Markov Transition Probability Matrix Research Articles

Research on the coupling coordination characteristics and convergence of digital finance and regional sustainable development: evidence from Chinese city clusters

The study examines the digital finance (DF) and regional sustainable development (RSD) across 90 cities within six major city clusters in China over the period from 2011 to 2020. By constructing an evaluation index system for DF and RSD, we employed the entropy value method to assess their levels, and the coupling coordination degree (CCD) model to evaluate their interplay. Our analysis extended to temporal and spatial disparities, distribution dynamics, and the convergence of CCD through kernel density estimation, Markov chain analysis, σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma$$\\end{document}-convergence, and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-convergence techniques. The results indicate a consistent upward trend in CCD, yet it remains at a low level with pronounced regional disparities and temporal characteristics. The kernel density distribution’s central tendency has shifted rightward progressively, albeit with a decelerating pace annually. The Markov transition probability matrix suggests a stable CCD across various levels, hinting at “club convergence”. Furthermore, both σ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sigma$$\\end{document}-convergence and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta$$\\end{document}-convergence analyses reveal significant convergence trends in CCD, enhanced by economic growth factors. Using the Quadratic Assignment Procedure (QAP) method, we found that regional economic growth disparities significantly influence the CCD’s regional variances.

Three-dimensional stratigraphic reconstruction based on improved coupled Markov chain

The natural stratigraphic distribution is uncertain due to the geological tectonic movements and sedimentation. It is a challenge for traditional deterministic models to capture geological uncertainty. The objective of this study is to develop an improved three-dimensional coupled Markov chain (ICMC3D) model based on limited boreholes. The proposed method enhances the traditional three-dimensional CMC model by modifying the transition probability formula for predicting unknown elements. The dip data is added to estimate the transition probability matrix with the borehole information. On this basis, a back analysis method is proposed for estimating the horizontal transition probability matrics. The method makes the predicted results more suitable for the possible stratigraphic distribution. The accuracy of the proposed method is verified through three simple applications. In this paper, an improved three-dimensional coupled Markov chain model and transition probability matrix estimation method are illustrated by the borehole data collected from a submarine tunnel project in Qingdao. The results show that the presented method can reflect the asymmetry, continuity and anisotropy of the three-dimensional stratum. The exceedance probability is proposed to predict the fault zone development range in order to reduce the geological uncertainty.

Modelling of Prosumer Behaviour in Peer-to-Peer Energy Trading Environment Through Markov Chain Analysis

The emergence of distributed generation has become significant over the last few years, bringing several challenges to traditional grid-connected electricity distribution systems. Technical limitations of integrating these new renewable distributed generation to the existing electricity grid made new avenues to change the way of energy consumption, which converted traditional consumers to prosumers. Peer-to-peer energy trading platforms enable these prosumers to trade electricity with their neighbours in microgrids where new electricity markets emerge with new technologies. This research introduces a concept of peer-to-peer energy trading for grid-connected electricity distribution networks. In its initial phase, the study models prosumer load sharing for households equipped with solar PV and battery energy storage. This modelling employs a Markov chain, where energy share states are determined by parameters in a Markov transition probability matrix. These parameters are varied during different time intervals of the day, reflecting varying cost components under a Time-of-Use (TOU) tariff structure. This approach enables prosumers to meet their load demand cost-effectively, fostering engagement in peer-to-peer energy exchanges. The proposed Markov model is simulated with 15-minute spot pricing intervals, demonstrating effective management of prosumer load demands in the peer-to-peer market environment, showcasing the potential benefits of this innovative energy trading approach.

Feedback control strategy of networked multi-LSRMs system with semi-Markov topology switching and time delay

This paper studies the networked control system (NCS) with semi-Markov topology switching and network delay. The time delays of the system are considered in the measurement and control channels. The control channel is between the controller and the actuator, the measurement channel is between the sensor and the controller. The topology switching and the transition process among modes are described by semi-Markov sojourn-time probability density function and Markov transition probability matrix respectively. The mean square stability conditions for the networked multi-LSRMs system are obtained by constructing a new Lyapunov function. To ensure the σ-error mean square stability of the closed loop system, a state feedback controller is designed by combining the variation technique of inequalities and Lyapunov stability theory. Finally, several experiments results verify the effectiveness and rationality of the proposed control strategy.

