{
  "source": "comphrdoc-answer-free-input",
  "pages": [
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      "elements": [
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          "type": "text",
          "bbox_px": [
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          "text": "ger value to the star coordinate in the image, which is ≃ 0.3826,",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "physically motivated set of parameters.",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "optical response, and in particular of the radial distortion, would",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "sources and the computed position of their matching stars in the",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "suggests however that any more sophisticated modelling of the",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            49,
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          ],
          "text": "7 https://harrisgeospatial.com/docs/CURVEFIT.html",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "discrepancy between the measured and modelled positions of the Nm stars found in the frame.",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "listed in Table 1. As expected, using instead a discrete pixel lo-",
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        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "curvefit7 routine included in the standard IDL library, and its",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "night, and #6 obtained four months later. Figures 2 and 3 correspond to row R2. The focal length f1 was converted from pixels to mm",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "the horizon, making the resulting processed images and movies",
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        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "in ( x, y) coordinates. To do this non-linear fitting, we tried and",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "produced by the right camera, maybe due to its optics, which",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "and right (rows R1 to R6) cameras. All runs were shot on consecutive nights, except for #2 to 4 which were produced on the same",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "runs may be due to a partial (anti-)correlation between these two",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "( f1, f3 , f5 , ∆x , ∆y ) and the level of residual discrepancies in po-",
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        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "Their discrepancies, shown as magenta arrows (after multiplica-",
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        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "As mentioned in Sect. 3.1, different options were considered",
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        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "for the set of parameters that minimize the 2Nm discrepancies",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "5",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "any clear trend. The residual distances have a mean value of 0.29",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
            232,
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            245
          ],
          "text": "assuming a pixel size of 8.40µm. The errors quoted on the parameters f1, f3 , f5, ∆x , ∆y are those returned by the non-linear fitting",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "less than one pixel in the region of interest, ie, everywhere above",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            57,
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            298,
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          ],
          "text": "As shown in Table 1, the same reconstruction procedure was",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "f3 and f5 are treated together, and not considered separately. This",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "spread over a four month period. The optics related parameters",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "centroid on a 5x5 patch (so-called option (c)) instead of 3x3",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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            196,
            471
          ],
          "text": "viding a stable set of fitted parameters.",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "procedure, based on the assumed discretization error on star location. The two rightmost columns show the mean and maximum",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "is increased, and we again look for a new estimate of the parame-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "as shown in Sect. 2.",
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        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "returned meaningful error bars on those parameters. Injecting",
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        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "require either the use of a basis of orthogonal polynomials, or a",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "seems to perform a bit better than the left one on this respect.",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "found is compatible with the error created by assigning an inte-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "and did not improve the residual discrepancies compared to those",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "ters minimizing the 2Nm discrepancies. The process is repeated a",
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        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "8 http://purl.com/net/mpfit",
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        {
          "type": "text",
          "bbox_px": [
            171,
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            46
          ],
          "text": "E. Hivon, J. Mouette & T. Legault: Making 3D Movies of Northern Lights",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "compatible with the quoted error bars, and larger mean and worst",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
            539,
            298,
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          ],
          "text": "(in pixel units), with a worst case of 0.68. The mean residual",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
            340,
            298,
            350
          ],
          "text": "Marquardt algorithm (Marquardt, 1963; Press et al., 1992): the",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "parameter model considered in Mori et al. (2013), which ig-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
            361,
            298,
            372
          ],
          "text": "drop-in replacement mpcurvefit8 by Markwardt (2009) based",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "cation (option (a)) lead to different parameter values, with a shift",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "best fit model of the camera response, for one specific image.",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "their position easier.",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "for the 12 images tested, the sky to pixel mappings of Eq. (7)",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "and the close bright pixel to be the same object, we then look",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "these new parameters in Eq. (7), the number of coincidences Nm",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "or below what is expected from quantization error of the star",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "(22 ≤ Nm ≤ 28 depending on the image being treated), and pro-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "on the MINPACK algorithm of Moré (1978). We found the best fit",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "parameter values to be nearly identical, but only the latter routine",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          ],
          "text": "Table 1. Parameters of the camera response, for frames taken from six different shooting sequences with the left (rows L1 to L6)",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          "text": "used here made no significant difference on the parameter values",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          "text": "mounted and remounted between observations performed on dif-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "coordinates (0.3826 pixels), and we note that the right camera",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            325,
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            429
          ],
          "text": "In each case, the mean residual error in position is compatible",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "applied, for each of the two cameras, on images extracted from",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          "text": "tion by 200) seem fairly randomly distributed and do not exhibit",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "few times, rapidly converging toward a stable number of matches",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          "text": "to determine the stars position on the camera frame. Using the",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
            595,
            566,
            606
          ],
          "text": "case discrepancies (by ∼30% and ∼20% respectively). However,",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            310,
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          ],
          "text": "by bluring lightly the stars makes the sub-pixel determination of",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          "text": "largest relative changes affecting ∆x , ∆y when the lenses were un-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          ],
          "text": "compared two different IDL implementations of the Levenberg-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "of Auroras nearly indistinguishable.",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            57,
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          ],
          "text": "Figure 3 compares the measured position of the bright",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "The 8-parameter mapping model considered here therefore",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
            42,
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          "text": "six different shooting sequences, filmed on four different nights",
          "confidence": 1
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        {
          "type": "text",
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          "text": "[table p0005 g0002]",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "sition, were found to be quite stable for each camera, with the",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "f3 + f5 varies less between runs than either f3 or f5 . However, this",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "ferent nights. The relatively large changes of f3 and f5 between",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "degeneracy does not hamper the modelling of Eq. (7) as long as",
          "confidence": 1
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        {
          "type": "text",
          "bbox_px": [
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          "text": "resulting from options (a) and (b) respectively differed by quite",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "parameters, which also shows on the fact that the combination",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "seems to generate smaller reconstruction errors than the 6-",
          "confidence": 1
        },
        {
          "type": "text",
          "bbox_px": [
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          "text": "This may be due to the slightly lesser sharpness of the images",
          "confidence": 1
        }
      ]
    }
  ]
}