2013
DOI: 10.1016/j.protcy.2013.12.236
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Reversible Fragile Watermarking based on Difference Expansion Using Manhattan Distances for 2D Vector Map

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Cited by 14 publications
(7 citation statements)
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“…There are many approaches, like Manhattan distance [14], Minkowski distance [15], Euclidean distance [16] etc., to measure the distance between two data vector [3], [4]. In this work, the sum of squared Euclidean (SSE) distance between each data sample and the cluster center which data sample belongs is used as objective function to be minimized by algorithms.…”
Section: The Clustering Problemmentioning
confidence: 99%
“…There are many approaches, like Manhattan distance [14], Minkowski distance [15], Euclidean distance [16] etc., to measure the distance between two data vector [3], [4]. In this work, the sum of squared Euclidean (SSE) distance between each data sample and the cluster center which data sample belongs is used as objective function to be minimized by algorithms.…”
Section: The Clustering Problemmentioning
confidence: 99%
“…In order to guarantee the high quality of the watermarked 2D vector map, it is crucial to restrict as much as possible the distortion causing by the embedding process. This must be restricted by the map's precision tolerance [15]. Euclidean distances can be employed here to work out the extent of the distortions (Eq.…”
Section: )mentioning
confidence: 99%
“…Once the outlined process is complete, then the original difference for each unit will be obtained. When collaborating these with the integer-mean , it is then possible to work out the original coordinates of each unit by applying equations (13) to (15). To work out the watermark W' through the given method, the process above must be used.…”
Section: )mentioning
confidence: 99%
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“…However, the data structure of vector data is complex, including geometric information, attribute information, and topology information, which has four basic features of spatial, attribute, temporal, and scale, which increases the difficulty of vector data digital watermarking research. Currently, most scholars use the spatial features of vector data to study vector data digital watermarking technology due to the inapplicability of the attribute, temporal, and scale features of vector data [11][12][13][14][15][16][17][18][19]. Thus, the robustness of the watermarking algorithm after the spatial features of vector data is subjected to different geometric attack methods must be considered in the research of vector data digital watermarking algorithms.…”
mentioning
confidence: 99%