Economic Resilience and Sustainable Finance Path to Development and Convergence in Romanian Counties

Economic resilience and sustainable finance are two interlinked and crucial issues for development and convergence in Romania’s counties increasing cohesion. These issues can contribute to sustainable and balanced growth of local and regional economies and to the reduction of inequalities in regional development. Economic resilience in counties refers to their capacity to adapt and survive in the face of unforeseen economic shocks or challenges, and sustainable finance refers to ensuring responsible management of financial resources to support long-term development and protect the environment. Identifying and understanding the significant variations in economic resilience and sustainable financing between counties is essential for the formulation of regional development policies and strategies. These variations provide valuable information about the vulnerabilities and opportunities of individual counties and guide resource allocation and investment decisions. The research provides new data and relevant information on the significant variations among counties in economic resilience and sustainable financing, using a Markov transition probability matrix and exploratory–visual method. This study on Romanian counties aims to provide valuable information for the formulation of public policies to support balanced economic development across the country. The results showed that economic diversification is essential to increase the resilience of the economy to shocks and fluctuations. Counties that have a diversified economic structure, with multiple sources of income and economic activities, are less vulnerable to the negative impact of economic or natural events. Governance and political stability are key factors in creating a favorable environment for investment and economic development. Well-managed government policies can help maintain macroeconomic stability and increase the resilience of the economy to external fluctuations.

Spatiotemporal Evolution, Coupling Coordination Degree and Obstacle Factors of Urban High-Quality Development: A Case Study of Anhui Province

Anhui Province is located in the superposition area of the “Strategy of the Rise of Central China” and the “Strategy of Integrated Development of the Yangtze River Delta”. Analyzing the high-quality development of Anhui Province is crucial for regional development. This paper proposes a comprehensive evaluation system based on the “New development philosophy”. Then, the information entropy method is applied to measure the high-quality development index (HQDI). The Markov transition probability matrix is used to explore the evolutionary trend of the HQDI. This paper also analyzes the coupling coordination relationships between high-quality development subsystems. Finally, the obstacle factor diagnostic model is adopted to find the factors that impede high-quality development. The result shows that: (1) There exists a significant spatial gradient difference in Anhui Province. The overall spatial distribution of the HQDI shows a pattern of “high in the central and east, low in the north and south”. (2) The “club convergence effect” and the “Matthew effect” of urban high-quality development are observed. (3) Subsystem analysis verified the existence of regional differences. Hefei has the leading position in all development subsystems. (4) The coupling coordination degree of subsystems is relatively low, and the problem of disorder development within Anhui Province is significant. (5) The fixed assets’ investment, the total amount of imports and exports, the GDP, the total urban wastewater treatment and the urban road passenger volume are the main obstacle factors.

Investigating Profit Persistence Among Hungarian Plastic Manufacturing Companies

This study examines the competitive nature of the Hungarian plastics industry sector based on 2010-2019 data from the Crefoport database.. The aim of the study is to examine that how close the market of plastic industry companies is to perfect competition. Market efficiency was investigated using a Markov chain and profit persistence estimation (Arellano & Bond, 1991). Corporate profitability was measured using the ROA indicator. Variables reflecting industry and market effects are also included in the analysis as controls. Based on the Markov transition probability matrix, market competition is harmed. Based on the panel model estimation, the profit persistence value shows a low value (0.129) compared to the existing literature. The profitability of plastic companies can be statistically proven to be affected by company size (p = -0.046), short (p = 0.016) and long risk (p=-0.093), and the volatility of profitability (p = 0.633). Among the exogenous variables, industry income (p=0.081) and market concentration (p = 0.974) have a significant effect on the profitability of companies. Limited market competition reduces overall social benefit and efficiency in several ways: it reduces price competition, quality orientation, and the pursuit of innovations. Therefore, from the point of view of economic policy , it is definitely justified that the sector receives subsidies in an appropriate amount that improves the efficiency and productivity of small and medium-sized enterprises, as well as encourage technological development and innovation.

