Many of the eCognition form features are based on the statistics of the spatial distribution of the pixels that form an image object. As a central tool to work with these statistics, eCognition Developer uses the covariance matrix:
Parameters
coordinates of all pixels forming the image object
coordinates of all pixels forming the image object
Expression
Another frequently used technique to derive information about the form of image objects is the bounding box approximation. Such a bounding box can be calculated for each image object and its geometry can be used as the first clue to the image object itself.
The main information provided by the bounding box is its length 
, its width 
and its area 
.
Shape Approximations Based on Eigenvalues
The shape approximations based on eigenvalues measures the statistical distribution of the pixel coordinates 
of a set 
.
The center of gravity of the set 
is:
The variances of the pixel coordinates are:
The covariance matrix 
of the coordinates is:
The diagonalization of the covariance matrix gives two eigenvalues 
, which are the main and minor axes of an ellipsoid.
, where 
is the eigenvalue and 
is the eigenvector.
Elliptic Approximation
The elliptic approximation uses the eigenvalues 
of the covariance matrix and computes an ellipsis with axis along the eigenvector 
with length 
, and along the eigenvector 
with length 
.
The formula is 
