:_ Choose the typical 1-dimension QIM as comparison with CA-QIM, in
which $\mathbb{Z}$ is ${\Lambda}_{f}$ and $2\mathbb{Z}$ is ${\Lambda}_{c}$.
The host signal $s\in\mathcal{S}$ is watermarked with a message
$m\in\\{0,1\\}$ by

$s_{w}=Q_{{\Lambda}_{i}}(s)$ (20)

where

$\Lambda_{0}=2\mathbb{Z},\,\Lambda_{1}=2\mathbb{Z}+1.$ (21)

As shown in Fig. 2a, the labeling scheme would lead to a quantization scheme
that move $8$ of the $9$ carriers to “far” cosets
($|s_{w}-Q_{{\Lambda}_{i}}(s)|>1/2$), and the adjacency matrix is

$\mathbf{W}=\begin{bmatrix}1&3\\\ 5&0\end{bmatrix}.$

Regarding CA-QIM shown in Fig. 2b, it only moves $1$ carrier to a “far” coset.
$8$ of the $9$ carriers satisfy $|s_{w}-Q_{{\Lambda}_{i}}(s)|<1/2$.

_Example 2:_ In terms of lattice construction, this example employs $D_{2}$
lattice as ${\Lambda}_{f}$, and the self-nested $2{\Lambda}_{f}$ as
${\Lambda}_{c}$. The generator matrix of $D_{2}$ lattice is

$\mathbf{G}=\begin{pmatrix}1&0\\\\[8.0pt] 1&2\\\ \end{pmatrix}.$

The 4 cosets are given by

$\displaystyle\Lambda_{0}=\mathbf{G}([0,0]^{\top}+\mathbb{Z}^{2}),$
$\displaystyle\Lambda_{1}=\mathbf{G}([0,1]^{\top}+\mathbb{Z}^{2}),$
$\displaystyle\Lambda_{2}=\mathbf{G}([1,0]^{\top}+\mathbb{Z}^{2}),$
$\displaystyle\Lambda_{3}=\mathbf{G}([1,1]^{\top}+\mathbb{Z}^{2}).$

Assume that the cover vectors/carriers are {(127,111), (35,120), (34,118),
(89,37), (210,171), (145,101)}. Then the indexes of their closet cosets,
$\mathrm{Neighbor}(\mathbf{s})$, can be found: {2, 3, 0, 2, 2, 1}. Without
loss of generality, set the probability of bit $0$ of the messages as $0.9$.
Then we have the indexes of these messages as {0, 1, 0, 0, 0, 2}. Thus the
adjacency matrix of this example is

$\mathbf{W}=\begin{bmatrix}1&0&0&0\\\ 0&0&1&0\\\ 3&0&0&0\\\
0&1&0&0\end{bmatrix}.$

After solving the maximum-weight matching problem, the optimal matching is
given by {(2,0), (3,1), (1,2), (0,3)}. The implication is that CA-QIM would
quantize $\mathbf{s}$ via $\Lambda_{2}$ for $\mathbf{m}_{0}$, $\Lambda_{3}$
for $\mathbf{m}_{1}$, $\Lambda_{1}$ for $\mathbf{m}_{2}$, and $\Lambda_{0}$
for $\mathbf{m}_{3}$. Thus in CA-QIM, only $1$ carrier is quantized to a “far”
coset, while that number of QIM is $5$.

###  III-B The minimum-distortion variant: CAMD-QIM

A recent work by Lin et al. [12] introduced a minimum distortion (MD)
principle to reduce the embedding distortion of QIM, known as MD-QIM. In MD-
QIM, the quantization step differs from conventional QIM in that the carriers
are not required to be quantized to a lattice point. Instead, they are
quantized to a nearby point within the correct decoding region. This trade-off
sacrifices robustness to additive noises in favor of reduced embedding
distortion. Inspired by this idea, we can apply the non-lattice quantization
function of MD-QIM to construct a minimum-distortion content-aware QIM (CAMD-
QIM) algorithm.

Similar to CA-QIM, CAMD-QIM also employs canonical labeling. If a cover vector
$\mathbf{s}$ lies within the Voronoi region of the fine lattice point
$Q_{\Lambda_{\gamma_{i}}}(\mathbf{s})$, then $\mathbf{s}_{w}$ remains
unchanged ($\mathbf{s}_{w}=\mathbf{s}$). However, if $\mathbf{s}$ falls
outside the Voronoi region of $Q{\Lambda{\gamma_{i}}}(\mathbf{s})$, then
$\mathbf{s}w$ is chosen as the closest point to $\mathbf{s}$ within the
Voronoi region. This is achieved by the following equation:

$\mathbf{s}_{w}=Q_{\Lambda_{\gamma_{i}}}(\mathbf{s})-\frac{\mathbf{p}}{|\mathbf{p}|}\times(r_{\text{pack}(\Lambda_{f})}-\epsilon),$
(22)

where $\epsilon$ is a small positive number used to move $\mathbf{s}_{w}$ away
from the decision boundaries, and
$\mathbf{p}=Q_{\Lambda_{\gamma_{i}}}(\mathbf{s})-\mathbf{s}$. The detection
algorithm for CAMD-QIM remains the same as that of CA-QIM.

