Video surveillance, object tracking and activity monitoring are some of the important issues for a home-care robotic system. In this work, an omnidirectional video camera is adopted to provide a 360 degree view angle of the indoor scene with a single image sequence. Some basic functions for smart living and elderly care, such as motion detection, object tracking and target behavior analysis, are implemented. For the motion detection, a background model is first created and the CamShift algorithm is used for object tracking by extracting color information of the target. To make the motion detection and object tracking fully automatic and robust under different illumination conditions, an optical flow approach is cooperated to detect small changes of the mobile object In addition, the camera is calibrated to obtain the one-to-one correspondences between the image pixels and the locations on the ground. They are used for fall detection of the target by comparing the object length appeared in the image and the computed length according to the object's physical height.