Proceedings Article | 21 June 2015
KEYWORDS: Mathematical modeling, Optical sensors, Detection and tracking algorithms, Imaging systems, Cameras, Sensors, Calibration, Error analysis, Distortion, Photogrammetry
Plane circular targets are widely used within calibrations of optical sensors through photogrammetric set-ups. Due to this
popularity, their advantages and disadvantages are also well studied in the scientific community. One main disadvantage
occurs when the projected target is not parallel to the image plane. In this geometric constellation, the target has an
elliptic geometry with an offset between its geometric and its projected center. This difference is referred to as ellipse
eccentricity and is a systematic error which, if not treated accordingly, has a negative impact on the overall achievable
accuracy. The magnitude and direction of eccentricity errors are dependent on various factors. The most important one is
the target size. The bigger an ellipse in the image is, the bigger the error will be. Although correction models dealing
with eccentricity have been available for decades, it is mostly seen as a planning task in which the aim is to choose the
target size small enough so that the resulting eccentricity error remains negligible. Besides the fact that advanced
mathematical models are available and that the influence of this error on camera calibration results is still not completely
investigated, there are various additional reasons why bigger targets can or should not be avoided. One of them is the
growing image resolution as a by-product from advancements in the sensor development. Here, smaller pixels have a
lower S/N ratio, necessitating more pixels to assure geometric quality. Another scenario might need bigger targets due to
larger scale differences whereas distant targets should still contain enough information in the image. In general, bigger
ellipses contain more contour pixels and therefore more information. This supports the target-detection algorithms to
perform better even at non-optimal conditions such as data from sensors with a high noise level.
In contrast to rather simple measuring situations in a stereo or multi-image mode, the impact of ellipse eccentricity on
image blocks cannot be modeled in a straight forward fashion. Instead, simulations can help make the impact visible, and
to distinguish critical or less critical situations. In particular, this might be of importance for calibrations, as undetected
influence on the results will affect further projects where the same camera will be used. This paper therefore aims to
point out the influence of ellipse eccentricities on camera calibrations, by using two typical calibration bodies: planar and
cube shaped calibration. In the first step, their relevance and influence on the image measurements, object- and camera
geometry is shown with numeric examples. Differences and similarities between both calibration bodies are identified
and discussed. In the second step, practical relevance of a correction is proven in a real calibration. Finally, a conclusion
is drawn followed by recommendations to handle ellipse eccentricity in the practice.
