Focus on precision

Absolute precision is one of our areas of expertise.

With a stable construction on one hand, and MAVinci’s precision technology on the other, SIRIUS delivers impressive results.

In our results, we talk about absolute accuracy, as this is the only reliable index for your survey results. While relative accuracy still ignores a homogeneous displacement of the coordinates, absolute accuracy identifies the difference between the determined validation points and the corresponding coordinates in the 3D model. This difference can be calculated by means of three types of errors.

For the CLASSIC and BASIC versions, the cross-validation error is most suitable for calculating the absolute accuracy, since there is no RTK is used during the survey. The calculation using the true error, however, is applied in the PRO version.

Application example: Using data for infrastructure design

Calculation of error types: calibration error / cross-validation / true error

A comparison between calibration and cross-validation errors

Using data for infrastructure design

Detailed description of topographies and illustration of soundproofing barriers Application example in the city of Lumen in Belgium

Planning infrastructure projects requires a vast amount of preparation that almost inevitably starts with an accurate topographic survey. This allows construction engineers to calculate terrain leveling and ensure an exact fit of new constructions on existing infrastructures. On the other hand, full surveys can be laborious making them costly and time consuming. The Flemish Roads and Traffic Agency, upon planning the construction of noise barriers along the E314 and E313 highways in Lumen (Belgium), chose a smart alternative: A full topographic survey was replaced by a limited survey supplemented with a high resolution orthophoto and a high density elevation model, derived from UAS data acquired by MAVinci and processed by GeoID. The result: much richer surface information, and high quality 3D visualization. In a few hours time, three different UAS flights were made in three designated zones along both highways, covering over 170 hectares. Each flight resulted in 400 to 700 photos. Photogrammetry specialists at GeoID processed these photos into high resolution true-orthophoto’s and elevation models, with a 4 cm pixel size. Since high accuracy in this project was critical, in each zone at least 10 well marked ground control points were measured in each zone to exactly position (georeference) the model.

How to calculate the different types of errors:

Calibration errors

The calculation of calibration errors is the most common error calculation. For each Ground Control Point (GCP), it calculates the difference between the reference coordinate and the elevation model coordinate specified in the orthophoto. However, calibration errors are not a reliable index of the degree of accuracy. The reason is that the same GCPs are also used in the geo-referencing of the models, which makes them unsuitable for an independent review.

Cross-validation

Cross-validation error is a much more reliable measure of accuracy. The 3D model is calculated several times during the calculation. Each time, a different GCP (excluding the one used for verification later on) is omitted and used as a validation point. The median position accuracy of these validation points is the cross-validation error.

Rule of thumb for SIRIUS CLASSIC and BASIC:

2 x GSD on the x- and y-axes 3 x GSD on the z-axis of the 3D model  

True errors

To calculate a true error, additional control points (validation points) are measured, which are used exclusively for error measurement. A true error is defined as the difference between these validation points and the corresponding coordinates of the 3D model.

SIRIUS PRO achieves an absolute accuracy of:

down to 1.6 cm on the x- and y-axes, and down to 2.7 cm in the z-axis.

For example, a comparison between calibration and cross-validation error

Let u’s look at an example: In the southern zone of the project area, calibration errors were 4 cm for planimetry (X and Y) and 5 cm for altimetry (Z). This is what would normally be reported by automated image processing algorithms. The cross-validation errors were 6 cm for planimetry and 13 cm for altimetry. How reliable is this? For the same zone, an independent set of over 1,700 validation points, distributed along the highway, could be obtained from a related project. This allowed a detailed validation experiment, producing a validation error in Z of 11 cm. This is only slightly smaller than the reported cross-validation error but substantially larger than the calibration error. For other zones, comparable results were obtained. This demonstrates the usefulness of cross-validation as a reliable statistic for accuracy assessment.

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