Bag of Shape Features with a learned pooling function for shape recognition

Bag of Shape Features (BoSF), such as Bag of Contour Fragments (BoCF) and Bag of Skeleton-associated Contour Parts (BoSCP), derived from the well-known Bag of Features (BoF), is an effective framework for shape representation. The feature pooling in this framework is a critical step, while either max pooling or average pooling is not a learnable process. In this paper, we aim at learning a pooling function which is adaptive to the input shape features instead. Towards this end, we formulate our pooling function as a weighted sum of max pooling and average pooling, where the weight is expressed by an activation function of the input shape features. To automatically learn this weight, the output of the pooling function is fed into a SVM classifier and they are trained jointly to minimize a shape classification loss. Experimental results on several standard shape datasets demonstrate the effectiveness of the proposed learned pooling function, which can achieve considerable improvements compared with both BoCF and BoSCP.