|Posted by George Freund on May 16, 2015 at 12:30 AM|
by OLEG OLEYNIK, Ph.D.c
Previously of the Department of Physics and Technology
Kharkov State University, Ukraine
Photographs taken on the lunar surface during the Apollo missions are regarded as the most compelling pieces of evidence that mankind went to the Moon.
The photographic validation method presented here is based on the detection of two-dimensional objects among three-dimensional objects, and determining the mutual arrangement of these objects in space and the distance to them by applying a technique known as stereoscopic parallax.
The word parallax derives from the Greek parallaxis meaning "alteration" where parallax is the difference in the apparent position of objects caused by shifting camera position. To achieve such a result, images are overlapped and are deducted/subtracted from each other using the function "difference" in an image processing application such as Photoshop®. Optical transformations are used when images are subtracted. During image convergence simple operations are applied: x and y axis scaling, rotation and distortion plus two additional processes: perspective and shift.
Such processes are referred to below as "optical transformations". Objects further than two kilometres distant, with a minor camera shift, have zero parallax.
Using Photoshop® the sequence of steps deployed is as follows:
Fig. 1. A stereoscopic image or ‘wiggle’ stereoscopy. GIF-animation allows the creation of a crude sense of dimensionality, even with monocular vision. Stereoscopic imagery can also determine the relative position of objects in space and enable judgment of their remoteness. Image Wikipedia
The distance to the power plant is about 4 kms and to the tree planting (left horizon) is about 2 kms.
The image convergence shown below (the main criteria is the most complete background subtraction, and since the distance is more than 3 kms, the parallax is zero).
A rectangle marks the sections of the photographs which were deducted for parallax examination and separation of 3D objects from any 2D objects.
Fig. 6. The LM with Jim standing at the rear of the rover; the Apennine front and the crater St. George are located in the background. The distance from the camera to the lunar module and rover is about 10 metres, and the Apennines and the crater should be 4-8 kms away.
Nearby objects: the LM, the rover, and astronaut Jim are shifting relative to each other. The Apennines and the crater St. George are also moving as a whole. (Moreover, the shadow is changing on the mountains and the crater.) This finding indicates that it is less than 300 metres to the background (the ‘mountains’ instead of 5 kilometres!
Fig. 7. The subtraction of the two photos after the transformations of scaling, rotation, and distortion is shown on the left. The right image shows the parallax achieved after merging the two frames.
Fig. 8. On the left Dave collects samples; Mount Hadley; LM in the centre; behind the LM the sun is shining into the camera and the Apennines are in the distance – over 35 kms; the Apennines and the crater St. George are on the right at a distance of 5-8 kms.
Despite a slight offset of the camera, the mountains are moving, which contradicts the condition of distant mountains. If the image subtraction criteria are changed, the most darkened background condition is replaced with the most darkened front area.
Fig. 10. The subtraction of two images after scaling, rotation, and distortion is shown on the left. The stereoscopic image after merging two images is on the right.
An error estimate is now performed. Assuming that this is a real lunarscape, then the distance from the astronauts to the lunar horizon should be 1.5 kms and the distance to the objects in the background, such as the foot and summit of Mount Hadley, is 20-35 kms.
Fig. 11. The subtraction of the front parts of the two images is on the left. The parallax resulting from the two merged images is on the right. This image was obtained by the subtraction of two photos taken with a camera shift of not more than 20 cms. Transformations of scale, rotation, reverse distortion, perspective, shift and the convergence of the two images into a stereoscopic image were applied.
In two panorama frames is the bottom of Rima Hadley, which extends to Apennines Front and the crater St. George. The distance from the camera to Rima edge is about 5 m, to the Apennines and the crater is 4-8 kms. The frames are taken with a shift of no more than a few tens of centimetres. AS15-82-11178 and AS15-82-11179.
Fig. 12. Jim is holding the camera. Rima Hadley is in the foreground. Dave is collecting samples near the rover. Mount Hadley is in the background. The sun is shining into the camera in the centre. The Apennines are over 35 kms away. Apennines Front and the crater St. George are on the left.
(Panorama assembled by the author)
Fig. 14. The foreground subtraction of the two images after scaling, rotation, distortion, shift and perspective is on the left. On the right is the resulting parallax obtained after merging the two frames.
Images AS15-85-11423 and AS15-85-11424 were selected, taken at station 2 with Rima Hadley observation.
Fig. 15. Landscape and Traverse map of Apollo 15 landing site by NASA artist (showing stations 1-14).
Fig. 16. Images AS15-85-11423 and AS15-85-11424 station 2 with a view of Rima Hadley. Photo camera stereobase is not more than 0.5m.
Fig. 17. Lunar Topophotomap of Rima Hadley, Apollo 15. Green dot marks the photo sessions site.
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