Thesis

THE LUNAR SURFACE: Visualizing Changes Chitra Sivanandam

INTRODUCTION

Each year meteors bombard the earth’s atmosphere and burn up before ever reaching the surface. Since the moon has no atmosphere, an approaching meteor could potentially hit it and form a crater. Historically, many lunar craters and other surface features have also been created through volcanic activity.¹ By examining the images from the Lunar Orbiter missions (1960's) and from Clementine (1990's), it may be possible to see if any new surface features or craters were formed during the thirty-years that separated the two missions. The thrust of the research will be in obtaining and processing the images that are selected such that the images from the Lunar Orbiter correspond to the images from Clementine. Once the two images can be processed to rectify angle, scale, and size, they may be compared to locate differences in topography that has occurred in the intervening time.

This research focuses on a specific region around the crater Aristarchus. A procedure was developed to rectify images from the Lunar Orbiter and Clementine. One of the key obstacles in this procedure was that the resolution of the Lunar Orbiter image was much better (smaller spot size) than that from Clementine. As a result, no obvious changes were visible in this region of the lunar surface. Note that this procedure would be more effective if there was one aspect that was consistent between the images (i.e. ground resolution). Because there were so many variables, it was more difficult to see what was affecting what result.

If the entire lunar surface were to be examined using such comparison techniques, a large database of information could be created. A utility that facilitates comparison of images makes it feasible to document surface changes over time. In the future, it may be possible to extend this technique to utilize the multispectral images from Clementine. If similar missions document the lunar surface in the spectral regions that Clementine examined, then comparisons may show some changes that can not be seen within the visible spectrum. Knowledge and understanding of the moon and planetary bodies in general can increase. During the course of this year, the goals of this research were to see if the lunar surface has changed over the past thirty years near Aristarchus.

BACKGROUND

The moon has been studied for centuries, but only within this century has it been possible to obtain photographic databases of the entire lunar surface, to aid in understanding its origins and topography. It has been the most extensively studied celestial body in our solar system, but unfortunately, many questions are still unanswered. Two important missions that had photographed the moon were the Lunar Orbiter program and Clementine.

In the 1970’s it was believed that “the greatest contributions to our present knowledge of the morphology of the lunar surface were made by the photographic cameras of Lunar Orbiters in 1966-68.” ¹

FIGURE 1. THE LUNAR ORBITER SPACECRAFT	FIGURE 2. CLEMENTINE SATELLITE

The Lunar Orbiter program consisted of five unmanned missions to the moon during the mid 1960’s whose main purpose was to locate and investigate areas on the moon that would be most appropriate for landing areas. The program had three main objectives.

Photography – with a goal to obtain detailed lunar topographic and geologic information of various lunar-terrain types to assess their suitability for use as landing sites by Apollo and Surveyor spacecraft and to increase man’s scientific understanding of the moon.
Selenodesy – to provide precision trajectory information that would improve the definition of the lunar gravitational field. Selenodesy is defined as the branch of astronomy concerned with measuring, or determining the shape of , the moon or its surface features, by exactly locating several points on its surface etc.
Analysis of the moon’s environment – to provide measurements of the micrometeoroid and radiation flux in the lunar environment for spacecraft performance analysis. ²

The first three missions (Lunar Orbiters 1-3) spent more time finding 20 landing sites, while the last two missions (Lunar Orbiters 4-5) spent more time imaging surface features of the moon. Lunar Orbiter 4 photographed the near side and most of the far side of the moon. Lunar Orbiter 5 completed survey of the far side of the moon and also took high-resolution photographs of 36 preselected areas. After the completion of the Lunar Orbiter program, 99% of the surface of the moon had been imaged at a ground resolution of 60 meters (60 meters per pixel) or better. ³ The best resolution in images obtained from Lunar Orbiters 2 and 3 is 1 meter; the best from Lunar Orbiter 5 is 2 meters.

The imaging protocol for the Lunar Orbiter mission was well planned. Each Lunar Orbiter would photograph the surface, develop the photograph, digitize the images, and transmit the gray values by downlinking to ground stations on earth. The transmitted images were then printed on 20x24 inch photographic film, and archived with the NSSDC (National Space Science Data Center). From these “original” frames of film, NSSDC makes available reflection or transmission copies. The Lunar Orbiter program produced more than a million images of the lunar surface, a significant achievement even today.

