# measure_pos (Operator)

## Name

`measure_pos` — Extract straight edges perpendicular to a rectangle or annular arc.

## Signature

`measure_pos(Image : : MeasureHandle, Sigma, Threshold, Transition, Select : RowEdge, ColumnEdge, Amplitude, Distance)`

## Description

`measure_pos` extracts straight edges which lie perpendicular to the major axis of a rectangle or annular arc.

For an explanation of the concept of 1D measuring see the introduction of chapter 1D Measuring.

The algorithm of `measure_pos` works by averaging the gray values in “slices” perpendicular to the major axis of the rectangle or annular arc in order to obtain a one-dimensional edge profile. The sampling is done at subpixel positions in the image `Image` at integer row and column distances (in the coordinate frame of the rectangle) from the center of the rectangle. Since this involves some calculations which can be used repeatedly in several measurements, the operator `gen_measure_rectangle2` or `gen_measure_arc` is used to perform these calculations only once, thus increasing the speed of `measure_pos` significantly. Since there is a trade-off between accuracy and speed in the subpixel calculations of the gray values, and thus in the accuracy of the extracted edge positions, different interpolation schemes can be selected in `gen_measure_rectangle2`. (The interpolation only influences rectangles not aligned with the image axes.) The measure object generated with `gen_measure_rectangle2` is passed in `MeasureHandle`.

After the one-dimensional edge profile has been calculated, subpixel edge locations are computed by convolving the profile with the derivatives of a Gaussian smoothing kernel of standard deviation `Sigma`. Salient edges can be selected with the parameter `Threshold`, which constitutes a threshold on the amplitude, i.e., the absolute value of the first derivative of the edge. Note that the amplitude values are scaled by the factor . Additionally, it is possible to select only positive edges, i.e., edges which constitute a dark-to-light transition in the direction of the major axis of the rectangle or the arc (`Transition` = 'positive'), only negative edges, i.e., light-to-dark transitions (`Transition` = 'negative'), or both types of edges (`Transition` = 'all'). Finally, it is possible to select which edge points are returned. If `Select` is set to 'all', all edge points are returned. If it is set to 'first', only the first of the extracted edge points is returned, while it is set to 'last', only the last one is returned.

The extracted edges are returned as single points which lie on the major axis of the rectangle or arc in (`RowEdge`, `ColumnEdge`). The corresponding edge amplitudes are returned in `Amplitude`. In addition, the distance between consecutive edge points is returned in `Distance`. Here, Distance[i] corresponds to the distance between Edge[i] and Edge[i+1], i.e., the tuple `Distance` contains one element less than the tuples `RowEdge` and `ColumnEdge`.

## Attention

`measure_pos` only returns meaningful results if the assumptions that the edges are straight and perpendicular to the major axis of the rectangle or arc are fulfilled. Thus, it should not be used to extract edges from curved objects, for example. Furthermore, the user should ensure that the rectangle or arc is as close to perpendicular as possible to the edges in the image. Additionally, `Sigma` must not become larger than approx. 0.5 * Length1 (for Length1 see `gen_measure_rectangle2`).

It should be kept in mind that `measure_pos` ignores the domain of `Image` for efficiency reasons. If certain regions in the image should be excluded from the measurement a new measure object with appropriately modified parameters should be generated.

## Execution Information

• Multithreading type: reentrant (runs in parallel with non-exclusive operators).
• Processed without parallelization.

## Parameters

`Image` (input_object)  singlechannelimage `→` object (byte / uint2 / real)

Input image.

`MeasureHandle` (input_control)  measure `→` (handle)

Measure object handle.

`Sigma` (input_control)  number `→` (real)

Sigma of gaussian smoothing.

Default value: 1.0

Suggested values: 0.4, 0.6, 0.8, 1.0, 1.5, 2.0, 3.0, 4.0, 5.0, 7.0, 10.0

Typical range of values: ```0.4 ≤ Sigma ≤ 100``` (lin)

Minimum increment: 0.01

Recommended increment: 0.1

Restriction: `Sigma >= 0.4`

`Threshold` (input_control)  number `→` (real)

Minimum edge amplitude.

Default value: 30.0

Suggested values: 5.0, 10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 90.0, 110.0

Typical range of values: ```1 ≤ Threshold ≤ 255``` (lin)

Minimum increment: 0.5

Recommended increment: 2

`Transition` (input_control)  string `→` (string)

Light/dark or dark/light edge.

Default value: 'all'

List of values: 'all', 'negative', 'positive'

`Select` (input_control)  string `→` (string)

Selection of end points.

Default value: 'all'

List of values: 'all', 'first', 'last'

`RowEdge` (output_control)  point.y-array `→` (real)

Row coordinate of the center of the edge.

`ColumnEdge` (output_control)  point.x-array `→` (real)

Column coordinate of the center of the edge.

`Amplitude` (output_control)  real-array `→` (real)

Edge amplitude of the edge (with sign).

`Distance` (output_control)  real-array `→` (real)

Distance between consecutive edges.

## Result

If the parameter values are correct the operator `measure_pos` returns the value 2 (H_MSG_TRUE). Otherwise an exception is raised.

## Possible Predecessors

`gen_measure_rectangle2`

## Possible Successors

`close_measure`

## Alternatives

`edges_sub_pix`, `fuzzy_measure_pos`

`measure_pairs`, `fuzzy_measure_pairs`, `fuzzy_measure_pairing`