fuzzy_measure_posT_fuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosfuzzy_measure_pos (Operator)

Name

fuzzy_measure_posT_fuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosfuzzy_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_posfuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosFuzzyMeasurePosfuzzy_measure_pos extracts straight edges which lie perpendicular to the major axis of a rectangle or an annular arc. In addition to measure_posmeasure_posMeasurePosMeasurePosMeasurePosmeasure_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_posfuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosFuzzyMeasurePosfuzzy_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 ImageImageImageImageimageimage 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_rectangle2gen_measure_rectangle2GenMeasureRectangle2GenMeasureRectangle2GenMeasureRectangle2gen_measure_rectangle2 is used to perform these calculations only once, thus increasing the speed of fuzzy_measure_posfuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosFuzzyMeasurePosfuzzy_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_rectangle2gen_measure_rectangle2GenMeasureRectangle2GenMeasureRectangle2GenMeasureRectangle2gen_measure_rectangle2. (The interpolation only influences rectangles not aligned with the image axes and annular arcs.) The measure object generated with gen_measure_rectangle2gen_measure_rectangle2GenMeasureRectangle2GenMeasureRectangle2GenMeasureRectangle2gen_measure_rectangle2 is passed in MeasureHandleMeasureHandleMeasureHandleMeasureHandlemeasureHandlemeasure_handle.

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 SigmaSigmaSigmaSigmasigmasigma. Salient edges can be selected with the parameter AmpThreshAmpThreshAmpThreshAmpThreshampThreshamp_thresh, 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 (TransitionTransitionTransitionTransitiontransitiontransition = 'positive'"positive""positive""positive""positive""positive"), only negative edges, i.e., light-to-dark transitions (TransitionTransitionTransitionTransitiontransitiontransition = 'negative'"negative""negative""negative""negative""negative"), or both types of edges (TransitionTransitionTransitionTransitiontransitiontransition = 'all'"all""all""all""all""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_measureset_fuzzy_measureSetFuzzyMeasureSetFuzzyMeasureSetFuzzyMeasureset_fuzzy_measure. Which edges are selected can be determined with the parameter FuzzyThreshFuzzyThreshFuzzyThreshFuzzyThreshfuzzyThreshfuzzy_thresh, 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 (RowEdgeRowEdgeRowEdgeRowEdgerowEdgerow_edge, ColumnEdgeColumnEdgeColumnEdgeColumnEdgecolumnEdgecolumn_edge). The corresponding edge amplitudes are returned in AmplitudeAmplitudeAmplitudeAmplitudeamplitudeamplitude, the fuzzy scores in FuzzyScoreFuzzyScoreFuzzyScoreFuzzyScorefuzzyScorefuzzy_score. In addition, the distance between consecutive edge points is returned in DistanceDistanceDistanceDistancedistancedistance. Here, Distance[i] corresponds to the distance between Edge[i] and Edge[i+1], i.e., the tuple DistanceDistanceDistanceDistancedistancedistance contains one element less than the tuples RowEdgeRowEdgeRowEdgeRowEdgerowEdgerow_edge and ColumnEdgeColumnEdgeColumnEdgeColumnEdgecolumnEdgecolumn_edge.

Attention

fuzzy_measure_posfuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosFuzzyMeasurePosfuzzy_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, SigmaSigmaSigmaSigmasigmasigma must not become larger than approx. 0.5 * Length1 (for Length1 see gen_measure_rectangle2gen_measure_rectangle2GenMeasureRectangle2GenMeasureRectangle2GenMeasureRectangle2gen_measure_rectangle2).

It should be kept in mind that fuzzy_measure_posfuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosFuzzyMeasurePosfuzzy_measure_pos ignores the domain of ImageImageImageImageimageimage 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).
Multithreading scope: global (may be called from any thread).
Processed without parallelization.

Parameters

ImageImageImageImageimageimage (input_object) singlechannelimage → object (byte / uint2 / real)

Input image.

MeasureHandleMeasureHandleMeasureHandleMeasureHandlemeasureHandlemeasure_handle (input_control) measure → (handle)

Measure object handle.

SigmaSigmaSigmaSigmasigmasigma (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 Sigma Sigma Sigma sigma sigma ≤ 100 (lin)

Minimum increment: 0.01

Recommended increment: 0.1

Restriction: Sigma >= 0.4

AmpThreshAmpThreshAmpThreshAmpThreshampThreshamp_thresh (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 ≤ AmpThresh AmpThresh AmpThresh AmpThresh ampThresh amp_thresh ≤ 255 (lin)

Minimum increment: 0.5

Recommended increment: 2

FuzzyThreshFuzzyThreshFuzzyThreshFuzzyThreshfuzzyThreshfuzzy_thresh (input_control) number → (real)

Minimum fuzzy value.

Default value: 0.5

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

Typical range of values: 0.0 ≤ FuzzyThresh FuzzyThresh FuzzyThresh FuzzyThresh fuzzyThresh fuzzy_thresh ≤ 1.0 (lin)

Recommended increment: 0.1

TransitionTransitionTransitionTransitiontransitiontransition (input_control) string → (string)

Select light/dark or dark/light edges.

Default value: 'all' "all" "all" "all" "all" "all"

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

RowEdgeRowEdgeRowEdgeRowEdgerowEdgerow_edge (output_control) point.y-array → (real)

Row coordinate of the edge point.

ColumnEdgeColumnEdgeColumnEdgeColumnEdgecolumnEdgecolumn_edge (output_control) point.x-array → (real)

Column coordinate of the edge point.

AmplitudeAmplitudeAmplitudeAmplitudeamplitudeamplitude (output_control) real-array → (real)

Edge amplitude of the edge (with sign).

FuzzyScoreFuzzyScoreFuzzyScoreFuzzyScorefuzzyScorefuzzy_score (output_control) real-array → (real)

Fuzzy evaluation of the edges.

DistanceDistanceDistanceDistancedistancedistance (output_control) real-array → (real)

Distance between consecutive edges.

Result

If the parameter values are correct the operator fuzzy_measure_posfuzzy_measure_posFuzzyMeasurePosFuzzyMeasurePosFuzzyMeasurePosfuzzy_measure_pos returns the value TRUE. Otherwise an exception is raised.