In Figure 3, we present the rationale behind MD-QIM and CAMD-QIM using the
same settings as Example 1. The figure illustrates that the combination of
canonical labeling and the minimum distortion principle is highly effective,
as most of the cover vectors/carriers do not require any changes.

(a)

(b)

Figure 3: Demonstration of MD-QIM and CAMD-QIM. (a) MD-QIM. (b) CAMD-QIM.

##  IV Performance Analysis

Mean square error (MSE) is commonly used as a measure to quantify the
difference between an estimator and the estimated values. In the context of
watermarking algorithms, we can define the MSE to calculate the distortion as
follows:

$\text{MSE}=\frac{1}{NM}\sum_{k=1}^{M}|\mathbf{s}_{k}-\mathbf{s}_{w,k}|^{2},$
(23)

where $M$ is the total number of host vectors, $\mathbf{s}_{k}$ represents the
host signal vectors before watermarking, and $\mathbf{s}_{w,k}$ represents the
host signal vectors after watermarking.

The general distortion formula for QIM-alike algorithms can be expressed as:

$\text{MSE}{\text{QIM}}=\frac{1}{N}\int{\mathcal{V}_{\Lambda_{c}}}|\mathbf{x}|^{2}\cdot
f(\mathbf{x}),d\mathbf{x},$ (24)

where $f(\mathbf{x})$ is the probability density function of the host signals,
and $\mathcal{V}_{\Lambda_{c}}$ represents the Voronoi region of the coarse
lattice. It should be noted that the above equation assumes uniformly
distributed carriers over the Voronoi region of the coarse lattice, as
described in [12]. However, in this paper, we consider the case where the
carriers are not necessarily uniformly distributed and proceed with the
analysis accordingly.

###  IV-A Distortion of CA-QIM

Without loss of generality, denote the probability of message $\mathbf{m}_{i}$
as $p_{i}$, the probability of $\mathbf{s}_{k}$ as $q_{k}$. The probability of
quantizing $\mathbf{m}_{i}$ into the coset $\Lambda_{k}$ of $\mathbf{s}_{k}$
is $p_{i}\cdot q_{k}$. After applying CA-QIM, probabilities get sorted such
that $p_{i_{1}}\leq p_{i_{2}}\leq\cdots\leq p_{i_{\alpha^{N}}}$ and
$q_{k_{1}}\leq q_{k_{2}}\leq\cdots\leq q_{k_{\alpha^{N}}}$, and host signals
and messages with same order of probabilities are regarded as remapped pairs
as proposed in III-A.

According to the flat-host assumption, we can analyze the probability of
whether the carriers are in the corresponding coset or not, i.e.,

${}P_{1}=P(\mathbf{m}\in\mathcal{V}_{\Lambda_{f}})=\sum_{j=1}^{\alpha^{N}}p_{i_{j}}q_{k_{j}},$
(25)
${}P_{2}=P(\mathbf{m}\in\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{f}})=1-\sum_{j=1}^{\alpha^{N}}p_{i_{j}}q_{k_{j}}.$
(26)

Correspondingly, the overall expected MSE of CA-QIM can be formulated as

$\displaystyle MSE_{CA\text{-}QIM}=$ (27)
$\displaystyle\frac{1}{N}\Bigg{[}P_{1}\int_{\mathcal{V}_{\Lambda_{f}}}\|\mathbf{x}\|^{2}d\mathbf{x}+P_{2}\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{f}}}\|\mathbf{x}\|^{2}d\mathbf{x}\Bigg{]}.$

For the original QIM, the probabilities corresponding to the above two cases
respectively are

$P_{1}^{\prime}=P(\mathbf{m}\in\mathcal{V}_{\Lambda_{f}})=\sum_{j=1}^{\alpha^{N}}p_{j}q_{j},$
(28) $P_{2}^{\prime}=P(\mathbf{m}\in\mathcal{V}_{\Lambda_{c}}\backslash
V_{\Lambda_{f}})=1-\sum_{j=1}^{\alpha^{N}}p_{j}q_{j}.$ (29)

Obviously, $P_{1}\geqslant P_{1}^{\prime}$ and $P_{2}\leq P_{2}^{\prime}$. And
the overall expected MSE of QIM can be calculated as

$\displaystyle MSE_{QIM}$ (30)
$\displaystyle=\mathbb{E}\big{(}\frac{\int_{\mathcal{V}_{\Lambda_{c}}}\|\mathbf{x}\|^{2}\cdot
f(\mathbf{x})d\mathbf{x}}{N}\big{)}$
$\displaystyle=\frac{1}{N}\Bigg{[}P_{1}^{\prime}\int_{\mathcal{V}_{\Lambda_{f}}}\|\mathbf{x}\|^{2}d\mathbf{x}+P_{2}^{\prime}\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{f}}}\|\mathbf{x}\|^{2}d\mathbf{x}\Bigg{]}.$