Modelling spatiotemporal tendencies of climate types by Markov chain approach : A case study in Sanliurfa province in the south-eastern of Turkey

Identification of spatiotemporal tendencies of climate types may help water managers mitigate the negative impacts of droughts on water-demanding sectors. The primary objective of this study was to figure out the spatiotemporal tendencies of climatetypes in Sanliurfa province by using Erinc’s aridity index (EDI). To that end, long-term (1965-2018) annual precipitation and average annual maximum temperature series of meteorological stations were obtained and utilized to calculate the EDI series on a yearly basis. The EDI series of each station was divided into three periods, non-overlapping and successive, i.e., P1 (1965-1981), P2 (1982-1999) and P3 (2000-2018). Outliers were detected, andremoved from the EDI series; missing data were completed by regression analysis. The Markov transition probability matrix of the climate classes for the three periods was estimated for each station. Maps of the initial probability vectors and steady-state probabilities for the three periods of each climate class were generated by the inverse distance-weighted technique. Hypsometric curves for each climate class, as well as period, were developed and areal coverage of occurrence probabilities (OP) was determined. Results indicated that, as time progressed, the areal extent of severe-arid and arid climatic classes continued consistently to spread from the south to the north. Areas of semi-arid climate type showed a slight tendency towards the arid-climate type. Construction of large dams in the region could not prevent the shifts in the climate in favour of developing arid zones. The humid climate class is likely to vanish away in the future. Research led us to conclude that the expansion of the aridzone from south to northhas been alarming in terms of the adequacy of water resources. It is strongly recommended that spatiotemporal climate change studies should be periodically conducted in tandem with forest management practices for the region.

Temporal-Spatial Evolution and Trend Prediction of the Supply Efficiency of Primary Medical Health Service-An Empirical Study Based on Central and Western Regions of China.

China has established a comprehensive primary medical health service system, but the development of primary medical health services in the central and western regions is still unbalanced and insufficient. Based on data from 2010 to 2019, this paper constructs a super efficiency Slack-Based Measure model to calculate the supply efficiency of primary medical health services in 20 provinces and cities in central and western China. Using Kernel density estimation and Markov chain analysis, this paper further analyzes the spatial-temporal evolution of the supply efficiency of primary medical health services in central and western China, and also predicts the future development distribution through the limiting distribution of Markov chain to provide a theoretical basis for promoting the sinking of high-quality medical resources to the primary level. The results show that firstly, during the observation period, the center of the Kernel density curve moves to the left, and the main peak value decreases continuously. The main diagonal elements of the traditional Markov transition probability matrix are 0.7872, 0.5172, 0.8353, and 0.7368 respectively, which are significantly larger than other elements. Secondly, when adjacent to low state and high state, it will develop into convergence distributions of 0.7251 and 0.8243. The supply efficiency of primary medical health services in central and western China has the characteristics of high (Ningxia) and low (Shaanxi) aggregation respectively, but the aggregation trend is weakened. Thirdly, the supply efficiency of health services has the stability of keeping its own state unchanged, but the transition of state can still occur. The long-term development of the current trend cannot break the distribution characteristics of the high and low clusters, the efficiency will show a downward trend in the next 10-20 years, and still the problem of uneven long-term development emerges.

A Loosely Coupled Model for Simulating and Predicting Land Use Changes

The analysis and modeling of spatial and temporal changes in land use can reveal changing urban spatial patterns and trends. In this paper, we introduce a linear transformation optimization Markov (LTOM) model that can be exploited to estimate the state transition probability matrix of land use, building a loosely coupled ANN-CA-LTOM model for simulating and predicting land use changes. The advantages of this model are that it is flexible and high expansibility; it can maintain semantic coupling between the Artificial Neural Networks (ANN), Cellular Automata (CA), and LTOM model and enhance their functions; and it can break the limitation of requiring two periods of land use data when calculating the transition probability matrix. We also construct a suitability atlas of land use as the transition rules into the CA-LTOM model, taking into account the regional natural and socioeconomic driver factors, by exploiting the ANN model. The ANN-CA-LTOM model is employed to simulate the distribution of the three major types of land use, i.e., construction land, agricultural land, and unused land, in the Nansha District, China, in 2018 and 2020. The results show that the model performs well and the overall accuracy of the land use simulation was 97.72%, with a kappa coefficient of 0.962761. Furthermore, the simulated and predicted results of land use changes from 2021 to 2023 in Nansha District show changing trends in construction, agricultural, and unused land use. This study provides an approach for estimating a Markov transition probability matrix and a coupled mode of the models for simulating and predicting land use changes.

