Satellite Image Time Series (SITS), MRI sequences, and more generally image time series, constitute 2D+t data providing spatial and temporal information about an observed scene. Given a pattern recognition task such as image classification, considering jointly such rich information is crucial during the decision process. Nevertheless, due to the complex representation of the data-cube, spatio-temporal features extraction from 2D+t data remains difficult to handle. We present in this article an approach to learn such features from this data, and then to proceed to their classification. Our strategy consists in enriching pixel time series with spatial information. It is based on Random Walk to build a novel segment-based representation of the data, passing from a 2D+t dimension to a 2D one, without loosing too much spatial information. Such new representation is then involved in an end-to-end learning process with a classical 2D Convolutional Neural Network (CNN) in order to learn spatio-temporal features for the classification of image time series. Our approach is evaluated on a remote sensing application for the mapping of agricultural crops. Thanks to a visual attention mechanism, the proposed $2D$ spatio-temporal representation makes also easier the interpretation of a SITS to understand spatio-temporal phenomenons related to soil management practices.