3D object recognition with shape changes is a challenging task. The irregular data structure of the mesh model prevents the operation of the conventional convolution

which brings difficulties to feature extraction of the 3D non-rigid objects. In this paper

we propose a method of mesh convolution for 3D non-rigid objects to extract shape features and use them for classification. Firstly

we obtain the distribution of typical patch shapes by the mesh convolution. Then

we model the spatial co-occurrence relationship by Markov chains to complete the global feature description. Finally

we use the support vector machine to classify the 3D objects. Our method adopts the continuous polynomial function as the convolution kernel for the irregular data structure

and learn the kernel by an unsupervised learning method. Experimental results on the standard non-rigid 3D model datasets show our method can effectively extract the features and achieve classification accuracy of 92.88% on SHREC10 and 96.54% on SHREC15

respectively.