|
|
数字纹理图像生成算法研究
|
Abstract:
本研究提出一种利用参数方程生成数字纹理图像的方法。该算法通过灵活运用参数方程，生成各类矢量图元(如半圆矢量图元)以构建基础纹理图像，同时对图元进行随机平移或旋转操作，增强纹理的随机性。在对基础图像进行字符化时，从多种类型的总字符集随机选取字符，最终生成兼具特殊艺术效果与卓越防伪特性的数字纹理图像。实验结果有力证明，此算法在生成的数字纹理图像不仅艺术效果独特，且凭借高度的唯一性和随机性，极大提升了防伪性能，为产品提供可靠的防伪保障。
This research proposes a method for generating digital texture images by utilizing parametric equations. The algorithm, through the flexible application of parametric equations, generates various vector primitives (such as semicircular vector primitives) to construct the basic texture image. Meanwhile, random translation or rotation operations are performed on these primitives to enhance the randomness of the texture. During the process of characterizing the basic image, characters are randomly selected from a diverse set of total character sets. Ultimately, a digital texture image that combines special artistic effects and excellent anti-counterfeiting properties is generated. The experimental results strongly demonstrate that the digital texture images generated by this algorithm not only possess unique artistic effects, but also, by virtue of their high degree of uniqueness and randomness, significantly enhance the anti-counterfeiting performance, providing reliable anti-counterfeiting protection for products.
| [1] | 李文秀. 自然纹理图像生成技术研究[D]: [硕士学位论文]. 哈尔滨: 哈尔滨工程大学, 2005. |
| [2] | 李昊. 基于分形算法的轻样本图像生成研究[D]: [硕士学位论文]. 景德镇: 景德镇陶瓷大学, 2024. |
| [3] | Mandelbrot, B.B. (1982) The Fractal Geometry of Nature, Volume 1. W. H. Freeman and Company. |
| [4] | Bunde, A. and Havlin, S. (2012) Fractals and Disordered Systems. Springer Science & Business Media. |
| [5] | Xu, T., Moore, I.D. and Gallant, J.C. (1993) Fractals, Fractal Dimensions and Landscapes—A Review. Geomorphology, 8, 245-262. https://doi.org/10.1016/0169-555x(93)90022-t |
| [6] | Falconer, K. (2003) Fractal Geometry: Mathematical Foundations and Applications. John Wiley & Sons. https://doi.org/10.1002/0470013850 |
| [7] | Barnsley, M.F. (2014) Fractals Everywhere. Academic Press. |
| [8] | Hutchinson, J. (1981) Fractals and Self Similarity. Indiana University Mathematics Journal, 30, 713-747. https://doi.org/10.1512/iumj.1981.30.30055 |
| [9] | Barnsley, M.F. and Harrington, A.N. (1989) The Calculus of Fractal Interpolation Functions. Journal of Approximation Theory, 57, 14-34. https://doi.org/10.1016/0021-9045(89)90080-4 |
| [10] | Massopust, P.R. (1997) Fractal Functions and Their Applications. Chaos, Solitons & Fractals, 8, 171-190. https://doi.org/10.1016/s0960-0779(96)00047-1 |
| [11] | Massopust, P.R. (2016) Fractal Functions and Wavelets. In: Massopust, P.R., Ed., Fractal Functions, Fractal Surfaces, and Wavelets, Elsevier, 261-327. https://doi.org/10.1016/b978-0-12-804408-7.00008-4 |
| [12] | Massopust, P.R. (1990) Fractal Surfaces. Journal of Mathematical Analysis and Applications, 151, 275-290. https://doi.org/10.1016/0022-247x(90)90257-g |
| [13] | Strichartz, R.S. (2003) Fractafolds Based on the Sierpinski Gasket and Their Spectra. Transactions of the American Mathematical Society, 355, 4019-4043. https://doi.org/10.1090/s0002-9947-03-03171-4 |
| [14] | Yang, X.J., Baleanu, D. and Srivastava, H.M. (2016) Local Fractional Fourier Series. In: Yang, X.J., Baleanu, D. and Srivastava, H.M., Eds., Local Fractional Integral Transforms and Their Applications, Elsevier, 57-94. https://doi.org/10.1016/b978-0-12-804002-7.00002-4 |
| [15] | Barnsley, M.F., Devaney, R.L., Mandelbrot, B.B., et al. (1988) The Science of Fractal Images, Volume 1. Springer. |
| [16] | Keller, J.M., Chen, S. and Crownover, R.M. (1989) Texture Description and Segmentation through Fractal Geometry. Computer Vision, Graphics, and Image Processing, 45, 150-166. https://doi.org/10.1016/0734-189x(89)90130-8 |
| [17] | Barnsley, M.F. and Hurd, L.P. (1993) Fractal Image Compression. AK Peters Ltd. |
| [18] | Pentland, A.P. (1984) Fractal-Based Description of Natural Scenes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 661-674. https://doi.org/10.1109/tpami.1984.4767591 |
| [19] | Draves, S. (2005) The Electric Sheep Screen-Saver: A Case Study in Aesthetic Evolution. In: Lecture Notes in Computer Science, Springer, 458-467. https://doi.org/10.1007/978-3-540-32003-6_46 |
| [20] | Ebert, D.S., Kenton Musgrave, F., Peachey, D., Perlin, K. and Worley, S. (2003) Preface. In: Ebert, D.S., Peachey, D., Worley, S., Hart, J.C. Peachey, D., Worley, S., et al., Eds., Texturing and Modeling: A Procedural Approach, Elsevier, 20-23. https://doi.org/10.1016/b978-155860848-1/50029-2 |
| [21] | Prusinkiewicz, P. and Lindenmayer, A. (2012) The Algorithmic Beauty of Plants. Springer Science & Business Media. |
| [22] | Campbell, R.D. (1996) Describing the Shapes of Fern Leaves: A Fractal Geometrical Approach. Acta Biotheoretica, 44, 119-142. https://doi.org/10.1007/bf00048419 |
| [23] | Hartvigsen, G. (2000) The Analysis of Leaf Shape Using Fractal Geometry. The American Biology Teacher, 62, 664-669. https://doi.org/10.2307/4451007 |
| [24] | Godin, C. and Ferraro, P. (2010) Quantifying the Degree of Self-Nestedness of Trees: Application to the Structural Analysis of Plants. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 7, 688-703. https://doi.org/10.1109/tcbb.2009.29 |
| [25] | Perlin, K. (1985) An Image Synthesizer. Proceedings of the 12th Annual Conference on Computer Graphics and Interactive Techniques, New York, 1 July 1985, 287-296. https://doi.org/10.1145/325334.325247 |
| [26] | 曹鹏, 赵珊珊. 伪随机矢量数字纹理图像、生成与检测方法[P]. 中国专利, 202410828667.4. 2024-11-12. |
