International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part BI. Istanbul 2004
2. METHODS AND MATERIALS
The basis of the algorithm used in this work is the slanted edge
MTF measurement technique identified above. Details of the
algorithm used are described below along with image and
sensor characteristics of the OV-3 system.
2.1 Algorithm
2.1.1 Edge Identification: The initial task in MTF
measurement is the identification of suitable edges for analysis.
Edges must be oriented near the principal along scan or cross
scan axes. A minimum angle to the principal direction is
required as well as sufficient length for suitable ESF
construction. The candidate edge must also meet contrast and
noise requirements for selection.
A Sobel edge detection operator followed by thresholding and
binary morphological processing is used to identify edges with
the proper orientation and minimum magnitude (Jain, 1989). An
initial estimate of the location and angle of the edge is then
determined by performing a least squares regression of selected
points along the edge. For each identified edge, metrics are
acquired such as the magnitude of the edge, noise level and
length. These metrics are used in a voting process for edge
selection and retained for later use in determining bias and
precision estimates.
2.1.2 Edge Spread Function Construction: The ESF is the
system response to the input of an ideal edge. As the output of
the system is a sampled image, the fidelity of the edge spread
function using a single line of image data is insufficient for
MTF analysis. Aliasing due to undersampling in the camera,
along with phase effects and the angle of the actual edge with
respect to the sampling grid will cause variable results for a
single line. The phase effects and edge angle may be exploited,
however to provide a high fidelity measurement of the ESF.
Construction of the ESF is graphically represented in Figure |
(Schott, 1997). The edge (1) is identified in the image as
described above. A line is then constructed perpendicular to the
edge (2). For a given line of image data, each point (3) around
the edge transition is projected onto the perpendicular line (4).
This process is then repeated for each subsequent line of image
data along the edge. The difference in sub-pixel location of the
edge with respect to the sampling grid for different lines in the
image results in differences in the location of the projected data
point onto the perpendicular. This yields a high fidelity
representation of the system response to an edge.
Small changes in the edge angle used during construction of the
super-sampled edge affect the quality of the resulting ESF. The
angle is systematically adjusted by small increments around the
initial estimate. The quality of the resulting curve fit is used to
refine the edge angle estimate for the final ESF construction.
(3) Point
in Image
(4) Projected to
Perpendicular
(2) Perpendicular
to Edge
Figure 1. ESF Projection Technique
After the individual ESF data points have been determined, the
data must be conditioned and resampled to a fixed interval. In
general, the angle of the edge with respect to the sampling grid
does not produce uniformly distributed data points along the
perpendicular to the edge. Also, with longer edges, many data
points may be located in close proximity to one another. The
LOESS curve fitting algorithm is used to resample the data to
uniformly spaced sample points (Cleveland, 1985). In order to
obtain the desired number of samples in the MTF result, thirty-
two uniformly spaced ESF samples are calculated for each pixel
pitch in the image through the LOESS fit. An example ESF
from an OV-3 image is shown in Figure 2. Data points used in
the curve fit are shown in black. The resulting curve fit to the
ESF is shown in red.
Edge Spread Function
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