Synthetic Orthophotograph of the Mars Face Based on Stereographic Measurements


A previous article presented a set of elevation values derived from stereographic measurements for points on the Mars Face landform and the surrounding plains. Each elevation value was derived from the difference in position of some identifiable small feature between two images taken at different emission angles. It was noted that these displacements, which are due to parallax, could be used to create what could be termed a "synthetic orthophotograph," a view of the landform looking straight down at the surface from above. Such a view, also referred to as a "plan view," is critical for assessing the general symmetry of the landform. The skew-and-stretch procedure used by NASA to process MGS images cannot produce a true plan view unless the imaged surface is perfectly flat and planar. I refer to such  enhancements as "partially rectified" images. For three-dimensional objects such as the Mars Face, the partial rectification retains distortions caused by parallax associated with the off-nadir (off-vertical) angle of the camera's line of sight.

Briefly, an orthophotograph can be synthesized from a a partially rectified image  by moving each pixel by an amount equal to the parallax displacement of the pixel from the off-nadir view to the plan view. The method of producing the otrhophoto is described in more detail subsequently for those who are interested.

Such an orthophotograph has been created from the April, 2001 Mars Global Surveyor image of the Mars Face using software written specifically for this task. It is shown in Figure 1.
 
 

Figure 1. Synthetic Orthophotograph based on the April, 2001 MGS image (MOC E0300824) of the Mars Face. Scale is 25% of full size.
 

The two dark diagonal lines extending from lower left to upper right are streaks caused by variations in the MGS camera's CCD array sensitivity. In the raw image, they are vertical and straight. The curvature of these lines was created by the pixel-shifting operations performed to generate the orthophotograph. The line furthest to the right is more curved because it passes through an area where the elevations were greater, therefore resulting in greater shifts of position.

Those familiar with the partially rectified version of the image released by NASA last year may not notice much difference at first glance. But subtle and perhaps significant differences should be apparent in the comparison of the two versions in Figure 2.
 
 

Figure 2. Left: Version of the April 2001 Face image partially rectified by Malin Space Science Systems. Right: Synthetic orthophotograph.
 

Perhaps the most notable difference is the greater degree of alignment of the "nose" ridge and "hare-lip" features along the vertical centerline of the image in the orthophoto. While the dichotomy between the left and right sides of the "face" persists, it is interesting that the "humanoid" and "feline" sides are almost exactly the same width because of the shift to the viewer's right of higher-elevation features in the orthophoto. (The "feline" side appears wider than the "humanoid" side in the original unrectified image because the camera was viewing the landform from the right, so surfaces facing the camera on the right side of the landform appear wider than those facing away from the camera on the left). The "nose" ridge, while of course still very rough in appearance, is less broad. The left and right walls of the platform are also more equal in width. While the width-to-length ratios of the overall landform are almost identical in the two versions, in the orthophoto the higher-elevation surfaces on the platform have been shifted downward from the top of the "head" toward the "chin," giving the appearance of a sligthly longer and narrower "face" and a slightly higher "forehead." While none of the differences between the two versions are quantitatively large, their cumulative effects in my opinion produce a greater impression of orderliness and symmetry in the synthetic orthophotograph than in the partially rectified MSSS version.

Unfortunately, no complete orthophotograph has been taken of the Mars Face by MGS as of yet. But if and when MGS or some other spacecraft ever acquires a true orthophotograph of the Mars Face, I am confident that it will not differ significantly from this synthetic version. As described below, the method by which it was created does not involve any of the subjective judgements that Mark Kelly was compelled to make in his earlier attempt at creating what was essentially a synthetic orthophotograph. Kelly had to work with  the 1998 MGS image, the only MGS image of the Mars Face available at that time, and the old Viking images. The 1998 MGS image was taken at a very large off-nadir angle (45 degrees off the vertical from the martian surface). The Viking images were taken at a much lower resolution than the MGS image (50 meters versus 4). Combined, these two data limitations made it virtually impossible to perform any stereographic measurements. In contrast, this orthophotograph was created by completely objective procedures using only the elevation data from the various combinations of stereo pairs from four different MGS images of the Face (two orthophotographs, both of which showed only a small area of the landform and two images of the complete landform, both taken at off-nadir viewing angles).
 
 

Procedure for Constructing the Synthetic Orthophotograph

A file of 75 entries for pixel coordinates versus elevation measurements was made for the 2001 image from stereographic measurements of it and three other MGS images showing parts of the Face. This data was used to create a lattice enclosing the Face as shown in Figure 3.
 
 

Figure 3. Lattice of automatically generated line segments from a set of 75 elevation measurements. Each point where lines intersect was a point for which an elevation value had been derived from measured parallax shifts. The lattice is shown superimposed over the "partially rectified" version of MOC E0300824 that was programmatically reshaped to create the orthophoto in Figure 1. The arrow indicates the direction to the MGS camera, which is also the direction in which all pixels were shifted to produce the orthophoto.
 

The algorithm used to construct this lattice produced a set of line segments with the properties that

  1. each line segment ends at points where an elevation value had been computed (the "control points");
  2. it is not possible to add any new line segment to the set of selected segments without intersecting a shorter segment already in the set. This ensures that the selected line segments do not cross each other at locations that are not control points and that they are of the shortest length possible.
The line segments generated in this way partition an area enclosing the landform into triangles, with each vertex of each triangle being a control point with an associated elevation value derived from stereographic measurements. The program constructed 140 such triangles of varying size and shape. The triangles define planar surfaces in three-dimensional space. (The X and Y coordinates are the pixel coordinates of the conrol points in the image and the Z coordinate is the elevation). Given the X and Y coordinates for any point known to lie in a given plane, the Z coordinate can be calculated.  From each pixel's X and Y image coordinates, an interpolated value of its elevation was computed based on the assumption that it lies in the plane defined by the enclosing triangle. Every pixel is then shifted in the direction of the line of sight of the MGS camera projected onto the image plane by an amount equal to the tangent of the camera emission angle times the elevation.

Pixels on slopes facing the camera (which is to the right on this image) tend to "pile up" in the same new location, so their values are averaged to get the final pixel value. Conversely, surfaces that slope away from the camera are stretched in such a way that some pixels in the resultant orthophotograph are unoccupied after the shifting operation is completed. The final step in the procedure is to assign a value to each such vacant pixel that is the average of the values of the two closest occupied pixels along the camera line-of-sight direction to either side of the vacant pixel.

The number of control points for which elevations could be determined is too small for a good profile view of the Face to be constructed based on the assumption that the Face consists of a set of faceted planar surfaces. It obviously does not. But the planar assumption seems quite reasonable for the relatively moderate value of the emission angle of the 2001 image (25 degrees). The largest displacement of pixel position required for this orthophoto was only about 100 pixels in the full-scale image, about 10% of the width of the landform.

The validity of this method and the elevation measurements on which it is based are supported by the comparison in Figure 4 with the low-resolution Themis image of April, 2002.
 

Figure 4. Comparison of the positions of features the Odyssey Themis image of the Face taken from almost directly overhead to the synthetic MGS orthophoto.

The Themis image, taken at a very small emission angle, is essentially already an orthophoto, but its resolution is about 10 times lower  than the MGS image. For the comparison, the MGS  synthetic orthophoto has been reduced to the same size as the Themis image (down from 1.9 meters resolution  to the Themis resolution of 18 meters).  As shown in Figure 4, features that can be identified in both images are at the same positions both vertically and horizontally to the limits of the Themis resolution.
 
 
 
 

    --- Lan Fleming

VGL Mars Page