# Congruency testing

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In very rare cases, the visual inspection or evaluation on sight may not relieve remaining doubts that the state of the parcel represented in the LPIS is still identical to the one that can be observed on the imagery. Such situation can occur in case of shifts (displacement) of imagery of a parcel, even if all data are well within specifications. Such a shift could cause a dirt road bordering the parcel’s perimeter, become portrayed inside that perimeter on a more recent image. The test could allow to discard the shifted portrayal as a regrettable but inevitable technical artefact, not as a real change.

As this technical test is much more complicated and cumbersome than the other procedures, it is strictly reserved for exceptional cases where discussion between stakeholders has already arisen. The Commission services do not expect the congruency test to be applied on a regular basis, but merely propose a tool of last resort that could be used __on voluntary basis__.

**"Congruent"** refers to a situation where two polygons (parcel representations) have the same shape and dimension.

As a result, all their corresponding sides (perimeter segments) have the same length, and the angle between any two corresponding segments has the same value. In a simplified form, this concept is used for two purposes:

**Vindication of a reported change.** When the visual inspection could not detect alleged changes on the land, this congruency test offers a way to demonstrate that no change has occurred. The test does not check the full perimeter or the interior of the reference parcel as these were investigated by the prior visual inspection. It relies on (the lack of) displacements on well identifiable ground points in each cardinal direction.

**Calculation of coordinate shift between two shapes.** The congruency test procedure and formulas can also be used to determine the length and direction of the local translation (coordinate shift) between two congruent representations of a single object. For instance between:

- The object’s vector and orthoimage representation
- Two separate orthoimages covering that object.

Performing the congruency test obviously requires that relevant orthoimagery, and vector representation of the parcel (that can come from a new measurement too) are available and referenced to a common Coordinate Reference System.

Any test on the full reference parcel perimeter (all sides and vertices of the polygon) would result in numerous tests of shapes, sides, angles and dimension, so this test compares a simplified representation of the reference parcel with a corresponding representation on more recent or other alternative source. The simplified representation is provided by the axis aligned bounding box (AABB) that envelopes the complete reference parcel perimeter. The four cardinal points coordinates of each AABB are mapped for each representation in the test.

The actual test involves three steps:

- Construct the AABB for one representation (LPIS RP) and calculate its parameters
- Construct the AABB for the other representation (orthoimage) and calculate its parameters.
- Compare the two derived vector parameter sets for the absence of scale variation and rotation.

A well performed congruency test ensures that:

- if the result is conforming, the geometry of the parcel should not be changed and the anomaly can be archived.
- if non-conforming, the parcel indeed has a problem with the geometry, and the anomaly processing has to be continued.

*Figure 14: Workflow in the congruency test*

The congruency test steps are:

- Start by retrieving the reference (RP vector) data produced and retrieve the measurement data produced in the field either from the farmer, inspector and/or operator
- Construct the reference AABB (e.g. via orthoimage) through cardinal points, and calculate reference (e.g. orthoimage) parameters.
- Construct the AABB to be tested (e.g. from the field measurement) through cardinal points, and calculate alternative (e.g. field measurement) parameters
- Calculate the differences between reference and alternative AABB’s as described http://139.191.148.147/wikicap/index.php/Upkeep_-_Congruency_test
- Compare the differences in length and in angle rotation between the two AABB’s vectors as described http://139.191.148.147/wikicap/index.php/Upkeep_-_Congruency_test
- If the difference of AABB’s angles >1 degree AND diagonal differences >2.5 m the congruency test result is nonconforming and the anomaly is confirmed, so update processing is needed.) A conforming result indicates the anomaly can be ignored; document the result and archive the anomaly.
- Calculate coordinate shift between two representations from the image and from the field.

Constructing each axis aligned bounding box involves

- Select the 2 vertices on the reference parcel perimeter that represent the most distant from each other. These vertex points should be ground level points (i.e. not on an elevated positions as tree tops, hedges, walls) and clearly visible (i.e. the view should not be obstructed by a nearby object.)
- Record the (x, y) coordinates of each of these opposite vertexes and visualize the long diagonal on screen (A and C)
- Select the vertex on one side of this long AC-diagonal axis that has the largest Euclidean distance perpendicular to that diagonal (the most distant corner) t l, record the (x, y) coordinates (B)
- Select the most distant vertex of the other side of the long diagonal and record the (x, y) coordinates (D).
- The AABB is constructed as the rectangular box that connects all points ABCD and with the longest sides aligned with the axis AC.

EXAMPLE: http://139.191.148.147/wikicap/index.php/Upkeep_-_Examples_congruency_test

A by-product of the congruency test procedure and formulas is the exact length and direction of the local translation (coordinate shift) between any two congruent representations of a single feature. For instance between:

- The object’s vector and orthoimage representation
- Two separate orthoimages covering that object.

Knowing these parameters is essential to remove the local coordinate shift, in particular when merging surveys.

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