Affine Invariant Watermarks for 3D Polygonal and NURBS Based Models

  • Oliver Benedens
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1975)

Abstract

We present a scheme for embedding secret or public readable watermarks into 3D models consisting of polygonal or NURBS surfaces. The scheme realizes affine invariant watermarks by displacing vertices (control points) and satisfies constraints regarding maximum tolerated vertex movements or, in the NURBS case, differences of original and watermarked surfaces. The algorithm uses the volume of two tetrahedrons as an embedding feature. The scheme described can be stacked on a more robust scheme allowing transmission of labeling information to the user or increasing blind detection capabilities of the underlying scheme. The paper makes two major contributions, both driven by real world requirements: The first one is a technique to cope with reduced precisions of vertex coordinates. Real world modeling applications represent vertex coordinates with single floating point precision. Vertex coordinates in VRML scenes are represented by 6 decimal digits or even less. Mesh compression schemes may quantize vertex coordinates to even below precision of 4 decimal digits. The second contribution of this paper is a general technique for reducing processing time of watermark (label) extraction satisfying impatient users and enhancing robustness with respect to affiine transformations and, in particular, vertex randomization attacks. The technique is based on simplifying the mesh applying edge collapses prior to watermark embedding and retrieval. The technique depends on a consistent order of vertices in embedding and retrieval process. We sketch possible extensions of the proposed scheme.

Keywords

Watermarking 3D Polygonal Model NURBS Surfaces Public readable Watermark Secret Watermark Affine Transformation. 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Oliver Benedens
    • 1
  1. 1.Department of Security Technology forGraphics and Communication SystemsFraunhofer Institute for Computer GraphicsDarmstadtGermany

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