If the host signals and messages are modeled as uniform distribution, then
$P_{1}=P_{1}^{\prime}=\sum_{j=1}^{\alpha^{N}}\frac{1}{{\alpha^{N}}^{2}}=\frac{1}{{\alpha^{N}}}$
and $P_{2}=P_{2}^{\prime}=1-\frac{1}{{\alpha^{N}}}$. In this case the MSE
becomes

$\displaystyle MSE_{CA\text{-}QIM}$ $\displaystyle=MSE_{QIM}$ (31)
$\displaystyle=\frac{1}{N}\frac{1}{\rm{Vol}(\mathcal{V}_{\Lambda_{c}})}\int_{\mathcal{V}_{\Lambda_{c}}}\|\mathbf{x}\|^{2}d\mathbf{x}$
$\displaystyle=G(\Lambda_{c})\rm{Vol}(\mathcal{V}_{\Lambda_{c}})^{\frac{2}{N}},$

which indicates that CA-QIM does perceive the content of signals and messages.

###  IV-B Distortion of CAMD-QIM

MD is applied in the process of quantizing after labeling. We use
$MSE_{CAMD\text{-}QIM}^{\prime}$ and $MSE_{CAMD\text{-}QIM}^{\prime\prime}$ to
represent the MSE of CAMD-QIM in the case of (25) and (26), respectively.

In the case of $\mathbf{s}\in\mathcal{V}_{\Lambda_{f}}$ as shown in
Fig.4LABEL:sub@fig3b, the host signal is in the corresponding Voronoi region.
From III-B, the carriers remain in the initial positions. So the MSE of CAMD-
QIM is

$MSE_{CAMD\text{-}QIM}^{\prime}=0.$ (32)

In the case of
$\mathbf{s}\in\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{f}}$,
the host signal needs to be moved into the packing sphere of corresponding
Voronoi region. As depicted in Fig.4LABEL:sub@fig3c, the host signal is in
incongruous Voronoi region. The MSE in this scenario can be calculated as

$\displaystyle MSE_{CAMD\text{-}QIM}^{\prime\prime}$
$\displaystyle=\frac{1}{N}\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{f}}}\|\mathbf{x}-(r_{pack(\Lambda_{f})}-\epsilon)\|^{2}d\mathbf{x}.$
(33)

(a)

(b)

Figure 4: The example over an $A_{2}$ lattice. (a) Host signal vector in the
corresponding Voronoi region. (b) Host signal vector in incongruous Voronoi
region.

Then based on (32) and (33), the overall expected MSE of CAMD-QIM is

$\displaystyle MSE_{CAMD\text{-}QIM}$ (34) $\displaystyle=P_{1}\cdot
MSE_{CAMD\text{-}QIM}^{\prime}+P_{2}\cdot
MSE_{CAMD\text{-}QIM}^{\prime\prime}$
$\displaystyle=\frac{(1-\sum_{j=1}^{\alpha^{N}}p_{i_{j}}q_{k_{j}})}{N}\Bigg{[}\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{f}}}\|\mathbf{x}\|^{2}d\mathbf{x}$
$\displaystyle-2(r_{pack(\Lambda_{\mathit{f}})}-\epsilon)\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{\mathit{f}}}}\|\mathbf{x}\|d\mathbf{x}+\rm{Vol}(\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{\mathit{f}}})\Bigg{]}.$

With reference to (5), we have

$\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{\mathit{f}}}}\|\mathbf{x}\|^{2}d\mathbf{x}=NG(\Lambda_{c}\backslash\Lambda_{\mathit{f}})\rm{Vol}(\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{\mathit{f}}})^{\frac{2}{N}+1}.$
(35)

Through using Cauchy-Schwarz inequality, we have

$\displaystyle\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{\mathit{f}}}}\|\mathbf{x}\|d\mathbf{x}\leq\sqrt{\int_{\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{\mathit{f}}}}\|\mathbf{x}\|^{2}d\mathbf{x}}\times\sqrt{\rm{Vol}(\mathcal{V}_{\Lambda_{c}}\backslash\mathcal{V}_{\Lambda_{\mathit{f}}})}$
(36)
$\displaystyle\leq\sqrt{NG(\Lambda_{c})\rm{Vol}(\mathcal{V}_{\Lambda_{c}})^{\frac{2}{N}+2}-NG(\Lambda_{\mathit{f}})\rm{Vol}(\mathcal{V}_{\Lambda_{\mathit{f}}})^{\frac{2}{N}+2}}.$

Combining (34), (35) and (36), the MSE of CAMD-QIM has the upper bound of

$\displaystyle MSE_{CAMD\text{-}QIM}$ (37)
$\displaystyle\leq\frac{(1-\sum_{j=1}^{\alpha^{N}}p_{i_{j}}q_{k_{j}})}{N}\Bigg{[}NG(\Lambda_{c})\rm{Vol}(\mathcal{V}_{\Lambda_{c}})^{\frac{2}{N}+1}$
$\displaystyle-
NG(\Lambda_{\mathit{f}})\rm{Vol}(\mathcal{V}_{\Lambda_{\mathit{f}}})^{\frac{2}{N}+1}-2(r_{pack(\Lambda_{\mathit{f}})}-\epsilon)$
$\displaystyle\cdot\sqrt{NG(\Lambda_{c})\rm{Vol}(\mathcal{V}_{\Lambda_{c}})^{\frac{2}{N}+2}-NG(\Lambda_{\mathit{f}})\rm{Vol}(\mathcal{V}_{\Lambda_{\mathit{f}}})^{\frac{2}{N}+2}}$
$\displaystyle+\rm{Vol}(\mathcal{V}_{\Lambda_{c}})-\rm{Vol}(\mathcal{V}_{\Lambda_{\mathit{f}}})\Bigg{]}.$

It can be observed from the above formula that when the lattice construction
is fixed, the only parameter that determines the MSE is the probability of
mapping between carriers and messages. If $P_{2}=0$, the MSE of CAMD-QIM is
$0$.

