in continuous form, or
where 
is the value of the binary image (0 or 1) at the pixel
coordinate 
within an m by n image.
In other words, the area of the object is computed by counting the number of
object pixels.
The perimeter length is computed by tracing around the object boundary,
after scanning the image from top-to-bottom, left-to-right to find a
suitable start point.
The radial values are determined by measuring type distance from each perimeter
point to the centre of area, defined by the mean x and y values, where
and,
The bottom line in each case is simply the area of the object. In discrete form, these equations are given by
and,
Since the area of the image is simply the sum of the ``1'' pixels in the binary case, these can be simplified to a simple average of the x and y coordinates.
A second class of features often used for binary image processing and matching are those based on moments. Moments can be thought of as a generalisation of the calculation of area.
A moment of order p + q is given by:
So the area and centre of gravity can be expressed as:
It is also possible to use moments to define invariants by first
centralising
the moments on 
, this makes them translation independent,
normalisation can then be applied to get scale independence, and finally
they can be combined to become RST invariant (rotation, scale, translation).
These last two stages are awkward but the resulting measures
then characterise the shape independent of the view.
(Further details can be found in Schalkoff p304.)
