Hierarchical feed-forward networks have been successfully applied in object recognition. At each level of the hierarchy, features are extracted and encoded, followed by a pooling step. Within this processing pipeline, the common trend is to learn the feature coding templates, often referred as codebook entries, filters, or over-complete basis. Recently, an approach that apparently does not use templates has been shown to obtain very promising results. This is the second-order pooling (O2P). In this paper, we analyze O2P as a coding-pooling scheme. We find that at testing phase, O2P automatically adapts the feature coding templates to the input features, rather than using templates learned during the training phase. From this finding, we are able to bring common concepts of coding-pooling schemes to O2P, such as feature quantization. This allows for significant accuracy improvements of O2P in standard benchmarks of image classification, namely Caltech101 and VOC07.