###  IV-C Spatial-Frequency Domain Distortion

The relationship between mean square error (MSE) in the spatial domain and
frequency domain is examined in this section, specifically focusing on the
discrete cosine transform (DCT) domain. The $8\times 8$ block DCT transform is
defined by the following equation:

$\displaystyle\mathbf{Y}(u,v)$ $\displaystyle=\frac{1}{4}C(u)C(v)$ (38)
$\displaystyle\cdot\sum_{m=0}^{7}\sum_{n=0}^{7}\mathbf{X}(m,n)\cos{\frac{(2m+1)u\pi}{16}}\cos{\frac{(2n+1)v\pi}{16}}$

where $\mathbf{X}(m,n)$ represents the pixel values of the original $8\times
8$ image block,

$C(u)=\begin{cases}1/\sqrt{2},\quad&u=0,\\\ 1,\quad&\rm{others},\end{cases}$

and

$C(v)=\begin{cases}1/\sqrt{2},\quad&v=0,\\\ 1,\quad&\rm{others}.\end{cases}$

$\mathbf{T}=\left[\begin{array}[]{cccccccc}\Gamma(4)&\Gamma(4)&\Gamma(4)&\Gamma(4)&\Gamma(4)&\Gamma(4)&\Gamma(4)&\Gamma(4)\\\
\Gamma(1)&\Gamma(3)&\Gamma(5)&\Gamma(7)&-\Gamma(7)&-\Gamma(5)&-\Gamma(3)&-\Gamma(1)\\\
\Gamma(2)&\Gamma(6)&-\Gamma(6)&-\Gamma(2)&-\Gamma(2)&-\Gamma(6)&\Gamma(6)&\Gamma(2)\\\
\Gamma(3)&-\Gamma(7)&-\Gamma(1)&-\Gamma(5)&\Gamma(5)&\Gamma(1)&\Gamma(7)&-\Gamma(3)\\\
\Gamma(4)&-\Gamma(4)&-\Gamma(4)&\Gamma(4)&\Gamma(4)&-\Gamma(4)&-\Gamma(4)&\Gamma(4)\\\
\Gamma(5)&-\Gamma(1)&\Gamma(7)&\Gamma(3)&-\Gamma(3)&-\Gamma(7)&\Gamma(1)&-\Gamma(5)\\\
\Gamma(6)&-\Gamma(2)&\Gamma(2)&-\Gamma(6)&-\Gamma(6)&\Gamma(2)&-\Gamma(2)&\Gamma(6)\\\
\Gamma(7)&-\Gamma(5)&\Gamma(3)&-\Gamma(1)&\Gamma(1)&-\Gamma(3)&\Gamma(5)&-\Gamma(7)\end{array}\right]$
(39)

The transformation matrix for the $8\times 8$ block DCT is defined using the
concept that the $K$-point DCT of any sequence $\mathbf{s}$ can be seen as a
projection onto an orthogonal basis [21]. In this case, the transformation
matrix is given by Equation (39), where $\Gamma(k)=\cos{({k\pi}/{16})}$. Thus,
the transform of $8\times 8$ block DCT is formulated as

$\mathbf{Y}=\mathbf{T}\mathbf{X}\mathbf{T}^{\rm{T}},$ (40)

where $\mathbf{X}$ and $\mathbf{Y}$ respectively represent an $8\times 8$
image block of spatial domain and DCT domain.

Assume that $\mathbf{Y}$ has gotten distortions to become
$\mathbf{Y^{\prime}}$. Then with
$\Delta\mathbf{Y}=\mathbf{Y}-\mathbf{Y^{\prime}}$,
$\Delta\mathbf{X}=\mathbf{X}-\mathbf{X^{\prime}}$, we have
$\Delta\mathbf{Y}=\mathbf{T}\Delta\mathbf{X}\mathbf{T}$. According to the
properties of Euclidean norms, the MSE over carrier $\mathbf{X}$ and
$\mathbf{Y}$ can be written respectively as

$MSE_{\mathbf{X}}=\frac{1}{64}\|\Delta\mathbf{X}\|^{2}_{2},$ (41)

and

$MSE_{\mathbf{Y}}=\frac{1}{64}\|\Delta\mathbf{Y}\|^{2}_{2}=\frac{1}{64}\|\mathbf{T}\Delta\mathbf{X}\mathbf{T}^{\rm{T}}\|^{2}_{2}.$
(42)

