The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist ...The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually. Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.展开更多
We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-...We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.展开更多
This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the re...This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE（3）, or I is SE（3）-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element for- mulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equiv- ariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this al- gorithm.展开更多
This paper proposes a novel robust image watermarking scheme for digital images using local invariant features and Independent Component Analysis （ICA）. Most present watermarking algorithms are unable to resist geom...This paper proposes a novel robust image watermarking scheme for digital images using local invariant features and Independent Component Analysis （ICA）. Most present watermarking algorithms are unable to resist geometric distortions that desynchronize the location. The method we propose here is robust to geometric attacks. In order to resist geometric distortions, we use a local invariant feature of the image called the scale invariant feature transform, which is invariant to translation and scaling distortions. The watermark is inserted into the circular patches generated by scale-invariant key point extractor. Rotation invariance is achieved using the translation property of the polar-mapped circular patches. Our method belongs to the blind watermark category, because we use Independent Component Analysis for detection that does not need the original image during detection. Experimental results show that our method is robust against geometric distortion attacks as well as signal-processing attacks.展开更多
To protect the copyright of the image as well as the image quality, a kind of image zero-watermark method based on the Krawtchouk moment invariants and timestamp is proposed. A method is used to protect the image, in ...To protect the copyright of the image as well as the image quality, a kind of image zero-watermark method based on the Krawtchouk moment invariants and timestamp is proposed. A method is used to protect the image, in which features are drawn out from the image as the watermarking. The main steps of the method are presented. Firstly, some low-order moment invariants of the image are extracted. Secondly, the moment invariants and the key are registered to a fair third party to gain the timestamp. Finally, the timestamp can be used to prove who the real owner is. The processing method is simple, only with a few low-order moment invariants to be computed. Experimental results are obtained and compared with those of the method based on geometric moment invariants. Results show that the scheme can well withstand such geometrical attacks as rotating, scaling, cropping, combined attack, translating, removing lines, filtering, and JPEG lossy compression.展开更多
Contraposing the need of the robust digital watermark for the copyright protection field, a new digital watermarking algorithm in the non-subsampled contourlet transform （NSCT） domain is proposed. The largest energy...Contraposing the need of the robust digital watermark for the copyright protection field, a new digital watermarking algorithm in the non-subsampled contourlet transform （NSCT） domain is proposed. The largest energy sub-band after NSCT is selected to embed watermark. The watermark is embedded into scaleinvariant feature transform （SIFT） regions. During embedding, the initial region is divided into some cirque sub-regions with the same area, and each watermark bit is embedded into one sub-region. Extensive simulation results and comparisons show that the algorithm gets a good trade-off of invisibility, robustness and capacity, thus obtaining good quality of the image while being able to effectively resist common image processing, and geometric and combo attacks, and normalized similarity is almost all reached.展开更多
3D objects can be stored in computer of different describing ways, such as point set, polyline, polygonal surface and Euclidean distance map. Moment invariants of different orders may have the different magnitude. A m...3D objects can be stored in computer of different describing ways, such as point set, polyline, polygonal surface and Euclidean distance map. Moment invariants of different orders may have the different magnitude. A method for normalizing moments of 3D objects is proposed, which can set the values of moments of different orders roughly in the same range and be applied to different 3D data formats universally. Then accurate computation of moments for several objects is presented and experiments show that this kind of normalization is very useful for moment invariants in 3D objects analysis and recognition.展开更多
In this paper a blind image watermarking that can resist to rotation, scaling and translation （RST） attacks is proposed. Based on the spread spectrum, the watermark is modulated before embedding. The logpolar mapped...In this paper a blind image watermarking that can resist to rotation, scaling and translation （RST） attacks is proposed. Based on the spread spectrum, the watermark is modulated before embedding. The logpolar mapped discrete fourier transform （LPM-DFT） magnitude of a disk, a part of the origin image, constitutes the RST-invariant domain, where the origin of the LPM is the center of the disk and the sampling rates of the LPM are constant. After the middle frequency band of LPM-DFT magnitude, namely the watermark-embedding domain, is grouped according to the watermark length, the watermark is embedded by adjusting the difference between the two sub-region energy in each group. To improve the imperceptibility, the watermark-embedding domain is shuffled before embedding and the watermark is not embedded directly into the watermark-embedding domain. In watermark detection procedure, neither the original image nor any knowledge about the distortions is required. Experimental results show that the proposed scheme is very robust against RST distortion and common image processing attacks.展开更多
In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on t...In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.展开更多
文摘The weakness of classical watermarking methods is the vulnerability to geometrical distortions that widely occur during normal use of the media. In this letter, a new image- watermarking method is presented to resist Rotation, Scale and Translation (RST) attacks. The watermark is embedded into a domain obtained by taking Radon transform of a circular area selected from the original image, and then extracting Two-Dimensional (2-D) Fourier magnitude of the Radon transformed image. Furthermore, to prevent the watermarked image from degrading due to inverse Radon transform, watermark signal is inversely Radon transformed individually. Experimental results demonstrate that the proposed scheme is able to withstand a variety of attacks including common geometric attacks.
文摘We consider maps on positive definite cones of von Neumann algebras preserving unitarily invariant norms of the spectral geometric means. The main results concern Jordan *-isomorphisms between <em>C</em>*-algebras, and show that they are characterized by the preservation of unitarily invariant norms of those operations.
