Digital Watermarking by Mohammad Ali Nematollahi Chalee Vorakulpipat & Hamurabi Gamboa Rosales

Author:Mohammad Ali Nematollahi, Chalee Vorakulpipat & Hamurabi Gamboa Rosales
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

6.6 Distortion Evaluation in 3D Watermarking

When a 3D mesh model carries the watermark, it is important to recognize how the original model and the watermarked model differ and how errors modified the outcome model. Let us consider the original mesh object O and the processed object . Six classes of measurements are employed for distortion evaluation. They are Hausdorff distance comparison, volume-based measurement, energy minimization measurement, curvature-based measurement, projection image comparison, and human perceptual distance.

Hausdorff distance is the most applicable measurement [62]. It measures the similarity of simplified 3D image [63] and original 3D image [64]. As the Hausdorff distance is not symmetric, two distances are evaluated including forward Ef and backward . The maximum root mean square (MRMS) error between O and is then used for the evaluation of the distortion of watermarking scheme. Metro tool is a well-known tool for computing the MRMS by measuring the surface error between two 3D meshes. Among other distortion evaluation measurements, Hausdorff distance is the most accurate and comprehensive measurement in computer vision and computer graphics. Hausdorff distance is expressed as in Eq. (‎6.1).

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