From (39), it can be verified that $\mathbf{T}$ is an orthogonal matrix, and
$\|\mathbf{T}\|^{2}_{2}=1$. Then it follows from the property of norms that

$\displaystyle MSE_{\mathbf{Y}}$
$\displaystyle=\frac{1}{64}\|\mathbf{T}\Delta\mathbf{X}\mathbf{T}^{\rm{T}}\|^{2}_{2}$
(43)
$\displaystyle=\frac{1}{64}\|\mathbf{T}\|^{2}_{2}\|\Delta\mathbf{X}\|^{2}_{2}\|\mathbf{T}^{\rm{T}}\|^{2}_{2}$
$\displaystyle=\frac{1}{64}\|\Delta\mathbf{X}\|^{2}_{2}=MSE_{\mathbf{X}},$

which shows that with distortion, images in the spatial domain and frequency
domain are affected to the same extent. If the stored pixels of the images can
only be of integer formats, we have $MSE_{\mathbf{X}}\leq MSE_{\mathbf{Y}}$ in
general.

###  IV-D Symbol Error Rate Analysis

In the proposed schemes, CA-QIM has noise tolerance ability while CAMD-QIM
does not. So this section only analyzes the detection error rate performance
of CA-QIM. Considering the watermarked carriers $\mathbf{s}_{w}$ may go
through malicious additive noise attacks or oblivious addition noise
pollution, the received signal vector at the receiver’s side is
$\mathbf{y}=\mathbf{s}_{w}+\mathbf{n}$. Since the lattice is geometrically
uniform, the point error probability has the upper bound [20]

$\displaystyle
P_{e}(\Lambda_{f})\leq\sum_{\mathbf{z}\neq\mathbf{s}_{w},\mathbf{z}\in\Lambda_{f}}P_{e}(\mathbf{s}_{w}\to\mathbf{z}),$
(44)

where $P_{e}(\mathbf{s}_{w}\to\mathbf{z})$ is the probability that
$\mathbf{y}$ lies in the Voronoi region centered at $\mathbf{z}$ while
transmitting $\mathbf{s}_{w}$.

In the AWGN channel, (44) becomes

$\displaystyle
P_{e}(\Lambda_{f})\leq\frac{\tau}{2}\mathrm{erfc}(\frac{d_{\mathrm{min}}/2}{\sqrt{2N_{0}}}),$
(45)

where $\tau$ is the kissing number, $d_{\mathrm{min}}$ is the minimum
Euclidean distance of the lattice and $N_{0}$ is the noise power spectral
density. Thus the vector error rate in the transmission model can be regarded
as the probability of $\mathbf{y}$ lying outside the Voronoi region
$\mathcal{V}_{\Lambda_{f}}$ centered at $\mathbf{s}_{w}$. Thus we have the
following upper bound for the vector error rate:

$\displaystyle P(\mathbf{y}\notin\mathcal{V}_{\Lambda_{f}})\leq
P_{e}(\Lambda_{f}).$ (46)

By averaging over the received signal vectors $\mathbf{y}_{j}$, the symbol
error rate (SER) of CA-QIM is given by

$\displaystyle
SER=\frac{\sum_{j=1}^{M}P(\mathbf{y}_{j}\notin\mathcal{V}_{\Lambda_{f}})}{M}\leq\frac{\tau}{2}\mathrm{erfc}(\frac{d_{\mathrm{min}}/2}{\sqrt{2N_{0}}}),$
(47)

where $M$ is the total number of host vectors.

##  V Simulations

In this section, we conduct numerical simulations to verify the effectiveness
of the proposed CA-QIM and CAMD-QIM.

###  V-A Setups

We utilized two standard image databases for conducting watermarking
experiments. Set12 [22] comprises grayscale images of diverse scenes, with
each image’s size being either 256×256 or 512×512 pixels. Another database,
BSD68 [23], consists of 68 grayscale images that vary in size. The AC
coefficients of images subjected to discrete cosine transform (DCT) follow an
approximate Laplacian distribution [24]. To simulate the common JPEG image
compression technique, we divide the image into non-overlapping blocks of size
8×8 pixels. Since JPEG compression employs DCT, embedding messages into the
frequency domain aligns with this process. The low, mid, and high-frequency
coefficients correspond to the front, middle, and rear parts of the zig-zag-
scan sequence within each block. Different frequencies of each block can
accommodate single or multiple messages.

To ensure comprehensive evaluation, we utilize $A_{2},D_{4}$, and $E_{8}$
lattices as the fine lattices (denoted as $\Lambda_{f}$). The corresponding
coarse lattices for these fine lattices are $\alpha\Lambda_{f}$, where
$\alpha$ represents the parameter governing the code rate of messages. We
reference benchmark algorithms from [25] and [12], collectively referred to as
QIM, for comparison. Additionally, we implement an enhanced version of the MD-
QIM algorithm to evaluate against our proposed schemes.

On one hand, according to the definition of the code rate, as the code rate
increases, the distortion also increases. On the other hand, since image
pixels are rounded to integers, it is necessary to set a larger code rate to
ensure that the Voronoi region includes multiple integers. Therefore, we set
the code rate as $R=2$ and maintain a probability of $0.9$ for the occurrence
of bit $0$ in the message, aligning with the hypothesis proposed in this
paper.

