For fixed , the kernel gives the RF profile of a cell located at position , i.e., how the input stimulus is weighted in determining the output excitation of the cell at position . The RF profiles are characterized on the basis of various aspects (position, orientation, size, sign, etc.) that determine to which type of stimuli they are sensitive. Quantitatively, the various aspects can be related to the values of a set of parameters characterizing the RF. In general, their space-variant distribution over the cortical surface can be expressed through parametric mappings  and the kernel can be rewritten in a more  explicit form:
The dependencies of the kernel on the cortical coordinates , described by the parametric maps , shows how, changing position on cortical plane, RFs vary in orientation specificity, position in the visual field, overlapping, field size, contrast sensitivity, etc [2,13,59,60,95,107,127]. In the following, we shall focus on variations of position and orientation.
Exploiting the concept of topographic mapping [76,115], [75,114] each point in the visual field can be assigned to a point in the cortical plane by means of a transformation
is assumed to be bijective, hence, to find the position in the visual field in which the RF of a certain neuron in is centered, it is sufficient to follow backwards the transformation .
Orientation varies jointly with the cell's position on the cortical plane according to the orientation map
so that every point of cortical surface has associated with it a preferred orientation ranging from 0 to [6,8,12,127]. In this case, given and , the properties of the kernel are summarized, through the rototranslation transformation, by the function :
is the rotation matrix for the angle .
Under these assumptions, the distribution of excitation
provides a mixed spatial representation of both stimulus position and orientation.