“The Lunar Orbiters had an ingenious imaging system, which consisted of a dual-lens camera, a film processing unit, a readout scanner, and a film handling apparatus. Both lenses, a 610-mm narrow angle high-resolution (HR) lens and an 80-mm wide-angle medium resolution (MR) lens, placed their frame exposures on a single roll of 70 mm film. The axes of the two cameras were coincident so the area imaged in the HR frames were centered within the MR frame areas. The film was moved during exposure to compensate for the spacecraft velocity, which was estimated by an electric-optical sensor. The film was then processed, scanned, and the images transmitted back to Earth.” ³

In 1996, NASA and the Ballistic Missile Defense Organization (BMDO) sponsored the Clementine mission that was designed to prove the usefulness and ability of lightweight sensors. This project, known as the Deep Space Program Science Experiment (DSPSE) , also imaged the entire surface of the moon.⁴ Clementine was used to test new sensors and spacecraft components, along with making scientific observations of the moon and of Geographos, an asteroid whose orbit approaches earth. Clementine imaged the moon in various wavelengths extending from the ultraviolet to the infrared regions of the electromagnetic spectrum (of which 11 were spectral bands in the visible and near-infrared). It imaged at an average ground resolution of 200 meters/pixel. This resolution varied due to Clementine’s elliptical orbit. The imager obtained a maximum resolution of approximately 20 meters/pixel of select areas. These high resolution images were taken in single color, using a larger bandwidth and displayed as grayscale. They were also taken using shorter bandwidths creating multicolor images ranging from 2 to 4 colors (by merging 2 to 4 of these "color" images together).⁵ Due to malfunctions aboard the spacecraft, Clementine was unable to complete its study of Geographos, and completed its mission with the largest database of images of the moon. ⁶
The Clementine mission included the following experiments:

UV/VIS (ultraviolet/visible) camera imagery

Near-Infrared camera imagery

Long-wave Infrared camera imagery

High resolution camera imagery

Star Tracker camera imagery

Laser Altimeter

Bistatic Radar experiment

Gravity experiment

Charged Particle telescope. ⁶

The size of the images taken with the Ultraviolet/Visible (UV/VIS) Camera were 288 x 384 pixel images. These images were taken on one of six available bands in the ultraviolet and visible regions of the spectrum. The size of the images from the Near-Infrared (NIR) Camera were 256 x 256 pixel images, taken in one of 6 filters on the near infrared wavelengths. The size of the images from the Long Wavelength Infrared (LWIR) Camera were 128 x 128 pixel images, taken with one broadband filter in the far infrared wavelengths. The size of the images from the High Resolution (HIRES) Camera were 384 x 288 pixel images, taken in one of 5 filters in the UV and visible wavelengths. Finally, the size of the images from the Star Tracker, a camera with a wide field-of-view, were 576 x 384 pixel images, taken in one broadband filter.⁷

This research concentrated on rectifying the Clementine images from the UV/VIS and High Resolution cameras along with scanned imagery from Orbiter photographs. The UV/VIS camera was a CCD framing imager that contained a six-position filter wheel. The sensor consisted of a coated Thompson CCD camera with a passband of 250-1000 nm and the six-position filter wheel. The response was limited at short wavelengths by the transmissivity of the optics and the MTF of the lens. The system used a catadioptric telescope with an aperture of 46 mm and its fused silica lenses focused onto the sensor. The CCD was a frame transfer device which allowed three gain states (150, 350, and 1000 electrons/bit). Integration times varied from 1 to 40 ms depending on gain state, solar illumination angle, and filter.⁸ The passbands of the six filters were centered at 415, 750, 900, 950 and 1000 nm, along with a broadband filter.⁵ Because Clementine carried a CCD camera, no film processing was required. Instead, Clementine recorded the images on a CCD and transmitted them back to the earth via compression based on the Discrete Cosine Transform (DCT). A database of the images from Clementine was collected and stored on 88 CD’s using this same DCT compression algorithm, and was made available through NSSDC. The entire lunar surface was imaged with the UV/VIS camera, whereas select areas were imaged with the other cameras. However, the UV/VIS camera imaged the moon primarily from a perspective at low sun angles making things more difficult to see morphology. Clementine returned over 2.5 million images of the moon from all sensors, 300 topographic profiles of the entire moon, and radio tracking data. The conclusion of the Clementine mission was that the sensors met or exceeded expectations, providing a global, comprehensive data set of the moon.⁵