Analysis of the Gross Ecosystem Product—Gross Domestic Product Synergistic States, Evolutionary Process, and Their Regional Contribution to the Chinese Mainland

The trade-off and synergy relationship between ecosystem services (ESs) and human well-being (HWb) in the land-use process has become a research hotspot. The evolutionary process and regional contribution of the accurate quantification of ESs and HWb can provide a reference for government departments to formulate macroeconomic policies. Therefore, this study first constructed an analysis framework to identify the synergistic states/evolutionary stages of the gross ecosystem product (GEP) per capita (PGEP) and gross domestic product (GDP) per capita (PGDP) and the regional contribution of the GEP–GDP synergy of 362 municipal units in mainland China from 2000 to 2015. We did this by employing the Markov transition probability matrix, land use data, and economic data based on satellite remote sensing images. The findings of this study show that (1) the PGEP of the Chinese mainland has a remarkable spatial divergence featuring a higher value in the northwestern Chinese mainland and a lower value in the southeastern Chinese mainland on both sides of the Hu Line during the investigation period; despite the eastern Chinese mainland having a higher PGDP, the PGDP at the national level is distributed in dispersion on both sides of the Hu Line; (2) during the first half of the investigation period, the GEP–GDP synergy in the Chinese mainland was generally in the pseudo-synergy stage or the transition stage from pseudo-synergy to primary/intermediate synergy, while in the second half of the period, the GEP–GDP synergy in the Chinese mainland continued to improve; (3) the GEP–GDP synergy was relatively stable on the Chinese mainland during the investigation period, with 24.28% of the units shifting to a lower or higher level synergy, and the GEP–GDP synergy was more stable in the western and central Chinese mainland, while it was more likely to shift to a higher state in the northeastern and eastern Chinese mainland. This study suggests that the GEP–GDP relationship varies with spatial scales; a hierarchical, multiscale approach is necessary to study and improve both of these relationships, as simply extrapolating policies across single administrative levels may lead to unintended outcomes.

Heterogeneous Markov Chain Model to Predict Pavement Performance and Deterioration

In an era where system needs exceed available funding across all infrastructure components, planners and decision makers need tools to make informed decisions about the value of their assets, such as accurate models to predict pavement condition over time. This prediction is essential in pavement management systems because it provides information that allows forecasting repair demands and optimizing life-cycle costs. Markov chains have been proposed in the past as a tool for forecasting pavement performance and deterioration. A weakness of the traditional Markov chain is that the conventional transition matrix has limited ability to account for site-specific variability. To address this problem, this study proposes a combination of ordinal logistic regression and Markov chains. The logistic regression models were found to bring two major improvements to the Markov model. First, the enhanced Markov transition probability matrix allows for site-specific predictions because the models use specific characteristics of each pavement section. Second, the enhanced matrix offers additional benefits by allowing the comparison of several factors and the analysis of how each of them influences the pavement performance and deterioration, as well as providing an understanding of the interaction between these several external factors, such as district location, repair history, functional class, base thickness, speed limit, and pavement thickness. A numerical example is provided to demonstrate how the Markov transition matrix can be used to model future pavement deterioration.

Spatiotemporal pattern assessment of China’s industrial green productivity and its spatial drivers: Evidence from city-level data over 2000–2017

