MASTCAM-Z GEOMETRIC CALIBRATION: AN ALTERNATIVE APPROACH BASED ON PHOTOGRAMMETRIC AND AFFINE SOLUTIONS SPECIFIC TO FILTER, FOCUS, AND ZOOM

Introduction and Goals: Being the first cameras with optical zoom on a planetary rover [1,2], the Mars2020 Mastcam-Zs present new challenges in deriving robust camera models for multispectral analysis and 3D stereo processing. In contrast to the heritage CAHVOR model, this approach uses the photogrammetric Zheng’s method [3] for discrete camera states in concert with affine corrections that generalize the camera models for all of the multispectral filters, focus, and zoom positions that will be used for science and operations on Mars. The greater ease of obtaining and processing the calibration data for this photogrammetric method complements the standard CAHVOR method [4] by first providing an independent validation on the derived camera parameters and second by its flexibility in applying first-order corrections accounting for the changes in focal-length and pointing introduced by changing focus position and filter number. A new algorithm of converting between the CAHVOR and photogrammetric camera models is also developed in this research. Finally, many commercial computer vision tools define their camera parameters in a photogrammetric manner, making both independently derived and converted models key in expanding the usability and impact of Mastcam-Z’s data [5,6]. Method Summary: This method includes three interdependent datasets and processes: (1) images of a fixed dot-target (see Figure 1) at various focus, filter, and zoom camera states to determine the relative affine transformations; (2) images of a dot-target in many positions when the focus, filter, and zoom are fixed to one or a few reference camera states at which the camera’s intrinsic camera model is solved [5]; and (3) stereo pairs at the reference camera state(s) to calculate the extrinsic parameters including the baseline translation and toe-in rotation of the stereo-camera system. The photogrammetric method uses images of a dot-target in various positions to solve the camera parameters in a single least-squares bundle-adjustment. In steps 2 and 3, the focal-lengths, principal-points, and distortion patterns of both cameras are solved with the relative offset and rotation between the cameras. The functions used are from OpenCV, the open-source computer vision software library [6] as well as JOANNEUM RESEARCH [7]. The coordinate systems of these solutions are centered on the left camera, with Y and X aligned with the image’s rows and columns, and Z pointing through the principal point. To transform this camera-centered reference frame to another, at least one dot-target placement must be known in the rover’s reference frame. The tests for this calibration differs from CAHVOR, in which the location of each dot-target placement must be surveyed. Besides the calibration procedure, the mathematical expressions of CAHVOR and photogrammetric camera models are sufficiently similar for comparison (though their distortion models are not equivalent) [4,5]. The Mastcam-Zs are geometrically calibrated at seven discrete focal-lengths, the shortest and longest focal-lengths of which are 26mm and 110mm (Table 1). Table 1. Photogrammetric calibration results for Mastcam-Z focal-lengths 26mm and 110mm