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Wavelet Transform Based Digital Watermarking for 3-D Surface Meshes and Mesh Sequences
Reports NRF is supported by Research Projects( Wavelet Transform Based Digital Watermarking for 3-D Surface Meshes and Mesh Sequences | 2005 Year 신청요강 다운로드 PDF다운로드 | 김민수(영남대학교) ) data is submitted to the NRF Project Results
Researcher who has been awarded a research grant by Humanities and Social Studies Support Program of NRF has to submit an end product within 6 months(* depend on the form of business)
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  • Researchers have entered the information directly to the NRF of Korea research support system
Project Number D00063
Year(selected) 2005 Year
the present condition of Project 종료
State of proposition 재단승인
Completion Date 2008년 10월 01일
Year type 결과보고
Year(final report) 2008년
Research result report
  • Abstract
  • This thesis deals with digital watermarking methods for copyright protection of 3-D surface meshes and mesh sequences. The proposed methods are based on wavelet analysis of the geometry of the surface meshes, or on wavelet analysis of the vertex coordinate signals along the time axis.

    3-D static meshes

    The first proposal embeds the watermark into the L2 norm of the geometric wavelet coefficients (vectors) by using spread spectrum method. The Cartesian coordinates should be converted into the spherical coordinates. The method can directly process semi-regular or irregular meshes. For the invariance of the wavelet coefficients after inverse wavelet transform, it is necessary to synchronize the connectivity by re-ordering the vertex indexes from a reference vertex. This approach ensures the blind detection which does not require the original meshes during watermark extraction procedures.
    The second proposal is based on a statistical approach. The histogram of the L2 norm of scale coefficients (approximation mesh) was divided into regular bins. The mean (or the variance) of each bin is modified according to the watermark by a non-linear exponential transformation. The watermark can be extracted from the distribution of the scale coefficients after wavelet analysis, as well as from the distribution of vertex norms of the watermarked meshes without using the wavelet analysis. This proposal is more robust against topological attacks than the first one.

    3-D mesh sequence (3-D dynamic meshes with fixed connectivity, 3D+t)

    The first proposal is based on the vertex coordinate signals along the time axis, and the second uses the vertex norm signals along the time axis of the mesh sequence. As a result, the number of signals to decompose by wavelet analysis equals three times of the number of vertices for the first proposal and equals the number of vertices for the second.

    The first proposal embeds the watermark into the temporal wavelet (high frequency) coefficients of each coordinates of the sequence. In this proposal, the histogram of L2 norm of the scale (low frequency) coefficients is divided into distinct bins with equal range according to their magnitude. Since the distribution of temporal wavelet coefficients can be approximated to Laplacian distribution, the variance of the distribution of each bin is asymmetrically modified according to the watermark bits to be embedded. This method is robust against frame-averaging attack and frame-by-frame attacks.

    In the second proposal, the Cartesian coordinates of the vertices are converted into the spherical coordinates and the L2 norm of each vertex is wavelet transformed along the time axis. Similar to the first proposal, the variance of the distribution of wavelet coefficients is modified according to the watermark. This proposal which uses L2 norm outperforms the first proposal in terms of the invisibility of the watermark and the robust against rotation attacks.

    Finally, we propose the method which embeds the watermark into both wavelet and scale coefficients. This method allows extracting the watermark from the distribution of scale and wavelet coefficients of each frame. In addition, it is possible to extract the watermark from a single frame in spatial domain.

    Note that all of our proposals do not require the mesh sequence (or original meshes) in the procedures of watermark extraction.

    The robustness against geometrical attacks (additive noise on the vertex coordinates, uniform vertex coordinates quantization, low-pass filtering, cropping, rotation, translation, scaling, frame-dropping for mesh sequence), and topological attacks (random vertex index reordering, simplification, subdivision) are evaluated on the semi-regular and irregular meshes.
  • Research result and Utilization method
  • 1) 순수과학 및 기술적 측면
    -손실/무 손실압축과 워터마킹이 가능한 새로운 알고리즘의 개발
    -3차원 영상 관련 신호 처리 기술 확보

    2) 응용분야 및 활용범위
    -3차원 원격의료진단 시스템으로 직접적 활용 가능.
    -손실/무 손실 영상압축 기술 응용
    -3차원 표면 영상의 IPMP(Intellectual Property Management and Protection) /DRM(Digital Right Management) 저작권 보호 기술
    -멀티미디어 신호의 점진적 전송기술 응용
    -3차원 게임/애니메이션 산업
  • Index terms
  • 3-D Surface Meshes, 3-D Mesh Sequence, Digital Watermarking, Copyright Protection, Wavelet, Blind Detection
  • List of digital content of this reports
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