Soft assignment of visual words as Linear Coordinate Coding and optimisation of its reconstruction error

Visual Word Uncertainty also referred to as Soft Assignment is a well established technique for representing images as histograms by flexible assignment of image descriptors to a visual vocabulary. Recently, an attention of the community dealing with the object category recognition has been drawn to Linear Coordinate Coding methods. In this work, we focus on Soft Assignment as it yields good results amidst competitive methods. We show that one can take two views on Soft Assignment: an approach derived from Gaussian Mixture Model or special case of Linear Coordinate Coding. The latter view helps us propose how to optimise smoothing factor of Soft Assignment in a way that minimises descriptor reconstruction error and maximises classification performance. In turns, this renders tedious cross-validation towards establishing this parameter unnecessary and yields it a handy technique. We demonstrate state-of-the-art performance of such optimised assignment on two image datasets and several types of descriptors.