Semantic segmentation method with second-order pooling

A method for second-order pooling, comprising the steps of:

• in a scheme where:
• is assume a collection of m local features D=(X, F, S), where descriptors X is represented as a vector with m entries, extracted over square patches centered at general image locations F, where F is a vector with m entries, with pixel width S, where S is a vector with m entries;
• is provided a set of k image regions R, where R is a vector with k entries, each composed of a set of pixel coordinates;
• a local feature di is inside a region Rj whenever fiεRj, then FRj={f|fεRj} and |FRj| is the number of local features inside RJ;
• pool local features to form global region descriptors, using second-order analogues of the most common first-order pooling operators;
• focus on multiplicative second-order interactions, together with either the average or the max operators;
• define second-order average-pooling (2AvgP) and second-order max-pooling (2MaxP), where the max operation is performed over corresponding elements in the matrices resulting from the outer products of local descriptors;
• log-euclidean tangent space mapping, defining only one principal matrix logarithm operation per region Rj and computing the logarithm using the very stable Schur-Parlett algorithm;
• and
• power normalization, rescaling of each individual feature value p, forming the final global region descriptor vector and concatenating the elements of the upper triangle.