State Key lab of Tibetan Intelligent Information Processing and Application, Xining, 810008, China.
Qinghai Normal University, the School of Computer Science, Xining, 810008, China.
Sci Rep. 2023 Feb 13;13(1):2518. doi: 10.1038/s41598-023-29047-4.
The Mexican Hat wavelet (MHW) is strictly derived from the heat kernel by taking its negative first-order derivative with respect to time t. As a solution to the heat equation that the heat kernel has a clear initial condition, the Laplace-Beltrami operator. Although the MHW descriptor can effectively characterize the model information, but it has poor robustness to the model with scale transformation, and the feature description performance is affected to some extent. Following a popular mathematical method, in this paper, we bases on the MHW to study scaling invariance and proposes a new shape descriptor, the scale-invariant Mexican Hat wavelet (SIMHW), which by logarithmic sampling and Fourier transform that obtains the expression of SIMHW in Fourier domain. The experimental results show that SIMHW has finer information description ability and stronger recognition ability, and has better robustness to various non-rigid transformations. It can correctly calculate the similarity between 3D shapes and realize the effective shape retrieval.
墨西哥帽小波（MHW）是通过对时间 t 求其热核的负一阶导数严格从热核中推导出来的。作为热方程的解，热核具有明确的初始条件，即拉普拉斯-贝尔特拉米算子。虽然 MHW 描述符可以有效地描述模型信息，但它对具有尺度变换的模型的鲁棒性较差，并且特征描述性能在一定程度上受到影响。本文采用一种流行的数学方法，基于 MHW 研究了尺度不变性，并提出了一种新的形状描述符，即尺度不变墨西哥帽小波（SIMHW）。通过对数采样和傅里叶变换，得到了 SIMHW 在傅里叶域的表达式。实验结果表明，SIMHW 具有更精细的信息描述能力和更强的识别能力，对各种非刚性变换具有更好的鲁棒性。它可以正确计算 3D 形状之间的相似度，实现有效的形状检索。
