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Crater Projection in Linear Pushbroom Camera Images

Michela Mancini, Ava Thrasher, Carl De Vries, John Christian

Abstract

Scientific imaging of the Moon, Mars, and other celestial bodies is often accomplished with pushbroom cameras. Craters with elliptical rims are common objects of interest within the images produced by such sensors. This work provides a framework to analyze the appearance of crater rims in pushbroom images. With knowledge of only common ellipse parameters describing the crater rim, explicit formulations are developed and shown to be convenient for drawing the apparent crater in pushbroom images. Implicit forms are also developed and indicate the orbital conditions under which craters form conics in images. Several numerical examples are provided which demonstrate how different forms of crater rim projections can be interpreted and used in practice.

Crater Projection in Linear Pushbroom Camera Images

Abstract

Scientific imaging of the Moon, Mars, and other celestial bodies is often accomplished with pushbroom cameras. Craters with elliptical rims are common objects of interest within the images produced by such sensors. This work provides a framework to analyze the appearance of crater rims in pushbroom images. With knowledge of only common ellipse parameters describing the crater rim, explicit formulations are developed and shown to be convenient for drawing the apparent crater in pushbroom images. Implicit forms are also developed and indicate the orbital conditions under which craters form conics in images. Several numerical examples are provided which demonstrate how different forms of crater rim projections can be interpreted and used in practice.
Paper Structure (23 sections, 100 equations, 13 figures, 5 tables)

This paper contains 23 sections, 100 equations, 13 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Linear Pushbroom Cameras
  3. Craters as Conics on the Lunar Surface
  4. Craters formation and morphology
  5. Conic parameterizations
  6. Conics in Pushbroom Images
  7. Generic Projection of a Conic into a Pushbroom Image
  8. Reduction to a conic in the pushbroom image
  9. Generic conic projection as the intersection of curves
  10. Estimating the Curve on the Pushbroom Image
  11. Motion from Pushbroom Images
  12. Polynomial formulation of the least-squares problem
  13. Homotopy continuation
  14. Parameter homotopy
  15. Implementation details
  16. ...and 8 more sections

Figures (13)

  • Figure 1: Pushbroom cameras tend to produce high aspect ratio images with the along-track dimension much larger than the cross-track dimension due to the observer's orbital motion. For scale, Curtis crater is approximately 2.9 km in diameter. NASA PDS product M1107903421RERobinson:2010b.
  • Figure 2: The pushbroom camera's instantaneous view plane is the camera frame's $y$-$z$ plane and contains the 1-D image formed at any instant in time.
  • Figure 3: The geometry of the projection on the image plane causes phenomena of shear and magnification that contribute to the appearance of the final pushbroom image. While the intersection between the lines of sight and the sensor array happens on the blue plane, the image plane is the red plane. In fact, while the blue plane has a constant distance from the camera center, only the red plane is orthogonal to the initial view plane.
  • Figure 4: The central angle which parameterizes the standard trigonometric form of an ellipse may be converted to the canonical representation parameter using a simple one-to-one cotangent mapping, and vice versa.
  • Figure 5: Two points imaged at different time instants will have the same $w$ only if the world plane and the camera motion are parallel.
  • ...and 8 more figures