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Journal : Journal of Research in Mathematics Trends and Technology

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Copula-Based Blind Detection of Copy-Move Image Forgery: A Robust Mutual Information Approach Marpaung, Tulus Joseph; Tulus; Sofiyah, Fivi Rahmatus
Journal of Research in Mathematics Trends and Technology Vol. 7 No. 1 (2025): Journal of Research in Mathematics Trends and Technology (JoRMTT)
Publisher : Talenta Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32734/jormtt.v7i1.20520

Abstract

Copula functions are powerful statistical tools for modeling the dependency structure between random variables and have been widely applied in domains such as finance, oceanography, and hydrology. However, their application in image processing, particularly for image forgery detection, remains underexplored. This study proposes a novel blind copy-move forgery detection algorithm based on copula-based mutual information, which evaluates statistical dependencies between overlapping image blocks. By leveraging copula theory, the method accurately identifies duplicated regions within a single image without requiring prior knowledge or external references. Experimental results on the CoMoFoD dataset demonstrate that the proposed method achieves high precision, recall, and F1-scores across various manipulation types, including translation, scaling, and rotation, and shows resilience to post-processing operations such as JPEG compression, blurring, noise, and color reduction. Comparative analysis reveals that the copula-based approach outperforms classical methods such as SIFT, SURF, and DWT-SVD. In addition to quantitative performance, qualitative visualizations confirm that the algorithm effectively localizes forged regions in complex scenes with minimal false detections. These findings highlight the potential of copula functions as a robust and efficient framework for digital image forensics.
Efficiency of Environmental Performance Measurement Using Data Envelopment Analysis (DEA) With Fuzzy Approach: English Nadhila, Nurul; Tulus; Mardiningsih
Journal of Research in Mathematics Trends and Technology Vol. 7 No. 2 (2025): Journal of Research in Mathematics Trends and Technology (JoRMTT)
Publisher : Talenta Publisher

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32734/jormtt.v7i2.21717

Abstract

This study aims to analyze and measure environmental performance efficiency in residential areas in Medan City using the Data Envelopment Analysis (DEA) method combined with a fuzzy approach. Environmental performance is measured based on relevant inputs and outputs, where the data used are secondary data obtained from previous research reports. Fuzzification is applied to address uncertainty in the data by converting input and output values into Triangular Fuzzy Numbers (TFN). The results of the study show that out of the 4 Decision Making Units (DMUs) studied without using the fuzzy approach, only the Helvetia housing complex achieved 100% efficiency. Meanwhile, the efficiency values for Tuntungan, Martubung, and Johor housing estates were 85.92%, 88.69%, and 94.87%, respectively. When the fuzzy approach was applied, the efficiency values of the Johor and Helvetia housing estates reached 100% efficiency, while the Tuntungan and Martubung housing estates had an efficiency of 78.22%, indicating inefficiency. This inefficiency is caused by excessive use of drainage inputs, indicating that these housing complexes are unable to produce environmental outputs commensurate with the inputs used. This study recommends improving the quality and quantity of environmental management and cleanliness, as well as the availability and quality of green spaces, to enhance environmental efficiency in housing. The findings of this study provide important insights into the efficiency of environmental performance measurement and highlight opportunities for improvement in environmental management within housing.
Co-Authors Ameilia Zuliyanti Siregar Ayu, Putri Chandra Diana Chalil Eva Sartini Bayu Evada, Zakiah Farida Ariani Fatimah Fivi Rahmatus Sofiyah Hasanuddin Herawati, Elvina Hrp, Hafizah Miranda Putri M Tafsin Mardiningsih Marpaung, J.L. Marpaung, T.J. Marpaung, Tulus Joseph Herianto Muhammad Zarlis, Muhammad Nababan, Ester Sorta Mauli Nababan, Esther Sorta Mauli Nadhila, Nurul Nasution, Muheri Indra Aja Nismah Panjaitan Parapat Gultom Rahmadini, Salsabila Riantri Barus, Riantri Sawaluddin Sembiring, Pramio Garson Sofyan, Rudy Susilo, Hariadi Syahputra, M.R. Syahputra, Muhammad Romi Tugiman Yunilas Yunilas Zulkifli Nasution