In general, you can use morphological operations, such as imopen to remove noise, and imclose to fill in small gaps.
In this particular case, the extra part seems to be caused by a shadow. You can try converting your frames to YCbCr color space using rgb2ycbcr, and only use the Cb and Cr channels for the foreground detector. This will get rid of shadows, but it will also remove any objects that are grey.