Automatic geometric calibration and unwarping of rotating line-scan imaging systems using elliptical distortion of circular patterns

Rotating line-scan cameras and laser profilers acquire a scene line by line while the target or stage rotates. The resulting sector-scan geometry bends both the 2D intensity image and the 3D height map, so circular holes on a calibration plate appear as ellipses rather than circles. This work uses that distortion as the calibration signal: the ellipse centers and aspect ratios reveal the rotation center and angular sampling rate without external encoders or mechanical measurement.

The method is built for practical rotating inspection systems. A single laser profiler captures the 2D intensity image and the 3D height profile under the same sector-scan geometry, and one polar-to-Cartesian correction is then applied consistently to both modalities.

Problem setting

Rotating line-scan cameras and laser profilers operate under a sector-scan geometry, which introduces systematic geometric distortions in both 2D intensity images and 3D line-scan height profiles. This paper presents an image- driven geometric calibration and unwarping framework for such systems using a simple circular-hole calibration plate. Under sector-scan sampling, circular holes are projected as ellipses whose centers and aspect ratios encode the underlying rotation geometry.

In the broader publication record, this work appears in Optics and Lasers in Engineering, 203:109793. The visual notes below pair the paper’s original figures with a concise reading of the method, experimental setup, and reported results.

Method and visual evidence

The method combines domain-specific measurements with an algorithmic representation that exposes the relevant structure, then refines it into a reconstruction, correspondence, segmentation, measurement, or decision result.

The extracted figures below show the main pipeline and representative experimental evidence.

Method overview. This image is extracted from an embedded PDF image object on page 8, then recomposed for web display.

Representation and setup. This image is extracted from an embedded PDF image object on page 10, then recomposed for web display.

Experimental evidence. This image is extracted from an embedded PDF image object on page 10, then recomposed for web display.

Result comparison. This image is extracted from an embedded PDF image object on page 11, then recomposed for web display.

Additional visual result. This image is extracted from an embedded PDF image object on page 12, then recomposed for web display.

Results and impact

The evaluation reported in Optics and Lasers in Engineering, 203:109793 uses the extracted figures above to show the method’s measurement, reconstruction, segmentation, matching, or diagnostic behavior on representative experiments. These visuals are paired with the paper’s quantitative or qualitative analysis to make the workflow easier to inspect from the homepage.

Source handling

I extracted 11 candidate image objects from paper.pdf and generated the compressed WebP figures used on this page. The local PDF was also optimized from 9,185,922 bytes to 9,114,023 bytes.