文摘This article is concerned with finite element implementations of the three- dimensional geometrically exact rod. The special attention is paid to identifying the con- dition that ensures the frame invariance of the resulting discrete approximations. From the perspective of symmetry, this requirement is equivalent to the commutativity of the employed interpolation operator I with the action of the special Euclidean group SE（3）, or I is SE（3）-equivariant. This geometric criterion helps to clarify several subtle issues about the interpolation of finite rotation. It leads us to reexamine the finite element for- mulation first proposed by Simo in his work on energy-momentum conserving algorithms. That formulation is often mistakenly regarded as non-objective. However, we show that the obtained approximation is invariant under the superposed rigid body motions, and as a corollary, the objectivity of the continuum model is preserved. The key of this proof comes from the observation that since the numerical quadrature is used to compute the integrals, by storing the rotation field and its derivative at the Gauss points, the equiv- ariant conditions can be relaxed only at these points. Several numerical examples are presented to confirm the theoretical results and demonstrate the performance of this al- gorithm.
基金Supported by the National Natural Science Foun-dation of China (60373062 ,60573045)
文摘This paper proposes a novel robust image watermarking scheme for digital images using local invariant features and Independent Component Analysis （ICA）. Most present watermarking algorithms are unable to resist geometric distortions that desynchronize the location. The method we propose here is robust to geometric attacks. In order to resist geometric distortions, we use a local invariant feature of the image called the scale invariant feature transform, which is invariant to translation and scaling distortions. The watermark is inserted into the circular patches generated by scale-invariant key point extractor. Rotation invariance is achieved using the translation property of the polar-mapped circular patches. Our method belongs to the blind watermark category, because we use Independent Component Analysis for detection that does not need the original image during detection. Experimental results show that our method is robust against geometric distortion attacks as well as signal-processing attacks.
文摘To protect the copyright of the image as well as the image quality, a kind of image zero-watermark method based on the Krawtchouk moment invariants and timestamp is proposed. A method is used to protect the image, in which features are drawn out from the image as the watermarking. The main steps of the method are presented. Firstly, some low-order moment invariants of the image are extracted. Secondly, the moment invariants and the key are registered to a fair third party to gain the timestamp. Finally, the timestamp can be used to prove who the real owner is. The processing method is simple, only with a few low-order moment invariants to be computed. Experimental results are obtained and compared with those of the method based on geometric moment invariants. Results show that the scheme can well withstand such geometrical attacks as rotating, scaling, cropping, combined attack, translating, removing lines, filtering, and JPEG lossy compression.
基金supported by the National Natural Science Foundation of China(61379010)the Natural Science Basic Research Plan in Shaanxi Province of China(2015JM6293)
文摘Contraposing the need of the robust digital watermark for the copyright protection field, a new digital watermarking algorithm in the non-subsampled contourlet transform （NSCT） domain is proposed. The largest energy sub-band after NSCT is selected to embed watermark. The watermark is embedded into scaleinvariant feature transform （SIFT） regions. During embedding, the initial region is divided into some cirque sub-regions with the same area, and each watermark bit is embedded into one sub-region. Extensive simulation results and comparisons show that the algorithm gets a good trade-off of invisibility, robustness and capacity, thus obtaining good quality of the image while being able to effectively resist common image processing, and geometric and combo attacks, and normalized similarity is almost all reached.
基金Supported by National Key Basic Research Program(No.2004CB318006)National Natural Science Foundation of China(Nos.60873164,60573154,60533090,61379082 and 61227802)
文摘3D objects can be stored in computer of different describing ways, such as point set, polyline, polygonal surface and Euclidean distance map. Moment invariants of different orders may have the different magnitude. A method for normalizing moments of 3D objects is proposed, which can set the values of moments of different orders roughly in the same range and be applied to different 3D data formats universally. Then accurate computation of moments for several objects is presented and experiments show that this kind of normalization is very useful for moment invariants in 3D objects analysis and recognition.
基金Supported by the National Natural Science Foundation ofChina (60502024)the Natural Science Foundation of Hubei Province(2005ABA267) the Electronic Development Fund of Ministry of Informa-tionIndustry of China and the Innovation Fundfor Technology Based Firmsof Ministry of Science and Technology of China (04C26214201284) .
文摘In this paper a blind image watermarking that can resist to rotation, scaling and translation （RST） attacks is proposed. Based on the spread spectrum, the watermark is modulated before embedding. The logpolar mapped discrete fourier transform （LPM-DFT） magnitude of a disk, a part of the origin image, constitutes the RST-invariant domain, where the origin of the LPM is the center of the disk and the sampling rates of the LPM are constant. After the middle frequency band of LPM-DFT magnitude, namely the watermark-embedding domain, is grouped according to the watermark length, the watermark is embedded by adjusting the difference between the two sub-region energy in each group. To improve the imperceptibility, the watermark-embedding domain is shuffled before embedding and the watermark is not embedded directly into the watermark-embedding domain. In watermark detection procedure, neither the original image nor any knowledge about the distortions is required. Experimental results show that the proposed scheme is very robust against RST distortion and common image processing attacks.
基金This work was supported by National Natural Science Foundation of China(Grant Nos.11631007 and 11971251).
文摘In this paper,the invariant geometric flows for hypersurfaces in centro-affine geometry are explored.We first present evolution equations of the centro-affine invariants corresponding to the geometric flows.Based on these fundamental evolution equations,we show that the centro-affine heat flow for hypersurfaces is equivalent to a system of ordinary differential equations,which can be solved explicitly.Finally,the centro-affine invariant normal flows for hypersurfaces are investigated,and two specific flows are provided to illustrate the behaviour of the flows.
