We can use simple descriptions (one numeric value) to represent features on and hence recognise objects:
Such numeric or statistical descriptions may be divided into two distinct classes:
Some of the above measures have obvious meanings. The others will be described briefly below in the context of two-dimensional images.
We can form seven new moments from the
central moments that are invariant to
changes of position, scale and orientation of the object represented
by the region (invariants will be discussed below shortly), although
these new moments are not invariant under perspective
projection. For moments of order up to three, these are:
We can also define
eccentricity using moments as
We can also find principal axes of inertia
that define a natural coordinate system for a region. Let
be given by
We will get two values for which are apart. The pair of lines which make an angle with the x axis passing through the centre of gravity of the region define a pair of principal axes which are generally aligned along what would intuitively be called the length and width of the region.
Most of these statistical measures may be useful in helping to control image reasoning and recognition, even if they are not sufficient for reasoning or recognition by themselves.
However, these measures are very cheap to calculate as byproducts of the segmentation strategies detailed, especially region growing. Consequently, when these measures are used in conjunction with other reliably extracted features, they can help to improve recognition techniques by constraining the search space for matches between image and object features.
Several of the statistical measures we have met are invariant measures, which is to say that the value of the measure does not vary with, for example, the position of the region in the image, or perhaps its orientation or scale.
This is clearly a good property as we cannot guarantee viewing an object from identical viewpoints.
Thus, while the centre of gravity of a region obviously varies with its position, its area does not. While area does vary with scale (and thus closeness of the camera to the object, for example), compactness as defined above is invariant with respect to scale as well as position and orientation.
Other invariant measures are:
are invariant with respect to scaling, rotation and translation.