THEORY

The Imagery

Obtaining digital images from Lunar Orbiter was trivial because the originals exist as negatives and can be bought either through NASA or NSSDC. The image can be ordered as a smaller scaled transparency, a second-generation contact print, or a third-generation reflection copy. These images can thus be scanned on any system and be made into digital images.

Obtaining the Clementine image is a bit more involved. Because of the technology at the time of this mission, the Clementine images exist as either raw scans or mosaicked scans (all digital) written in the PDS format. The PDS format was created to encode large planetary data (as from the name of the format) and can be bought on a CD through NSSDC. However, the major difference is that the Clementine images include header files that give full descriptions about the sensors and the manner in which the images were taken. So, one can conclude that the Clementine images may be more beneficial in the future.

Digital Image Processing - Resampling

Many software programs were utilized in this research, including: NasaView, Adobe Photoshop, ERDAS Imagine, and IDL. This section will not go into detail about each of these programs/tools but will address the image processing issues for which each of these components were used.

The differing resolutions requires that some of the images be resampled. Of the various ways to resample the image, three were considered in this research. These are classified based on the number of pixels that are considered in the resampling process: nearest-neighbor interpolation, bilinear interpolation, and cubic convolution. The nearest-neighbor interpolation considers the gray value of the closest pixel and is mathematically the simplest Bilinear interpolation considers two linear interpolations (hence the name) vertically and horizontally (thus takes into consideration 4 neighboring pixel values) and determines a value for the point based on these neighboring pixel values. The third option models the 2-D SINC-function interpolator over 16 pixels and computes the convolution of the original image. The following diagram illustrates the process.

FIGURE 3. RESAMPLING TECHNIQUES

Nearest Neighbor: Takes into consideration only the one pixel closest to it.	Bilinear Interpolation: Takes into consideration the four pixels that are around the point.	Cubic Convolution: Takes into consideration the 16 pixels that surround the point.

After performing the resampling, the image processing technique that was utilized was a simple differencing. By looking at the image as an array of numbers, it is possible to do simple vector math calculations on these images. A difference image is simply image no.1 - image no.2. More complicated processing techniques used involved taking the Fourier Transform, doing some edge detection, and applying a lowpass filter on the image. These techniques allowed for detection of large differences between the images rather than all of the small differences that may not be as meaningful. These will be explained in latter sections.

Digital Image Processing - Fourier Transforms and Filters

A Fourier Transform (F.T.) is a transform that takes a spatially varying function (like an image) and represents it in the frequency domain. By going into the frequency domain, it was possible to do some filtering of higher frequencies so that the large differences in resolution between the images do not dominate the difference image. Mathematically, if a function f(x) is given, then the F.T. is given by the following formula.

EQUATION 1. THE FOURIER TRANSFORM INTEGRAL

⁹

The F.T. typically has a real and imaginary part. The magnitude of the entire function is the Fourier spectrum, and the magnitude square of the entire function is known as the power spectrum. These two spectra can be more useful ways of actually visualizing the frequency components of the image.

Since images are two-dimensional, the F.T. is also two-dimensional. Two-dimensional F.T.s are basically the same as the one dimensional formula above, except for the fact that it takes two spatial variables (x,y) and transforms them into the two frequency variables (u,v). This is a representation using different coordinate planes.

The images were put through the F.T. and the higher frequencies were filtered. This was also achieved using a lowpass filter. This processing was done in IDL, and compared to see which method of filtering was most advantageous (discussed in the Methods section). The filters that are mentioned in this thesis are the lowpass filter and the Roberts' gradient (a method for edge detection). The lowpass filter, as suggested by its name, is a filter that allows the low frequency content to pass through while attenuating the high frequency content. By creating a kernel (of any pixel size dimensions, in this case 5X5), it is possible to convolve the filter with the image to attenuate the higher frequencies.

