# fuzzy_measure_pos (Operator)

## Name

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

## Signature

`fuzzy_measure_pos(Image : : MeasureHandle, Sigma, AmpThresh, FuzzyThresh, Transition : RowEdge, ColumnEdge, Amplitude, FuzzyScore, Distance)`

## Description

`fuzzy_measure_pos` extracts straight edges which lie perpendicular to the major axis of a rectangle or an annular arc. In addition to `measure_pos` it uses fuzzy functions to evaluate and select the edges.

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

The algorithm of `fuzzy_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` is used to perform these calculations only once, thus increasing the speed of `fuzzy_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 and annular arcs.) 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 `AmpThresh`, which constitutes a threshold on the amplitude, i.e., the absolute value of the first derivative of the edge. 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 (`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.

Having extracted subpixel edge locations, features of these edges are evaluated by a corresponding fuzzy function, which can be set by `set_fuzzy_measure`. Which edges are selected can be determined with the parameter `FuzzyThresh`, which constitutes a threshold on the weight over all fuzzy sets, i.e., the geometric mean of the weights of the defined sets.

The selected edges are returned as single points, which lie on the major axis of the rectangle or annular arc, in (`RowEdge`, `ColumnEdge`). The corresponding edge amplitudes are returned in `Amplitude`, the fuzzy scores in `FuzzyScore`. 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

`fuzzy_measure_pos` only returns meaningful results if the assumptions that the edges are straight and perpendicular to the major axis of the rectangle are fulfilled. Thus, it should not be used to extract edges from curved objects, for example. Furthermore, the user should ensure that the rectangle 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 `fuzzy_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: 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

Value range: ```0.4 ≤ Sigma ≤ 100``` (lin)

Minimum increment: 0.01

Recommended increment: 0.1

`AmpThresh` (input_control)  number `→` (real)

Minimum edge amplitude.

Default: 30.0

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

Value range: ```1 ≤ AmpThresh ≤ 255``` (lin)

Minimum increment: 0.5

Recommended increment: 2

`FuzzyThresh` (input_control)  number `→` (real)

Minimum fuzzy value.

Default: 0.5

Suggested values: 0.1, 0.3, 0.5, 0.6, 0.7, 0.9

Value range: ```0.0 ≤ FuzzyThresh ≤ 1.0``` (lin)

Recommended increment: 0.1

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

Select light/dark or dark/light edges.

Default: 'all'

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

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

Row coordinate of the edge point.

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

Column coordinate of the edge point.

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

Edge amplitude of the edge (with sign).

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

Fuzzy evaluation of the edges.

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

Distance between consecutive edges.

## Result

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

## Possible Predecessors

`gen_measure_rectangle2`, `gen_measure_arc`, `set_fuzzy_measure`

## Possible Successors

`close_measure`

## Alternatives

`edges_sub_pix`, `measure_pos`

`fuzzy_measure_pairing`, `fuzzy_measure_pairs`, `measure_pairs`