###  V-B Imperceptibility measurement

To ensure a comprehensive quantitative evaluation, we incorporate additional
metrics alongside Mean Squared Error (MSE). One widely used indicator is the
Peak Signal-to-Noise Ratio (PSNR), which assesses the similarity between the
original host signals and the embedded signals. The PSNR is defined for
vectors as:

$PSNR=10\times\log_{10}\left(\frac{{\text{MaxValue}}^{2}}{\text{MSE}}\right).$

Here, _MaxValue_ represents the maximum value that the host signals can reach.
In this simulation, since the host signals are the pixels of images, we set
_MaxValue_ to be ${2^{8}}-1$.

Another metric is the Percentage Residual Difference (PRD), which measures the
rate of change between the original value and the difference, given by:

$PRD=\sqrt{\frac{\sum_{i=1}^{M}|\mathbf{s}_{k}-\mathbf{s}_{w,k}|^{2}}{\sum_{i=1}^{M}|\mathbf{s}_{k}|^{2}}}.$

Here, $\mathbf{s}_{k}$ denotes the original value and $\mathbf{s}{w,k}$
represents the corresponding difference.

TABLE I: The MSE, PSNR, and PRD performance of different algorithms when
embedding messages to different parts of the DCT domain.

| $A_{2}$ | $D_{4}$ | $E_{8}$
---|---|---|---
| MSE | PSNR | PRD | MSE | PSNR | PRD | MSE | PSNR | PRD
QIM | low | 1.553 | 46.35 | 0.028 | 1.395 | 46.68 | 0.025 | 1.251 | 47.15 | 0.022
mid | 0.941 | 48.39 | 0.020 | 0.885 | 48.68 | 0.018 | 0.764 | 49.09 | 0.016
high | 0.563 | 50.71 | 0.018 | 0.495 | 51.18 | 0.015 | 0.451 | 51.58 | 0.013
low | 1.074 | 47.82 | 0.020 | 0.868 | 48.74 | 0.019 | 0.727 | 49.51 | 0.016
CA-QIM | mid | 0.706 | 49.39 | 0.016 | 0.511 | 51.04 | 0.014 | 0.454 | 51.56 | 0.013
high | 0.415 | 51.96 | 0.014 | 0.327 | 52.89 | 0.011 | 0.231 | 54.41 | 0.011
MD-QIM | low | 0.272 | 53.79 | 0.014 | 0.219 | 54.62 | 0.012 | 0.174 | 55.72 | 0.011
mid | 0.181 | 55.55 | 0.009 | 0.143 | 56.57 | 0.008 | 0.104 | 57.96 | 0.007
high | 0.094 | 58.39 | 0.007 | 0.075 | 59.38 | 0.004 | 0.063 | 60.13 | 0.004
low | 0.213 | 54.84 | 0.009 | 0.177 | 55.65 | 0.007 | 0.143 | 56.57 | 0.006
CAMD-QIM | mid | 0.138 | 56.73 | 0.007 | 0.098 | 58.21 | 0.006 | 0.076 | 59.32 | 0.005
high | 0.047 | 61.41 | 0.006 | 0.035 | 62.69 | 0.005 | 0.024 | 64.32 | 0.003

(a)

(b)

(c)

(d)

Figure 5: Effects of embedding watermarks by using CA-QIM over different
lattices. (a) Original image (b) $\Lambda_{f}=A_{2}$ (c) $\Lambda_{f}=D_{4}$
(d) $\Lambda_{f}=E_{8}$.

(a)

(b)

(c)

(d)

Figure 6: Effects of embedding watermarks by using CAMD-QIM over different
lattices. (a) Original image (b) $\Lambda_{f}=A_{2}$ (c) $\Lambda_{f}=D_{4}$
(d) $\Lambda_{f}=E_{8}$.

In Table I, we present the average values of MSE, PSNR, and PRD in the
frequency domain after embedding using four benchmark algorithms: QIM, CA-QIM,
MD-QIM, and CAMD-QIM on the images. Several conclusions can be drawn from the
table:

  1. 1.

Across all lattices, CA-QIM and CAMD-QIM consistently outperform QIM and MD-
QIM in terms of the metrics. This suggests that CA-QIM exhibits lower
distortion compared to the other algorithms.

  2. 2.

Analyzing the metrics with different lattices reveals that the embedding
process is influenced differently by the dimensions of the lattices.

  3. 3.

CAMD-QIM employs the MD method to enhance imperceptibility, resulting in
better performance than CA-QIM.

Considering the impact of DCT and image pixels, the MSE increases when the
image is converted from the frequency domain to the spatial domain. This
increase is larger than the theoretical value mentioned in Section IV
(Distortion Analysis). Figures 5 and 6 displays sample images by using
different lattices for the embedding of CA-QIM and CAMD-QIM.