TABLE 1. CONVOLVING WITH A LOWPASS FILTER

EQUATION 2. This is the definition of the convolution integral.¹⁰	This was the gaussian lowpass filter used.

Hence the function or image is f(x) and the kernel that is being convolved with the image is h(x). In a graphical sense, the kernel is a two-dimensional function that is flipped and carried across the image (performing a multiplication and continuous sum over the entire image). The kernel, in that sense, can be thought of as a two-dimensional comb function that has heights denoted by the values in the kernel.

The Roberts' gradient is slightly more involved. The gradient operation itself is used as a method of differentiation (actually it is the most commonly used method). Using vector mathematics, it calculates the difference across the x and y direction. The Roberts' gradient uses cross directions as well (and takes the square root of the square of these differences) to compute the edges.

TABLE 2. APPLICATION OF THE ROBERTS' GRADIENT

This is one of the Roberts' gradient kernels. ⁹	This is the other Roberts' gradient kernel. ⁹

EQUATION 3. Definition of the gradient	EQUATION 4. This is the approximation that IDL uses for the Roberts' gradient

METHODS

Obtaining the Images

The first task was to identify the region of the lunar surface that was desired for this study. After doing some brief research, the region around the crater Aristarchus was selected based on the fact that there was some historical evidence of activity. Aristarchus is a crater approximately 40 kilometers in diameter on the northeast quadrant of the near side of the moon near the great Mare Ibrium group (at approximately 23 degrees north latitude and 47 degrees west longitude).¹¹ This crater was chosen because flashes of light were observed in the vicinity on two occasions, around one rim of the crater. Several people in the U.S. saw an orange colored light flash occur for approximately half an hour. The phenomenon was later confirmed by an observatory in Britain. Because of such activity, it was assumed that something may have changed on the lunar surface in that area.

The Lunar Orbiter image of Aristarchus was obtained through NSSDC. It was an image taken by Lunar Orbiter No.5 photographed with the High Resolution camera. After considering the options (different size images, and reflection copy vs. transparency) it was decided that the best option was to obtain a second-generation reflection copy because it would be most similar to the original. This image was then scanned on a flatbed scanner, by Roger Easton and Keith Knox, at Xerox. The image was scanned at a resolution of 400 ppi, and saved in the lossless TIFF format. Thus it was desirable to have all of the imagery in this TIFF format.

FIGURE 4. THE LUNAR ORBITER SCAN

The processing of the Clementine image was more difficult. This image could be purchased from NSSDC on CD's as either the raw PDS images or as mosaicked images. The CD-ROM with the appropriate mosaicked image was obtained. The Clementine satellite imaged the visible range using different filters (see the Background section). The CD purchased included imagery obtained using the 750 nm filter. This process was complicated by the fact that the Clementine image is in the 16-bit PDS format and must be converted to a more common image format. This process became complicated when it was learned that the Clementine image was a 16-bit image and that it did not come with a tool to convert this unknown format into a useable format. When the image was opened in Adobe Photoshop (as a raw image, using dimensions given by the header file), it looked like the image below.

FIGURE 5. RAW PDS IMAGE IN PHOTOSHOP	FIGURE 6. JPEG VERSION OF THE IMAGE
This was the PDS image as it looked when opened as a RAW image in Adobe Photoshop. It was not known whether Photoshop was doing a byte-swapping or whether it was choosing simply half of the 16 bits.	This was a JPEG compressed version of the PDS image. Because the JPEG file format is not lossless, it was felt that it would be better if the PDS image could be used, thus using as much of the real data as possible.

After trying to understand the PDS format and find out how to create a usable image from the PDS format, it was discovered that the program NasaView could use this format and create an image that could be used. This became the first step in the procedure below.

The Processing Path

The processing path itself consisted of a variety of programs that needed to be utilized for specific functions. These programs were: NasaView, Adobe Photoshop, ERDAS Imagine, and an IDL code.

