Cleaning the Scanning Artifacts
An example of a typical subframe, as downloaded
from the web page of the Lunar and Planetary
Institute, is shown in Figure A.1.
Figure A.2: LO4-187H2 after removal of systematic
artifacts and filtering.
Steps of Stage 1: The steps performed by the
program that measures and removes systematic
artifacts (Stage 1) are:
1. Search from the top of the mosaic image for the
first identifiable bright line between framelets (a
framelet edge)
2. Jump half a typical 40-pixel framelet width and
search for the next identifiable framelet edge.
3. Repeat the jump-and-search process until the
bottom of the image is reached
4. Calculate the precise framelet width of the
image (which varies between 38 and 43 pixels
on the currently sampled images) by averaging
the framelet width between successive identified
framelet edges. Successive edges are those
separated by about one typical framelet width.
5. Extrapolate or interpolate those framelet edges
which were not identified by search processes.
6. Each framelet edge is scanned and, for each
horizontal coordinate of pixels, the excess
brightness is estimated by comparison with the
immediately adjacent pixels, The excess
brightness is removed from the pixels of the
affected scan lines.
7. Determine the average linearized brightness
ratio of the pixels, as a function of their relative
position between framelet edges, for the entire
Figure A.1: LO4-187H2, Mare Orientale and Montes
Rook.
The scanning artifacts (“venetian blind effect”)
make it difficult to visualize the lunar surface.
Current computing technology makes it possible to
estimate and remove most of the scanning and
reconstruction artifacts. A two-stage process is used
to clean the images in this book. First, the
systematic artifacts such as white lines between
framelets and brightness variations across framelets
are measured and removed. Second, a filter
suppresses remaining variable striping patterns. The
cleaned image is shown in Figure A.2.
The programs for each of the stages were written in
Visual Basic and run in a Windows 98 environment.
They use utility routines from a book by Rod
Stevens [5].
1
mosaic image. A model of the non-linear
contrast function is used in the linearization
process.
8. Correct the brightness of each pixel for the
average normalized brightness ratio
corresponding to its position between framelet
edges. The contrast model is used in the
correction.
excess brightness of the line and a weighted value is
subtracted from the brightness of the two or three
pixels near the line. This process preserves more
detail in the image than simply averaging the
brightness around the line.
Contrast model. The streaking artifact was applied
in the spacecraft on a low contrast image,
essentially linear in its relation between
photographed brightness and density, However, the
atlas images were printed at high contrast and are
therefore nonlinear. Thus in order to determine and
compensate for streaking, it is necessary to linearize
the brightness by reversing the contrast function. An
empirical study was conducted, varying the
assumed contrast function and minimizing the
residual fundamental and second and third
harmonics of the artifacts at the framelet frequency.
The resulting contrast function has a linear contrast
gain of 3 between output brightness values of 0.1 to
0.9 of the full range and exponential curves at each
end of the brightness range.
Specific Techniques of Stage 1: The program
addresses several problems that are specific to the
mosaics.
Finding the edges of framelets. Usually, framelet
edges are represented by bright lines caused by light
shining between the framelet filmstrips as the
mosaics were laid up. Although they are narrower
than the distance between scans of the digital
images, the lines appear in either two or three
adjacent lines of pixels because the scan spot used
in creating the digital images was larger than the
distance between scans. The scan lines are usually
tilted with respect to the framelet edges by two or
more pixels across a frame and have curvature of
the order of one pixel across a frame. In many
frames, the white lines are obscured by saturation or
overcome by image signal in large parts of the
frame. Development artifacts and some valid
signals can produce false segments of bright lines
that are not at framelet edges.
Special handling. A few images require special
techniques. For example, a feature has been added
to compensate for an alternating pattern of darker
and lighter framelets in some of the images.
Quantitative Results: A spectral analysis program
has been written to compare the spectra of the input
and output images to provide a quantitative measure
of improvement. Figure A.1 shows the fine-scale
normalized vertical spectral density of LO4-140H3
before and after processing.
The approach taken to find these lines is to search in
a band of scan lines 17 pixels high, looking in 17 by
21 blocks of pixels for a bright white line segment
of either two or three pixels in width. A quadratic
best-fit line is calculated using the centers of the
line segments. Successive fits are calculated,
eliminating those centers that are most off the line
until all remaining centers are within half a pixel of
the line. If the remaining centers are at least 25% of
the possible centers, the line is accepted as a
framelet edge. If not, the band is moved down the
picture to find an edge.
40.00
Normalized Spectral Density
35.00
30.00
25.00
Input
Output
20.00
15.00
10.00
5.00
0.00
38.0 38.2 38.4 38.6 38.8 39.0 39.2 39.4 39.6 39.8 40.0 40.2 40.4 40.6 40.8 41.0 41.2 41.4 41.6 41.8
Period (Pixels)
Figure A.3: Spectral density of LO4-140H3 for periods
near the framelet width (about 40 Pixels).
Removing each framelet edge line. For each
horizontal pixel index, the pixels above and below
the calculated vertical value of the best-fit line are
examined to determine the probable value of the
The removal of systematic artifacts greatly
improved the appearance of the pictures. The
2
venetian blind effect disappears, providing a
subjective effect of more direct visual contact with
the lunar surface. However, traces of the framelet
artifacts remain in parts of some of the images.
horizontal stripes while permitting topographic
detail to remain.
Both filters are of the second-order Darlington type.
A second-order low-pass Darlington filter has the
form:
1
G( f ) 
1  ( fT ) 2
where f is the frequency and T is the period
of the frequency that reduces the filter
function G(f) to 0.5.
Steps of Stage 2: Stage 2 is a two-dimensional
filter process:
1. Generate the two-dimensional fourier transform
of the image.
2. Multiply the transform by a two-dimensional
filter that suppresses streaks; that is, patterns
that extend horizontally more than vertically.
This filter is formed from the combination of a
low-pass filter and a high pass filter, as
suggested by Lisa Gaddis of USGS (Gaddis,
2001).
3. Return to the spatial domain by an inverse twodimensional fourier transform.
A high-pass Darlington filter has the form:
1
G( f )  1 
1  ( fT ) 2
Examination of the two-dimensional fourier
transform of an input image (whose systematic
artifacts have been removed) shows strong noise at
horizontal frequencies whose period is less than 150
pixels and vertical frequencies whose period is
more than 25 pixels. A compound (twodimensional) “Normal” filter with the following
form is used to suppress the noise:
The remaining artifacts are substantially removed
by application of the two dimensional filter (see
Figure A.2). Careful comparison of filtered images
with the originals verifies that shadows, topographic
variations, and albedo variations such as associated
with rays are preserved. This is true even when the
digital images are examined under magnification
that resolves the pixels.

