Design of two-dimensional digital filters using singular-value decomposition and balanced approximation method

1991 ◽  
Vol 39 (10) ◽  
pp. 2253-2262 ◽  
Author(s):  
W.-S. Lu ◽  
H.-P. Wang ◽  
A. Antoniou
Keyword(s):  
Singular Value Decomposition ◽  
Approximation Method ◽  
Digital Filters ◽  
Singular Value ◽  
Two Dimensional ◽  
Value Decomposition

scholarly journals Dual Zero-Watermarking Scheme for Two-Dimensional Vector Map Based on Delaunay Triangle Mesh and Singular Value Decomposition

2019 ◽  
Vol 9 (4) ◽  
pp. 642 ◽  
Author(s):  
Xu Xi ◽  
Xinchang Zhang ◽  
Weidong Liang ◽  
Qinchuan Xin ◽  
Pengcheng Zhang
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Two Dimensional ◽  
Triangle Mesh ◽  
Vector Map ◽  
Vector Maps ◽  
Feature Sequence ◽  
Zero Watermarking ◽  
Value Decomposition ◽  
Watermarking Scheme

Digital watermarking is important for the copyright protection of electronic data, but embedding watermarks into vector maps could easily lead to changes in map precision. Zero-watermarking, a method that does not embed watermarks into maps, could avoid altering vector maps but often lack of robustness. This study proposes a dual zero-watermarking scheme that improves watermark robustness for two-dimensional (2D) vector maps. The proposed scheme first extracts the feature vertices and non-feature vertices of the vector map with the Douglas-Peucker algorithm and subsequently constructs the Delaunay Triangulation Mesh (DTM) to form a topological feature sequence of feature vertices as well as the Singular Value Decomposition (SVD) matrix to form intrinsic feature sequence of non-feature vertices. Next, zero-watermarks are obtained by executing exclusive disjunction (XOR) with the encrypted watermark image under the Arnold scramble algorithm. The experimental results show that the scheme that synthesizes both the feature and non-feature information improves the watermark capacity. Making use of complementary information between feature and non-feature vertices considerably improves the overall robustness of the watermarking scheme. The proposed dual zero-watermarking scheme combines the advantages of individual watermarking schemes and is robust against such attacks as geometric attacks, vertex attacks and object attacks.

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