FIGURE 7. OUTLINE OF THE PROCEDURE INVOLVED

Step 1. NasaView: convert PDS to gif

Step 2. Photoshop: convert ".gif" to ".tiff" Step 4. Photoshop: check the transform

Step 3. ERDAS Imagine: perform the GCP transform and resample

Step 5. IDL image processing routines

Using NasaView

NasaView is available from NASA's PDS web page. It has the capability of reading the PDS image and allows the user to select the appropriate 8-bit range of gray levels to be saved. The complexity of the image required experiments with this "histogram selector" to determine the best range of gray levels. The 8-bit range could be selected by controlling the minimum, median, and maximum pixel values (on a sliding histogram scale). Several ranges of gray level were tested.

FIGURE 8. THE HISTOGRAM ADJUSTMENT FEATURE

Using Photoshop

Adobe Photoshop was used to read the GIF format available from NasaView. The Orbiter image was saved as a TIFF image, hence it was logical to convert the Clementine TIFF file to a TIFF file. Photoshop also became an easy tool to see how well the transform shifted the image to match the other (in the next section). Thus the use of Photoshop was minimum but necessary.

Using ERDAS Imagine

ERDAS Imagine is a remote sensing tool available at the Center. This research used its Ground Control Point (GCP) editor to spatially manipulate one image so that it can be compared to the other. Using the GCP editor, it is possible to find corresponding points in the two images and use them as GCPs. The algorithm will then derive the equation that would allow these points to match eachother and apply it to the image. The transformation type can be changed (i.e. linear, quadratic etc.) and RMS error values are given. It is possible to continuously moves the points and calculate transforms until the RMS error is as low as desired. Once the transformation is calculated, it may be performed using one of the resampling techniques mentioned in Figure 3, and then the image may be saved. The defaults for Imagine are to use a linear transform and the nearest-neighbor resampling technique.

FIGURE 9. THE GCP EDITOR ENVIRONMENT IN IMAGINE

Using IDL

The Interactive Data Language (IDL) was created by Research Systems to be able to handle imagery more easily than other languages. Research Systems says that "IDL is the pioneering software for data analysis, visualization, and application development. IDL's [pertinent] features include: advanced image processing, interactive 2D and 3D graphics, object oriented programming, a high-level programming language, integrated mathematics and statistics, flexible data I/O, and a cross-platform GUI tool kit. IDL is a powerful, cost-effective software package that helps you get accurate results faster."¹² It is a high-powered language, similar in structure to Matlab. The code was written to input two images (of the same size, and square), and compute differences using various techniques.

The Comparison

An IDL program was generated to make the comparison. This code would input two images and then perform the various digital image processing techniques desired. Test images were generated to simulate the possible differences that may exist between the two images. These test images look like the following.

FIGURE 10. Test Image no.1 .	FIGURE 11. Test Image no.2 .	FIGURE 12. The GCP editor was used to create a transform that would shift Test Image no.1 to look like Test Image no.2 .

    The process of using test images provided for a way to test routines in the program before using the real imagery. Because of the simplicity of these test images, many of the tools used on these images were done on a trial by trial basis. The program was tested, used on real imagery, and tested again with new routines after seeing results from the real images..

    The final code called for two square TIFF images (256x256 pixels). For each step, the code allowed the user to decide whether to save the displayed images. The code calculated the power spectra from the F.T. (See Theory section). IDL uses a similar formula for the F.T., and then computes the magnitude squared to calculate the power spectrum. The Orbiter image whose power spectrum exhibited more high-frequency content was filtered. The code was re-run to applying a gaussian lowpass filter to that image (See the Theory section above for the actual lowpass filter used). There was not much difference between using the power spectrum and the lowpass filter. In the final code, the lowpass filter was implemented because it used less processing time. Edge images were generated from the filtered image via the magnitude of the Roberts' Gradient, and difference images were produced from these edge images. These difference images showed differences in structure and shape rather than previous ones that appeared confusing due to differences in gradation. The edge difference images were then compared to the Lunar Orbiter image. This was done because the ultimate difference that was desired would be a difference due to the time gap between the two sets of imagery. This time difference is the reasoning behind taking the difference to the Clementine image minus the Lunar Orbiter image.

Results

Pre-Processing (Before Entering IDL)

Two procedures were selected for use on the Clementine images. The values for the minimum, median, and maximum where chosen by seeing which numbers (See Figure 8. in the Processing Path section) brought the most amount of detail out of the image. It seemed practical to assume that the image that displays more detail in the crater would have the most number of gray values within that region. Hence, the first image included more detail in the crater and was selected for comparison with the Lunar Orbiter images.

