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Difference Equations: From Rabbits to Chaos

Paul Cull Mary Flahive Robby Robson

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Institución detectada Año de publicación Navegá Descargá Solicitá
No detectada 2005 SpringerLink

Información

Tipo de recurso:

libros

ISBN impreso

978-0-387-23233-1

ISBN electrónico

978-0-387-27645-8

Editor responsable

Springer Nature

País de edición

Reino Unido

Fecha de publicación

Información sobre derechos de publicación

© Springer Science+Business Media, Inc. 2005

Cobertura temática

Tabla de contenidos

Fibonacci Numbers

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 1-10

Homogeneous Linear Recurrence Relations

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 11-31

Finite Difference Equations

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 33-65

Generating Functions

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 67-99

Nonnegative Difference Equations

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 101-135

Leslie’s Population Matrix Model

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 137-178

Matrix Difference Equations

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 179-216

Modular Recurrences

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 217-251

Computational Complexity

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 253-295

Some Nonlinear Recurrences

Paul Cull; Mary Flahive; Robby Robson

This paper presents a high-capacity data hiding method for 3D polygonal meshes. By slightly modifying the distance from a vertex to its traversed neighbors based on quantization, a watermark (i.e., a string of binary numbers) can be embedded into a polygonal mesh during a mesh traversal process. The impact of embedding can be tuned by appropriately choosing the quantization step. The embedded data is robust against those content-preserving manipulations, such as rotation, uniformly scaling and translation, as well as mantissa truncation of vertex coordinate to a certain degree, but sensitive to malicious manipulations. Therefore, it can be used for authentication and content annotation of polygonal meshes. Compared with the previous work, the capacity of the proposed method is relatively high, tending to 1 bit/vertex. Besides to define the embedding primitive over a neighborhood so as to achieve resistance to substitution attacks, the security is also improved by making it hard to estimate the quantization step from the modified distances. A secret key is used to order the process of mesh traversal so that it is even harder to construct a counterfeit mesh with the same watermark. The numerical results show the efficacy of the proposed method.

Pp. 297-336