TABLE II:  The MSE performance of different QIM variants when embedding
messages to different frequencies of the DCT domain.

| $A_{2}$ | $D_{4}$ | $E_{8}$
---|---|---|---
payload (bits/dim) | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3
QIM | low | 1.5061 | 1.5408 | 1.5932 | 1.4979 | 1.5312 | 1.5782 | 1.4978 | 1.5309 | 1.5770
mid | 0.5061 | 0.5468 | 0.5883 | 0.5039 | 0.5419 | 0.5816 | 0.4907 | 0.5258 | 0.5606
high | 0.1553 | 0.2012 | 0.2704 | 0.1441 | 0.2164 | 0.2416 | 0.1475 | 0.1872 | 0.2371
low | 1.0061 | 1.1304 | 1.1821 | 1.0139 | 1.0634 | 1.0966 | 0.8378 | 0.9037 | 1.0674
CA-QIM | mid | 0.5899 | 0.5961 | 0.6601 | 0.5186 | 0.5411 | 0.5655 | 0.4201 | 0.4764 | 0.5004
high | 0.1182 | 0.1752 | 0.2288 | 0.1012 | 0.1336 | 0.1532 | 0.1294 | 0.1480 | 0.1936
MD-QIM | low | 0.8771 | 0.8925 | 0.9311 | 0.8693 | 0.8970 | 0.8431 | 0.8568 | 0.8785 | 0.8917
mid | 0.3795 | 0.4857 | 0.4831 | 0.3590 | 0.3747 | 0.4365 | 0.3978 | 0.3840 | 0.4101
high | 0.0197 | 0.0674 | 0.1083 | 0.1617 | 0.3721 | 0.4170 | 0.3043 | 0.4672 | 0.4996
low | 0.7371 | 0.7607 | 0.7954 | 0.7193 | 0.7548 | 0.7892 | 0.7068 | 0.7313 | 0.7602
CAMD-QIM | mid | 0.4486 | 0.4689 | 0.4703 | 0.4590 | 0.4530 | 0.5194 | 0.4782 | 0.4827 | 0.4870
high | 0.0184 | 0.0585 | 0.1042 | 0.1498 | 0.2193 | 0.3049 | 0.1963 | 0.2389 | 0.2999

TABLE III: The PSNR and SSIM performance of different QIM variants when
embedding messages to different frequencies of the DCT domain.

| $A_{2}$ | $D_{4}$ | $E_{8}$
---|---|---|---
payload (bits/dim) | 1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3
low | PSNR | 51.0876 | 51.3114 | 51.3600 | 51.4156 | 51.0141 | 51.2356 | 51.1299 | 51.1291 | 51.0528
SSIM | 0.9585 | 0.9418 | 0.9346 | 0.9600 | 0.9368 | 0.9263 | 0.9716 | 0.9616 | 0.9554
mid | PSNR | 52.7065 | 51.4196 | 51.4069 | 51.5126 | 51.5695 | 50.9757 | 51.3341 | 51.2939 | 51.2552
SSIM | 0.9989 | 0.9975 | 0.9971 | 0.9963 | 0.9925 | 0.9908 | 0.9960 | 0.9899 | 0.9874
high | PSNR | 65.4625 | 60.4534 | 57.9480 | 56.3737 | 52.4230 | 52.0562 | 53.4127 | 51.7070 | 51.1443
SSIM | 0.9999 | 0.9999 | 0.9998 | 0.9997 | 0.9992 | 0.9985 | 0.9994 | 0.9981 | 0.9956

###  V-C Embedding Capacity Measurement

The embedding capacity is an important factor for evaluating the quality of
the proposed method. In this subsection, we measure the embedding capacity by
varying the number of messages and the positions of embedding AC coefficients.
Since each block has 63 AC coefficients, the number of embeddable messages per
block ranges from 1 to $\lfloor 63/N\rfloor$. To comply with the payload
limits, we embed one, two, and three labeling messages $\mathbf{m}$ into a
block, respectively.

Table 3 presents a more comprehensive set of metrics, including MSE in various
scenarios. From Table 3, it can be observed that CAMD-QIM outperforms MD-QIM
in low-dimensional lattices, and the distinction becomes more pronounced as
the lattice dimension increases. Additionally, CAMD-QIM also performs better
than MD-QIM at the same frequency.

In addition to the three aforementioned metrics, Structural Similarity Index
(SSIM) is introduced to provide a comprehensive evaluation. SSIM measures the
similarity between two images and is calculated as follows:

$SSIM(\mathbf{x},\mathbf{y})=\frac{(2\mu_{\mathbf{x}}\mu_{\mathbf{y}}+c_{1})(2\sigma_{\mathbf{xy}}+c_{2})}{({\mu_{\mathbf{x}}}^{2}+{\mu_{\mathbf{y}}}^{2}+c_{1})({\sigma_{\mathbf{x}}}^{2}+{\sigma_{\mathbf{y}}}^{2}+c_{2})},$
(48)

where $\mu_{\mathbf{x}}$ and $\mu_{\mathbf{y}}$ represent the mean of images
$\mathbf{x}$ and $\mathbf{y}$, respectively, and $\sigma_{\mathbf{x}}$ and
$\sigma_{\mathbf{y}}$ represent the variances of images $\mathbf{x}$ and
$\mathbf{y}$, respectively. The covariance of images $\mathbf{x}$ and
$\mathbf{y}$ is denoted as $\sigma_{\mathbf{xy}}$.

