Feature extraction, coding and pooling, are important components on many contemporary object recognition paradigms. In this paper we explore novel pooling techniques that encode the second-order statistics of local descriptors inside a region. To achieve this effect, we introduce multiplicative second-order analogues of average and maxpooling that together with appropriate non-linearities lead to state-ofthe- art performance on free-form region recognition, without any type of feature coding. Instead of coding, we found that enriching local descriptors with additional image information leads to large performance gains, especially in conjunction with the proposed pooling methodology. We show that second-order pooling over freeform regions produces results superior to those of the winning systems in the Pascal VOC 2011 semantic segmentation challenge, with models that are 20,000 times faster.