论文标题
基于小波的热核衍生物：迈向信息丰富的局部形状分析
Wavelet-based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis
论文作者
论文摘要
在本文中，我们为墨西哥帽子小波的形状上的新结构提出了新的结构，并应用了部分形状匹配。我们的方法从建立的扩散小波的方法中汲取了主要灵感。这种新颖的结构使我们能够通过近似热核的衍生物来快速计算墨西哥帽子小波功能的多尺度家族。我们证明，它导致了一系列功能系列，该功能继承了热核的许多有吸引力的特性（例如，局部支持，从单点，有效计算中恢复异构的能力）。由于其自然能够在形状上编码高频细节，因此所提出的方法比Laplace-Beltrami特征功能基础和其他相关基础更准确地重建$δ$ functions。最后，我们将方法应用于部分和大规模形状匹配的具有挑战性的问题。与最先进的比较进行了广泛的比较表明，它的性能是可比的，而虽然比竞争方法更简单和快得多。
In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well-established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multiscale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that it leads to a family of functions that inherit many attractive properties of the heat kernel (e.g., a local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high-frequency details on a shape, the proposed method reconstructs and transfers $δ$-functions more accurately than the Laplace-Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large-scale shape matching. An extensive comparison to the state-of-the-art shows that it is comparable in performance, while both simpler and much faster than competing approaches.
