Simulating corneal datasets
The function
simulateData permits to simulate a wide variety of datasets
that appear in clinical practice, as a result of measuring an individual
eye with a Placido-disk corneal topographer.
This function produces a dataset in the same format as the one read
by readFile from a file, i.e., a list with three columns (x
and y coordinates of each point and its ring index) and a row per data
point, according to the function parameters (by default, 6144 rows or
data points).
The following examples show different ways of using
simulateData, by adding different transformations or
perturbations to the basic circular pattern. Some of the obtained
patterns can correlate with certain clinical conditions, such as
keratoconus, comma, or others.
Example 1: Default simulation
If the function is used with default parameters, the dataset simulated consists of 24 rings or mires, 256 points per ring, yielding a total of 6144 points. These are frequent values among commercial topographers. The dataset will have perfectly circular and centered mires, within an area of 12 mm of diameter. This will be a deterministic simulation (i.e., it will always produce exactly the same result). This function produces
Example 2: Setting basic parameters (number of rings, points per ring, and diameter)
Through the parameters rings and
pointsPerRing, the number of rings or mires and the amount
of data sampled at each ring can be established, respectively. Besides,
the diameter of the resulting dataset can be set with parameter
diameter:
Example 3: Circles with unequally distributed radii
The function allows to change the distribution of circles radii by
using the parameter ringRadiiPerturbation. It modifies
stochastically the equally distributed radii of the mires between 0 and
diameter (by default, diameter=12). Thus, some
consecutive pairs of rings are closer (or farther) than others. Typical
values of ringRadiiPerturbation would be between 0 (no
perturbation) and 1 (high perturbation):
Example 4: Adding mire displacement
In a real measurement, the centers of the mires are not the same,
they are off-center. This situation can be also included in the
simulation using the parameters maximumMireDisplacement and
mireDisplacementAngle. This will produce a pattern of rings
in which their centers drift in a straight line. The maximum drift
magnitude is given by maximumMireDisplacement (expressed in
mm, and should be a reasonable number according to the
diameter used). The drift direction is set by
mireDisplacementAngle (an angle, expressed in degrees,
typically in the range 0-360 with 0 meaning positive x direction). Their
use will produce a pattern like this:
dataset = simulateData(rings = 12, maximumMireDisplacement = 2, mireDisplacementAngle = 45)
plot(dataset$x,dataset$y)
In the previous example, the drift magnitude between consecutive
rings is constant. In addition, the function allows to perturb this
equally-spaced distribution of drifts by setting the parameter
mireDisplacementNoise. Typical values of
mireDisplacementNoise would be between 0 (no perturbation)
and 1 (high perturbation):
dataset = simulateData(rings = 12, maximumMireDisplacement = 2, mireDisplacementAngle = 45, mireDisplacementPerturbation = 1.2)
plot(dataset$x,dataset$y)
Notice that in all the examples so far, the rings keep their perfectly circular shape.
Example 5: Elliptic mires
Another common measurement pattern is one consisting of elliptic, or
nearly elliptic mires. This ellipticity can also be modeled with
parameters ellipticAxesRatio and
ellipticRotation. The former controls the rate or quotient
between the major and minor axes of each ellipse, and the latter
controls the orientation of the ellipses (given as an angle, expressed
in degrees, typically in the range 0-360 with 0 meaning positive x
direction):
Example 6: Random Cartesian noise
The function simulateData also permits to include
random, white noise of a certain magnitude in the Cartesian coordinates
of the sampled points. This is done with the parameter
overallNoise. Even though this kind of pattern cannot be
obtained directly by a Placido-disk topographer (since the points in
each mire are sampled equiangularly by the topographer), it might be of
interest for some applications.
Example 7: Highly irregular pattern, combining different perturbations
Finally, we present an example where most of the previous transformations or perturbations are combined. This will produce a highly irregular pattern, but similar patterns can be found in clinical practice for severe eye diseases:
dataset = simulateData(maximumMireDisplacement = 1.5, mireDisplacementAngle = 135, ringRadiiPerturbation = 1, mireDisplacementPerturbation = 0.8, ellipticAxesRatio = 0.8, ellipticRotation = 30)
plot(dataset$x,dataset$y)
- Example 1: Default simulation
- Example 2: Setting basic parameters (number of rings, points per ring, and diameter)
- Example 3: Circles with unequally distributed radii
- Example 4: Adding mire displacement
- Example 5: Elliptic mires
- Example 6: Random Cartesian noise
- Example 7: Highly irregular pattern, combining different perturbations