FIGURE 13. Clementine Image No.1 Median = 127 Minimum = 127 Maximum = 256	FIGURE 14. Clementine Image No.2 Median = 16 Minimum = 0 Maximum = 127

After generating an image with the desired scaling, the images were imported into the GCP editor in Imagine so that an appropriate transform could be calculated. The use of Imagine will be briefly explained. The Imagine algorithms do not process the TIFF imagery, so the TIFF images are "imported" and converted into raster image format. The transformed images are computed from the raster-format images. Using these raster-format images, the higher resolution Orbiter image was transformed and resampled to look spatially similar to the lower resolution Clementine image. The ground control points (GCP) were chosen, the transformations were calculated, and finally, the transformed image was exported out as TIFF.

Analysis of maps of the lunar surface and the header information (i.e. latitudes and longitudes) in the Clementine image, made it possible to find ten points along the outline of the crater that seemed to correspond to each other. To verify that these points did really match on each image, traces were done and overlaid on each image to see if the general shapes of the craters fit relatively well. This entire process of trying to find the best possible points to use was repeated several times. The following two images depict the points that were found to correspond to each other and used for the transform.

FIGURE 15. From the Orbiter Image	FIGURE 16. From the Clementine Image (image no.1)

The resolution of the Clementine image was 72 ppi and that of the Orbiter image was 400 ppi, so the transformed Orbiter image would have an image resolution of 72 ppi. A third-order transform was used hoping that differences due to tilt, perspective, and shifting would be eliminated. Little difference is apparant between the processed images in the viewing angles of the scene and sensor. For the Clementine image (no.1) the computed transform parameters are:

TABLE 3. PARAMETERS OF THE TRANSFORMATION

TABLE 4. THE ERROR

	x	y		RMS
Constant	10474.904135	-511.33726	x	34.165436 pixels
x	0.263828	7.162087	y	55.283373 pixels
y	-7.051243	0.323978	Total	64.988679 pixels²
x²	0	0
y²	0	0

The transform for the second Clementine image was also computed, and the result was similar except for the fact that the RMS error (total) was about 68 instead of 65. Because these RMS errors are given in terms of number of pixels, the total RMS has square pixel units (squareroot of x-squared + y-squared), and the percent of error is very small. The size of the translated Orbiter image was 672 pixels wide X 490 pixels long (329231 pixels²). Correspondingly, the size of the Clementine image was 1704 pixels wide by 2127 pixels long (3624408 pixels²). Thus taking the first case as the scenario, the 65 pixels² of error equal to 65/329231 = 0.000197 or approximately 0.02% error. After the transformation, the images were exported to Adobe Photoshop(TM) in TIFF format to verify their correspondence.

The IDL Routine

When the images were imported by IDL, and a simple difference image was created, it was obvious that some other processing would need to be done to remove the effects of the difference in the image resolutions and the fact that the histograms of the two images were quit different. So a gaussian lowpass filter was created to smooth the Orbiter image slightly so that the smallest details that appear in that image do not show up so harshly in the difference image.

FIGURE 17. Transformed Orbiter Image.	FIGURE 18. Lowpass-Filtered Orbiter Image.

FIGURE 19. Difference of Clementine and Transformed Orbiter Image.	FIGURE 20. Difference of Clementine and Lowpass-Filtered Orbiter Image.

In these images, it seemed that the differences between the images themselves are hidden behind the differences in illumination angle and tone. It was decided an edge detection algorithm might be beneficial prior to taking the difference. From the lowpass-filtered difference image, it can be noted that the major differences are the shadows of the craters (See Figure 20). The dark regions on the left and top right are due to the shadows in the Orbiter and Clementine images respectively. A filtering of the power spectrum was also attempted. In this manner, the radial distances in the power spectrum were equalized, thus removing the extra high frequency detail in the Orbiter image. This proved to be just about as good as using the lowpass filter, except that it was more strenuous on the processor. Thus it seemed logical to simply use the lowpass filter to do the smoothing. The strong shadow effects introduced into the imagery because the illumination angles were quite different. Using Photoshop, the contrast, histogram, and brightness scales were toyed with to try and reduce this, but it made the difference image just as complicated, only toned down a bit in contrast. Hence it was unresolved as to how to compensate for this effect and hoped that by taking the difference image, this too would be taken care of.

