Sequential Straightforward Clustering for Local Image Block Matching Mohammad Akbarpour Sekeh ,Mohd. Aizaini Maarof, Mohd. Foad Rohani, Malihe Motiei Abstract—Duplicated region detection is a technical method to expose copy-paste forgeries on digital images. Copy-paste is one of the common types of forgeries to clone portion of an image in order to conceal or duplicate special object. In this type of forgery detection, extracting robust block feature and also high time complexity of matching step are two main open problems. This paper concentrates on computational time and proposes a local block matching algorithm based on block clustering to enhance time complexity. Time complexity of the proposed algorithm is formulated and effects of two parameter, block size and number of cluster, on efficiency of this algorithm are considered. The experimental results and mathematical analysis demonstrate this algorithm is more cost- effective than lexicographically algorithms in time complexity issue when the image is complex. Keywords—Copy-paste forgery detection, Duplicated region, Time complexity, Local block matching, Sequential block clustering. I. I NTRODUCTION W ITH today’s advance and widely accessible image edit- ing software, it is so easy to manipulate digital image. Unfortunately, it often causes to creation of forged images. This can reduce the reliability of the digital image. As digital images are one of the most important and useful information in some area such as forensic investigation, criminal investi- gation, insurance services, surveillance systems, intelligence services and other information system organizations, image forgery detection was created. Digital image forgery detection system is to discover evidence of tampering by scrutinizing the forgery’s clues on the image. As several existing types of forgery on the image, there are several methods to explore the digital image forgeries. Based on literature, it can be found that researchers are trying to detect the image forgeries via following proposed techniques: Duplicated region detection [1]- [2]- [3], Noise inconsistency [4]- [5], Light inconsistency [6], Color filter array processing [7] and Traces of the re-sampling detection [8]. In this paper we scrutinize copy-paste forgery’s clues and focus on duplication region detection. Duplicated region de- tection has two main facing open problems: The first problem is robustness and accuracy of the detection against under- modification operations such as rotation, noising, compression and retouching. Another important problem in duplicated Mohammad Akbarpour Sekeh is working on image forgery detection area, Email: asmohammad4@live.utm.my. Mohd. Aizaini Bin Maarof is focused Network and Multimedia Forensic, Email: aizaini@utm.my Mohd. Foad Rohani is working on Intrusion Detection Systems, Email: foad@utm.my Malihe Motiei is doing Information Security Awareness measuring, Email: mmalihe2@live.utm.my region detection is high time complexity of the block matching step. This paper concentrates on improving time complexity of the forgery detection with proposing a local block matching technique and is organized in five major parts. The first part is begun with introducing the image forgery detection and scope of the study. In part II, related works, duplicated region detec- tion, research area, problems and block clustering techniques will be overviewed. Part III explains the local block matching algorithm based on sequential block clustering in order to reduce computational time. In part IV, we formulate the time complexity function of proposed algorithm and mathematically analysis for comparing the algorithm with previous methods. And finally, we bring conclusion of the research and explain the future works. II. RELATED RESEARCH The first publication in copy-move forgery detection area has been proposed by Fridrich in [1]. The paper proposed DCT coefficients as block presentation method and detection of the duplicated region was based on matching the quantized lexicographically sorted discrete cosine transform coefficients of blocks. The lexicographically sorting has complexity in order of O(MNlogMN ) that M and N are width and height of image. The next two papers, Popescu and Farid [2] proposed Principal Component Analysis (PCA) instead of DCT to reduce the block feature dimension and Bayram [9] proposed Fourier Mellin Transform (FMT) to enhance the robustness against scaling and rotation, also applied lexicographically sorting for finding the duplicated regions in the image. Bayram [9] also proposed a new method to improve the efficiency and reduce the time complexity namely Counting Bloom Filters with hashing the feature vectors. However, finding the effective hash function is not easy and also this technique affects robustness of the system. Babak Mahdian [10] proposed blurring invariant feature to enhance the robustness against blurring and kd-tree presenta- tion for improving the complexity of the matching step. As complexity of kd-tree depends on the distribution of similar intensity blocks, one of the important problems in Babak’s method is yet high computational time [11]- [12]. Hwei-jen Lin et.al [13] proposed a new block feature ex- traction method. They represented each overlapping blocks by 9-dimensional feature vector in spatial domain for improving the robustness against compression and noising. They also applied efficient Radix-sort for performing the lexicographi- cally sorting with order of O(nk). The radix-sort limits type World Academy of Science, Engineering and Technology 74 2011 775