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An important aspect of human perception is anticipation, which we use extensively in our day-to-day activities when interacting with other humans as well as with our surroundings. Anticipating which activities will a human do next (and how to do them) in useful for many applications, for example, anticipation enables an assistive robot to plan ahead for reactive responses in the human environments. In this work, we represent each possible future using an anticipatory temporal conditional random field (ATCRF) that models the rich spatial-temporal relations through object affordances. We then consider each ATCRF as a particle and represent the distribution over the potential futures using a set of particles. In extensive evaluation on CAD-120 human activity RGB-D dataset, for new subjects (not seen in the training set), we obtain an activity anticipation accuracy (defined as whether one of top three predictions actually happened) of 75.4%, 69.2% and 58.1% for an anticipation time of 1, 3 and 10 seconds respectively. Finally, we also use our algorithm on a robot for performing a few reactive responses. 1