There are many methods for doing edge detection, but because IDL has a built-in process for using the Roberts' gradient, it was chosen to do the task. The Roberts' method outlined the shape of key features in the image, but unfortunately also brought out some of the small details that existed in the Orbiter image. It is hard to see these images, but it is evident that the more detailed image (the Orbiter image without the lowpass filter) did show more edge detail.

FIGURE 21. This is the Roberts' gradient of the Orbiter image without the lowpass filter.	FIGURE 22. This is the Roberts' gradient of the Orbiter image with the lowpass filter.	FIGURE 23. This is the Roberts' gradient image of the Clementine image.

From here, the Roberts' gradient images were differenced. The difference images (Figures 24 and 25) show that there is some speckle type of detail that came from the Lunar Orbiter image. This seems to act similar to salt and pepper noise, so a median filter was used to take care of the noise. The median filter basically calculates the median value in a given neighborhood. This allows it to get rid of the extreme values - the larger black and white differences - and does not blur the edges while doing so.¹³ The median filtered images below (Figures 24 and 25) show that a lot of the detail that existed before seemed more like noisy detail rather than meaningful differences. Also notice that the lowpass filtered set of imagery did not necessarily prove to be the best ones in this example. This will be discussed in future sections.

FIGURE 24. Difference between the Orbiter image without the lowpass filter and the Clementine image (both using Roberts' gradient).	FIGURE 25. Difference between the Orbiter image with the lowpass filter and the Clementine image (both using Roberts' gradient).

FIGURE 26. Result of using the median filter to get rid of the salt and pepper noise on the above image.	FIGURE 27. Result of using the median filter to get rid of the salt and pepper noise on the above image.

FIGURE 28. Result of performing a simple thresholding (at pixel value 60) on the above image.	FIGURE 29. Result of performing a simple thresholding (at pixel value 60) on the above image.

Discussion

These results indicate that all differences between images may be compensated except for illumination angle. To correct for difference in illumination, manipulation of histograms, filtering, and tone adjustments were used but did not prove to work. Looking at images in Figures 28-29, the differences seem mostly due to illumination angle. There was no metric used to see what aspect (i.e. resolution or illumination angle) of the images contributed most to differences. The only way any such evaluation could be done was on a purely subjective basis. It is estimated that 75% of the difference is due to illumination angle and 25% to resolution. Note that these percentages are purely subjective.

An error census is necessary to determine the most significant sources of error. In preliminary step, the Orbiter image was scanned using a flatbed scanner at a resolution of 400 ppi and the Clementine image had a fixed resolution of 72 ppi. There may be some error introduced by the scanning system and from the fact that a second-generation contact print was obtained. Thus, compared to photographic film, the dynamic range of the image is decreased. Thus, some detail may have been lost, but because the resolution is so much greater than that of the Clementine image it did not contribute to as much error. The only thing that may have affected the Clementine image was that the mosaicked image was purchased instead of the raw image. After processing, it seemed evident that the 72 ppi resolution was intended to be used merely for viewing as a softcopy. It is possible that the raw scans may be at a higher resolution, thus better suited for this research.

There is more room for error in the processing of the Clementine images. Step 1 involved using NasaView to open the PDS image, use the histogram scale to select an appropriate section of the 16 bits, and saving the image as GIF. The particular 8-bit range of the 16-bit data significantly affects the results. When the range was optimized for the entire image (as it looks in Figure 6) there are only about 2 gray values used to display the crater. Using that image, the difference looked very much like the Orbiter image, but with toned down gray values. Images stored in TIFF format exhibited less error than those stored as GIF files. This leads right up to step 2. Typically if an image is saved several times in various formats, some artifacts may evolve. Step 2 is not compressing the file in any way, so it is not likely that any major artifacts or errors are introduced. Step 3 involves using the GCP editor. The type of transformation used and the choice of control points may be a source of error. If only a few points are chosen, they can be held fixed, but warp other areas. Error will be introduced if the points used do not correspond to eachother, creating a wrong transformation. This was a problem because of the fact that maps do not contain much detail, and because the Orbiter image did not come with any description of how the image was taken. Thus the matching method was a bit crude, but the error analysis above shows that this error was not very significant. The final steps use the TIFF images and create new images. There is only some error that depends on how good IDL approximates the F.T. and Roberts' gradient. Because these approximations have been tested by Research Systems, they are assumed to be insignificant in terms of creating error.