1
G( fx, fy)  1  
2
1  ( fx  150)


1
 1 

2 
 1  ( fy  25)  
where fx is the frequency in the x direction
(East – West) and fy is the frequency in the
y direction (North – South).
Specific Techniques of Stage 2:
Fourier Transform and inverse transform: A fastfourier-transform algorithm runs in the vertical
direction and stores arrays of the real and imaginary
parts of the transform. The same algorithm runs in
the horizontal direction on these arrays to create the
real and imaginary two-dimensional arrays that are
now in the frequency domain. The same process is
used for the inverse transform. The fast fourier
transform algorithm used is limited to image arrays
that have dimensions M and N that must be integer
powers of two; therefore the dimensions of the
actual images are built up to the next power of two
by adding virtual blank brightness data.
The “Normal” filter is used as the default, and is
effective for most of the pictures. If streaks remain
after application of the “Normal” filter, a “Strong”
filter is used instead. This happens most often when
large areas of dark sky or shadow beyond the
terminator appear in an image. The form of the
“Strong” filter is:



1
1

G ( fx, fy)  1  
 1 
2
2 
1  ( fx  50)  1  ( fy  50)  
Filter characteristic: The filter has a low-pass
characteristic in the vertical (North-South) direction
to suppress the framelet frequency and its
harmonics. In the horizontal direction (East-West) it
has a high-pass characteristic to reject patches of
3