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Direct blue noise resampling of meshes of arbitrary topology

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Abstract

We propose in this paper a novel sampling method and an improvement of a spectral analysis tool that both handle complex shapes and sharp features. Starting from an arbitrary triangular mesh, our algorithm generates a new sampling pattern that exhibits blue noise properties. The fidelity to the original surface being essential, our algorithm preserves sharp features. Our sampling is based on a discrete dart throwing applied directly on the surface to get good blue noise sampling patterns. It is also driven by a feature detection tool to avoid geometric aliasing. Experimental results prove that our sampling scheme is faster than techniques based on brute-force dart throwing, and produces sampling patterns with blue noise properties even for complex surfaces of arbitrary topology. In parallel, we also propose an improvement of a tool initially developed for the spectral analysis of non-uniform sampling patterns, that may generate biased results with complex shapes. The proposed improvement overcomes this problem.

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Acknowledgments

We are particularly grateful to Mr. Paolo Cignoni and Miss Ruizhen Hu for answering our questions and sending us several data for our comparisons. We also thank Mr. Li-Yi Wei and Mr. Rui Wang for providing us with their executable. We also would like to thank Leonardo Hidd Fonteles for his help on Dijkstra’s implementation.

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Authors and Affiliations

  1. Laboratory I3S, University Nice, Sophia Antipolis, CNRS (UMR 7271), 2000, route des Lucioles, 06909, Sophia Antipolis, France

    Jean-Luc Peyrot, Frédéric Payan & Marc Antonini

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  1. Jean-Luc Peyrot
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  2. Frédéric Payan
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  3. Marc Antonini
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Correspondence to Jean-Luc Peyrot.

Additional information

This work is supported by a grant from Région Provence Alpes Côte d’Azur (France).

Appendix A: Analysis of white noise sampling

Appendix A: Analysis of white noise sampling

To show that our spectral analysis tool (presented in Sect. 4) is also efficient for other patterns, we tested it on white noise samples generated on surfaces, and compared with the results produced by the original tool of Wei et al. [31]. To be as fair as possible, we generated the patterns on Eight and Hand, two models shown in [31], and each sampling has been generated with the own code of Wei et al. [31]. Figure 15 compares the RAPS estimated with our tool and with the original tool of Wei et al. [31]. We obtained satisfactory results, since the RAPS produced by our tool are globally flat and equal to 1 at each frequency (typical features of white noise sampling). Note that there is a slope at very low frequencies that can be explained by our discrete approach that inevitably introduces a quantization bias during the sampling (computed on the subdivided meshes), and by the well-known bias of Dijkstra’s algorithm (the geodesics always lie on the graph edges).

Fig. 15
figure 15

Comparison of the RAPS for two models sampled with white noise patterns, estimated with our tool and with the tool of Wei et al. [31]

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This experimentation confirms the interest of our tool, since the RAPS provided by our spectral analysis algorithm matches well the typical white noise characteristics, which is not always the case of [31]: see the RAPS generated by the original tool which are sometimes significantly different from the value 1 even at higher frequencies, on Eight for instance. Moreover their tool also draws a slope at very low frequencies for the two models. So we consider that our adapted tool is valid for all our experimentations.

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Peyrot, JL., Payan, F. & Antonini, M. Direct blue noise resampling of meshes of arbitrary topology. Vis Comput 31, 1365–1381 (2015). https://doi.org/10.1007/s00371-014-1019-1

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