Conclusions

The results show that there were differences in the two images from the Clementine satellite and from the Lunar Orbiter program. The question becomes whether the differences can be distinguished as changes to the lunar surface or simply differences between the images. Looking at the images from the Results section, the only difference seems to be in the areas that were known to be different do to the illumination angle. Thus, no evidence of change was found.

But the objectives called for defining whether it was truly possible to do such a comparison. To answer this question, one must realize that simply doing the comparison is not the main task. The underlying objective is to be able to get results from which one can easily interpret the nature of the lunar surface, and do it with some amount of confidence. In this case, many of the interpretations that were made, were done simply based on what could be seen. A metric could not be devised to tell how much each variable was contributing to the final difference, but visually it seemed obvious that the shadow effects contributed the most. If a feature on the difference image existed in the Orbiter image but not in the Clementine image, it would translate to a resolution difference and not a surface feature. If the Clementine image was the more detailed, higher resolution image, it would have been wrong to take any position on the cause of the difference without further investigation. It could be that it would be a difference due to resolution differences (as it was in this case) or it could also be that it was a new feature that did not exist when the Orbiter imaged the moon. So it seems that it was easier for this specific task because the Orbiter image was more resolved, but in the future, the analysis would have to be more in-depth.

One main reason for having such difficulty in finding the causes of these differences is due to the fact that most of the old lunar maps that are available do not have very much detail. And if there are surface feature changes, it is likely that these small features would succumb more change than the large features that are diagrammed on maps. For this particular area, backtracking into maps only helped with determining the outer shape of the crater, Aristarchus, relative to specific latitudes and longitudes. When it came down to the exact features, maps do not have much information. Thus, if literature assumes that these high resolution images from the 1960's depict the true lunar surface, then this research will have to do the same. Because of this, one of the assumptions in this research was that if there are any new surface features, they would have to be fairly large (maybe half of the size of the crater or larger) to be considered an actual new feature. This was the reasoning behind taking out the small detail as if they represented salt and pepper noise in the image.

There were too many differences between the two images, as seen by Table 5.

	TABLE 5. DIFFERENCES BETWEEN THE IMAGES

ground resolution -	Orbiter image used a camera that had a maximum ground resolution of 2 m whereas the Clementine had a maximum ground resolution of 20 m. The Orbiter image wa fairly close to the maximum resolution, but the Clementine image received was not so close.
image resolution -	The Orbiter Image had an image resolution of 400 ppi whereas the Clementine image had an image resolution of 72 ppi.
perspective -	As can be seen by the transformed images, they seemed to be taken at similar angles (target to sensor angles) but at different times of the day, as can be seen by the shadow effects.
histograms -	The Orbiter image used a full range of values in the digital image, but the Clementine image did not have that same bit depth.
miscellaneous -	The Orbiter image was a scan made from a 2nd generation contact print (more detail would have been seen if the original transparency was used). The Clementine image was the mosaicked image taken from one of the filters of the UV/VIS sensor. This could have changed the information content if a different segment of the visible range was used, or if the RAW scans were used instead of the processed images.

These differences were all contributing factors to the final difference images. Thus the question becomes whether it is still possible to detect surface changes using this technique despite these differences in the imagery. Currently, it is hard to see if any changes occurred on the surface. In the future, if the angle of illumination could be corrected, and a large feature is scene elsewhere in the difference image, it may be due to a change on the lunar surface. But if a small detailed part of the surface changed, it may not be easy to detect. If atleast one of the above differences in the imagery was held constant, it would make a tremendous effect. At this point, it is unfair to completely eliminate the possibility that the surface changes could be detected, but it is important to note that small changes probably would not be seen through all of the other "inherent" image differences. Finally, it should be stated that the objectives for this research were met in the sense that a procedure to do such a comparison was identified, and a routine was created. However, this routine is not as versatile as was desired and would probably work better if there were not so many variables between the sets of images.

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