1. A system that employs a plurality of stages to remove blocking artifacts from moving and still pictures, each picture composed of blocks defined by horizontal and vertical block boundaries, comprising: a block boundary classification stage that classifies, in each picture, horizontal and vertical boundaries as having a difference in pixel values across the boundaries as being more or not more than a predetermined level; a filtered pixels region of interest (ROI) stage that is operative for each said classified boundary having a difference in pixel values across the boundaries as being not more than said predetermined level defining a one-dimensional filtered pixels ROI with an adaptive, picture content-dependent spatial extent, having two ends and bounded at each said end by a bounding pixel, said ROI including a first plurality of concatenated, adjacent pixels to be filtered, said ROI crossing said boundary having a difference in pixel values across the boundaries as being not more than said predetermined level, and wherein defining the adaptive, picture content-dependent spatial extent of the ROI comprises iteratively checking pixels on each side of the block boundary to determine whether the pixel is to be included in the ROI until each end of the ROI is closed by its bounding pixel; a filter definition stage that defines a finite filter with a length correlated with said first plurality of concatenated, adjacent pixels of said ROI; a filtering pixels expansion stage that defines a filtering pixels expansion having a second one dimensional plurality of pixels, said second plurality including said first plurality of pixels; and a filtering stage that is operative to filter said first plurality of pixels using said finite filter and said filtering pixels expansion stage.