Average increment scale-invariant heat kernel signature for 3D non-rigid shape analysis

In recent years, spectral shape descriptors have attracted much attention because the Laplace-Beltrami operator(LBO) has good characteristics for non-rigid deformation shapes. The scale-invariant heat kernel signature(SIHKS) can describe the local or global information of the shape with the change of time parameters, and has scaling invariance compared with heat kernel signature(HKS). However, since the SIHKS descriptor is a feature sequence, it is impossible to balance the shape description accuracy and computational complexity when measuring shape similarity. If all feature sequences are selected for high precision description that will produce high computational complexity. Conversely, if only features under partial time parameters are selected, the accuracy will be affected and some shape features will be lost. To solve this problem, we define a more compact and efficient spectral shape descriptor, the average increment scale-invariant heat kernel signature(AISIHKS), which can effectively extract geometric and topological information by calculating the average increment of the heat kernel under all time parameters, and all the attributes of the shape can be effectively retained while reducing the feature dimension, which greatly reduces the complexity of the similarity measure. At the same time, the shape features obtained based on the increment are more discriminative than SIHKS, and can finely describe the local details of the shape. The experimental results on benchmarks show that the AISIHKS decreiptor is invariant to isometric and scale transformation, robust to topology, sampling and noise transformations, and can more accurately and robustly describe the local differences between shapes than other spectral shape descriptors, which have good performance in 3D non-rigid shape distance calculation and shape retrieval, and the more encouraging results are achieved compared with several representative approaches.