Recent advances in camera architectures and associated mathematical representations now enable compressive acquisition of images and videos at low data-rates. While most computer vision applications of today are composed of conventional cameras, which collect a large amount redundant data and power hungry embedded systems, which compress the collected data for further processing, compressive cameras offer the advantage of direct acquisition of data in compressed domain and hence readily promise to find applicability in computer vision, particularly in environments hampered by limited communication bandwidths. However, despite the significant progress in theory and methods of compressive sensing, little headway has been made in developing systems for such applications by exploiting the merits of compressive sensing. In such a setting, we consider the problem of activity recognition, which is an important inference problem in many security and surveillance applications. Since all successful activity recognition systems involve detection of human, followed by recognition, a potential fully functioning system motivated by compressive camera would involve the tracking of human, which requires the reconstruction of atleast the initial few frames to detect the human. Once the human is tracked, the recognition part of the system requires only the features to be extracted from the tracked sequences, which can be the reconstructed images or the compressed measurements of such sequences. However, it is desirable in resource constrained environments that these features be extracted from the compressive measurements without reconstruction. Motivated by this, in this thesis, we propose a framework for understanding activities as a non-linear dynamical system, and propose a robust, generalizable feature that can be extracted directly from the compressed measurements without reconstructing the original video frames. The proposed feature is termed recurrence texture and is motivated from recurrence analysis of non-linear dynamical systems. We show that it is possible to obtain discriminative features directly from the compressed stream and show its utility in recognition of activities at very low data rates.