Background Estimation is a common computer vision task, used for segmenting moving objects in video streams. This can be useful as a pre-processing step, isolating regions of interest for more complicated algorithms performing detection, recognition, and identification tasks, in order to reduce overall computation time. This is especially important in the context of embedded systems like smart cameras, which may need to process images with constrained computational resources. This work focuses on accelerating SuperBE, a superpixel-based background estimation algorithm that was designed for simplicity and reducing computational complexity while maintaining state-of-the-art levels of accuracy. We explore both software and hardware acceleration opportunities, converting the original algorithm into a greyscale, integer-only version, and using Hardware/Software Co-design to develop hardware acceleration components on FPGA fabric that assist a software processor. We achieved a 4.4× speed improvement with the software optimisations alone, and a 2× speed improvement with the hardware optimisations alone. When combined, these led to a 9× speed improvement on a Cyclone V System-on-Chip, delivering almost 38 fps on 320 × 240 resolution images.