To visualize the impact of embedded messages on the image, we obtain new
images after embedding the messages. Taking CA-QIM as an example, Table 4
presents the average PSNR and SSIM values obtained by comparing the new images
with the original image in the spatial domain.

From Table II, it can be observed that the position of embedding has a
significant impact on the images, especially in low frequencies. On the
contrary, the effects of lattice dimension and the number of embedded messages
are relatively small. However, it is still noticeable that as the lattice
dimension increases, there is an increase in deviation, which may be caused by
the inverse discrete cosine transform.

Furthermore, from Figures 7, 8, and 9, it can be observed that embedding one
message at the low frequency DCT domain via $A_{2}$ already results in a
noticeable difference in the new image compared to the original image.
However, after embedding three messages in the medium and high frequencies in
$A_{2}$, there is still no significant difference observed in the new image.
Similarly, when embedding one message in low frequencies of $D_{4}$ and
$E_{8}$, the difference from the original image is clearly visible. In the
case of medium frequencies in $D_{4}$ and $E_{8}$, the new image shows a
difference from the original image after embedding two messages, while three
messages embedded in high frequencies are inconspicuous in both $D_{4}$ and
$E_{8}$.

In summary, due to the varying impact at different embedding sites, embedding
in high or medium frequencies results in less distortion. Additionally, the
embedding capacity is influenced by the embedding position. Higher frequencies
allow for more messages to be embedded without detection. Therefore, the
embedding position in the image should be selected as medium or high
frequency.

###  V-D Symbol Error Rate Measurement

The proposed method mainly modifies the labeling process, and its robustness
is equivalent to the original QIM. To evaluate the robustness, we introduce
five types of noise into the embedded images and extract the messages. Since
CAMD-QIM, which moves the host signals near the boundaries of the Voronoi
region, exhibits poor robustness, we only test CA-QIM in this section using
Symbol Error Rate (SER). We recorded the average SER in four cases: embedding
one message, two messages, three messages, and full embedding under $A_{2}$,
$D_{4}$, and $E_{8}$, and the results are displayed in Figure 10.

From Figure 10, we can make the following observations:

  1. 1.

In any type of noise, the SER under $A_{2}$ is lower than that under other
lattice bases.

  2. 2.

As the number of embedded messages increases, the SER also increases
continuously. Once the SER reaches a certain value, the final decoding effect
is not ideal. Therefore, while controlling the SER, it is recommended to use
the $A_{2}$ lattice and minimize the number of embedded messages.

In normal QIM, the symbol error rate typically decreases as the lattice
dimension increases. However, in this experiment, the results are opposite
because the image pixels in the experiment are integers. After the inverse
Discrete Cosine Transform (DCT), larger lattice dimensions lead to greater
pixel changes, and after rounding, the deviation becomes larger.

(a)  (b)

(c)  (d)

Figure 7: Embedding in images via CA-QIM with $\Lambda_{f}=A_{2}$. (a)
Original image (b) One message embedded in low frequency domain via $A_{2}$
(c) Two message embedded in medium frequency domain via $A_{2}$ (d)Three
message embedded in high frequency domain via $A_{2}$.

(a)  (b)

(c)  (d)

Figure 8: Embedding in images via CA-QIM with $\Lambda_{f}=D_{4}$. (a)
Original image (b) One message embedded in low frequency domain via $D_{4}$
(c) Two message embedded in medium frequency domain via $D_{4}$ (d)Three
message embedded in high frequency domain via $D_{4}$.

(a)  (b)

(c)  (d)

Figure 9: Embedding in images via CA-QIM with $\Lambda_{f}=E_{8}$. (a)
Original image (b) One message embedded in low frequency domain via $E_{8}$
(c) Two message embedded in medium frequency domain via $E_{8}$ (d)Three
message embedded in high frequency domain via $E_{8}$.

(a)  (b)  (c)  (d)  (e)

Figure 10: The SER performance of CA-QIM over different types of noise
attacks. (a) Gaussian noise (b) Salt noise (c) Pepper noise (d)Spicy Salt
noise (e) Speckle noise.

##  VI Conclusions

In conclusion, this paper introduced an enhanced version of the Quantization
Index Modulation (QIM) watermarking technique, incorporating a novel labeling
scheme. The proposed method effectively reduces embedding distortion by
adapting the codebook of host signals and messages, particularly benefiting
non-uniformly distributed messages. Through extensive simulations using
typical image datasets, the superiority of our approach has been demonstrated.
The research presented in this paper highlights the potential of combining QIM
watermarking with big data techniques, offering a promising direction for
improving the efficiency of watermarking systems. By leveraging data-driven
approaches and exploiting statistical properties, we can further enhance the
performance and effectiveness of image watermarking methods.

Future work in this area may involve exploring additional data-driven
techniques and optimizing the proposed labeling scheme to address different
challenges and scenarios. Continued research in image watermarking and its
integration with big data analytics holds significant potential for advancing
the field and enabling robust and efficient protection of digital media.

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