City-level accounting of industrial green productivity (IGP) is necessary to identify the different circumstances of industrial green transformation and development across Chinese cities. However, the lack of energy consumption data in the urban industrial sector leads to the assessment of China’s IGP at the macro provincial level, which is not conducive to further formulating systematic measures to improve IGP. Hence, based on the multi-source nighttime light (NTL) data fitted and corrected by DSMP/OLS and NPP/VIIRS images, this study simulates the total energy consumption of urban industrial sector and establishes an IGP analysis database combined with socio-economic data. Subsequently, the spatiotemporal pattern and drivers of IGP are systematically investigated by means of the Dagum Gini coefficient, spatial autocorrelation model, Markov transition probability matrix, and spatial econometric model. Four important findings arise from the analyses. Stylized facts show that an overall increase in IGP is accompanied by the exacerbation in spatial inequality, the year 2006 is a turning point from frequent fluctuations to steady growth. Specifically, interregional disparities have gradually become the main source of overall disparities in IGP across eight comprehensive economic zones, hypervariable density is the main source of overall disparities across three major urban agglomerations. Spatially, Global Moran’s I of IGP uninterruptedly increases from 0.043 in 2008 to 0.155 in 2017, showing a positive spatial correlation of high-high agglomeration and low-low agglomeration. Additionally, IGP has a strong spatial locking effect with the unchanged probability of 78.81%, 72.18%, 75.94%, 83.67%, and there is the coexistence of win–win and beggar-thy-neighbor phenomenon to a large extent. Results further reveal that IGP has a positively spatial spillover effect, economic development level, human capital, industrial agglomeration, and environmental regulations all work for driving IGP growth in local and neighboring areas. Based on the findings, policy recommendations for the improvement of IGP are provided.

Dynamics of Area Substitution of Pulses in India

Background: Pulses have been very curial in many aspects like; rich source of protein, economy aspect and contribute to agricultural and environmental sustainability. In this investigation an attempt has been made to evaluate the dynamics of area substitution between pulses and other crops, extent of spatial shift among pulses producing states and some policy measures have been suggested to stabilize the area under pulses across states. Methods: Secondary data on area of principal crops for the period 1966-2016 was used in this article. By computing quartile values, all states and groups of states were clubbed into four different quartiles for each decade. Area substitution among principal field crops including pulses has been analyzed using first order Markov transition probability matrix (TPM). Result: This TPM was further used to evaluate the mobility of membership status of states under pulses production. It was found that period 1986-2006 happened to be the golden period for area under pulses in India. Mean area under pulses had increased for first three decades and in the subsequent two decades mean area (quartile values) had declined substantially.

Complex network analysis of the thermal lens signal: a Markov model approach.

The paper reports a novel, to the best of my knowledge, complex network-based Markov model approach to analyze the thermal lens (TL) signal. The complex network is constructed by segmenting the experimental and fitted TL signals into three regions. Here, a new parameter, degree of fluctuation, is introduced to analyze the Markov transition probability matrix (M) and the increase of system enthalpy leading to increased Brownian motion. The spread of data about the diagonal elements of M distinguishes the experimental and fitted data and appears as an increased number of edges in the complex network. Thus, the system's network displays the transient heat flow giving information about the Brownian motion in the medium.

Higher Order Statistics Based Blind Steg analysis using Deep Learning

Universal isteganalysis of grey level JPEG images is addressed by modelling the neighbourhood relationship of the image coefficients using the higher order statistical method developed by two-step Markov Transition Probability Matrix (TPM). The implementation of TPM together with the neighbouring pixel relationship provides a better and comparable detection results. The detection accuracy is evaluated on the stego image database using eXtreme Gradient Boosting (XGBoost) with Principal Component Analysis (PCA) on nsF5 and JUNIWARD hiding techniques. Execution time is also compared for all the classifiers. The images are taken from Green spun library and Google website- eXtreme Gradient Boosting.

Analyzing land use structure efficiency with carbon emissions: A case study in the Middle Reaches of the Yangtze River, China

China has a large population and limited land resources. The dearth of available land poses considerable challenges for economic development and environmental protection. In order to realize maximum benefits through the optimization of land use structure, land use structure efficiency (LUSE) becomes an important planning guideline for the sustainable development of a region. This paper conducts a case study in the Middle Reaches of the Yangtze River (MRYR) and investigates the LUSE of the region considering the effect of carbon emissions from 1995 to 2018 by using the slack-based measure with undesirable output (SBM-Undesirable) model and Markov transition probability matrix with spatial effect. The results show that: (1) the average LUSE in the study area is 0.652 when the carbon emissions are not considered, compared with that of 0.569 when the carbon emissions are factored in. The comparative result indicates that carbon emissions have a great impact on the LUSE; (2) the LUSE has a rising trend during the study period (except for 2010) starting with a value of 0.463 in 1995 and ending with a value of 0.671 in 2018. Furthermore, the spatial pattern of the LUSE in the study area has been through a drastic change, with the high-value areas clustered at a single center in 1995 evolving to a multiple-center pattern in 2018; (3) High LUSE areas have a positive spillover effect on its neighboring areas, while low LUSE areas have negative spillover effects. The results can provide insights into the optimization of land use structure and the efficient utilization of land resources. This study also suggests that policy makers should optimize the industrial structure and propose policy initiatives oriented towards goals of energy-saving and emission reduction to facilitate regional planning and sustainable development.

