Compressive Sensing for Background Subtraction

Compressive sensing (CS) is an emerging field that provides a framework for image recovery using sub-Nyquist sampling rates. The CS theory shows that a signal can be reconstructed from a small set of random projections, provided that the signal is sparse in some basis, e.g., wavelets. In this paper, we describe a method to directly recover background subtracted images using CS and discuss its applications in some communication constrained, multi-camera computer vision problems. We show how to apply the CS theory to recover object silhouettes (binary background subtracted images) when the objects of interest occupy a small portion of the camera view, i.e., when they are sparse in the spatial domain. We cast the background subtraction as a sparse approximation problem and provide different solutions based on convex optimization and total variation. In our method, as opposed to learning the background, we learn and adapt a low dimensional compressed representation of it, which is sufficient to determine spatial innovations; object silhouettes are then estimated directly using the compressive samples without any auxiliary image reconstruction. We also discuss simultaneous appearance recovery of the objects using compressive measurements. In this case, we show that it may be necessary to reconstruct one auxiliary image. To demonstrate the performance of the proposed algorithm, we provide results on data captured using a compressive single-pixel camera. We also illustrate that our approach is suitable for image coding in communication constrained problems by using data captured by multiple conventional cameras to provide 2D tracking and 3D shape reconstruction results with compressive measurements.