Abstract: Feature extraction, coding and pooling, are important components on many contemporary object recognition paradigms. This method explores pooling techniques that encode the second-order statistics of local descriptors inside a region. To achieve this effect, it introduces multiplicative second-order analogues of average and max pooling that together with appropriate non-linearities that lead to exceptional performance on free-form region recognition, without any type of feature coding. Instead of coding, it was found that enriching local descriptors with additional image information leads to large performance gains, especially in conjunction with the proposed pooling methodology. Thus, second-order pooling over free-form 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.