Tracking spatio-temporal variation of geo-tagged topics with social media in China: A case study of 2016 hefei rainstorm

Tracking how discussion geotagged topics evolve over time in social media has the potential to provide emergency information in natural disasters. In the traditional evolution of social media topics of disaster events, there are some problems, such as the topic of spatial subcategory aggregation is rarely discussed. Due to the behavior patterns of the focus groups in disaster events, it is inevitable to focus on the transfer and evolution of the focus topics of individuals in different periods before, during and after the disaster. In this study, we establish a framework to collect social media data from Sina Weibo, extract and analyze valuable information for emergency management. By using the case of 2016 Hefei rainstorm and flood disaster in China, this paper proposes a novel attempt to introduce latent Dirichlet allocation (LDA) model into density-based spatial clustering of applications with noise (DBSCAN) for exploring topics of spatial sub-categories, and quantitatively analyze the temporal evolution characteristics of fine-grained topics related to natural disasters by combining LDA topics and Markov transition probability matrix. The results indicate that before the rainstorm, people are advised to prepare for rainy travel, and they show attention for traffic inconvenience caused by pavement flooding. During the rainstorm, the continuous rainfall has had a serious impact on the traffic situation between Hefei and other cities. Floods broke out in certain areas, and the action of flood fighting and rescue is imminent. After the rainstorm, the weather gradually improved, and post-disaster reconstruction is particularly important. This study has the potential to promote effective policies and will allow decision-makers to respond quickly in the mitigation of damage caused by natural disasters.

An Enhancement of Svm Based Semantically Enriched Variable Length Confidence Pruned Markov Chain Model Based Web Page Recommendation System

Semantic Variable Length Markov Chain Length Model (SVLMC) is a web page recommendation system which combined the fields of semantic web and web usage mining by the Markov transition probability matrix with rich semantic information extracted from web pages. Though it has high prediction accuracy, it has problem of high state space complexity. The high space complexity reduce the execution speed and reduce the performance of the system, which was resolved by Semantic Variable Length confidence pruned Markov Chain Model (SVLCPMC) model that provides high user satisfied recommendation and Confidence Pruned Markov Model (CPMM). The time consumption of CPMM was reduced by Support Vector Machine (SVM). But still the recommendation accuracy is still below the user satisfaction. So in this paper, quickest change detection using Kullback-Leibler Divergence method is introduced to improve the accuracy of recommendation generation by developing a scalable quickest change detection schemes that can be implemented recursively in a more complicated scenario of Markov model and it is included in the training data of SVM. Then the performance of web page recommendation is improved by ranking the web pages using page ranking technique. Thus the performance of web page recommendation generation system has been improved. The experiments are conducted to prove the effectiveness of the proposed work in terms of prediction accuracy, precision, recall, F1-measure, coverage and R measure.

Digital image forensic approach based on the second-order statistical analysis of CFA artifacts

The truthfulness of digital images can be evaluated by investigating the CFA artifacts introduced due to the interpolation process of the image acquisition phase. In this paper, an image tampering detection technique is proposed by exposing the CFA artifacts in difference domain through the higher-order statistical analysis based on the Markov transition probability matrix (MTPM). Firstly, the given image is re-interpolated with most commonly used four Bayer CFA patterns. The re-interpolation process is performed by using bilinear interpolation scheme for simplicity purpose. Then, the difference between the given image and its re-interpolated versions is evaluated to analyze the CFA inconsistencies. The target difference image is selected corresponding to the maximum sum which is further processed to evaluate the MTPM based second-order statistical feature. The recommended approach is assessed on different images from UCID dataset and various social networking websites based on scalar-based and SVM/machine learning based forensic detectors. The experiment results confirm that the projected method offers improved efficiency in comparison to the existing techniques based on different forgery scenarios.