Specify a fuzzy member function.

set_fuzzy_measure specifies a fuzzy member function passed in Function. The specified fuzzy functions enable fuzzy_measure_pos and fuzzy_measure_pairs / fuzzy_measure_pairing to evaluate and select the detected edge candidates. For this purpose, weighting characteristics for different edge features can be defined by one function each. Such a specified feature is called fuzzy set. Specifying no function for a fuzzy set means not to use this feature for the final edge evaluation. Setting a second fuzzy function to a set means to discard the first defined function and replace it by the second one. A previously defined fuzzy member function can be discarded completely by reset_fuzzy_measure.

Functions for five different fuzzy set types selected by the SetType parameter can be defined, the sub types of a set beeing mutual exclusive:

  - 'contrast' will use the fuzzy function to evaluate the
    amplitudes of the edge candidates. When extracting edge 
    pairs, the fuzzy evaluation is obtained by the geometric 
    average of the fuzzy contrast scores of both edges.

  - The fuzzy function of 'position' evaluates the signed distance
    of each edge candidate to the reference point of the 
    measure object, generated by gen_measure_arc or
    gen_measure_rectangle2. The reference point is
    located at the beginning whereas 'position_center' or
    'position_end' sets the reference point to the middle or
    the end of the one-dimensional gray value profile instead. 
    If the fuzzy position evaluation depends on the position
    of the object along the profile, 'position_first_edge' /
    'position_last_edge' sets the referece point at the
    position of the first/last extracted edge. When extracting
    edge pairs the position of a pair is referenced by the
    geometric average of the fuzzy position scores of both 
    edges.  

  - Similar to 'position', 'position_pair' evaluates the
    signed distance of each edge pair to the reference point of the measure
    object. The position of a pair is defined by the center point 
    between both edges. The object's reference can be set by 
    'position_pair_center', 'position_pair_end' and 'position_first_pair',
    'position_last_pair', respectively.  Contrary to 'position', this set 
    is only used by fuzzy_measure_pairs/fuzzy_measure_pairing

  - 'size' denotes a fuzzy set that evaluates the normed distance of
    the two edges of a pair in pixels. This set is only used by
    fuzzy_measure_pairs/fuzzy_measure_pairing. Specifying an
    upper bound for the size by terminating the member function 
    with a corresponding fuzzy value of 0.0 will speed up 
    fuzzy_measure_pairs / fuzzy_measure_pairing because not all 
    possible pairs need to be considered.

  - 'gray' sets a fuzzy function to weight the mean projected 
    gray value between two edges of a pair. This set is only 
    used by fuzzy_measure_pairs / fuzzy_measure_pairing.

A fuzzy member function is defined as a piecewise linear function by at least two pairs of values, sorted in an ascending order by their x value. The x values represent the edge feature and must lie within the parameter space of the set type, i.e., in case of 'contrast' and 'gray' feature and, e.g., byte images within the range 0.0 <= x <= 255.0. In case of 'size' x has to satisfy 0.0 <= x whereas in case of 'position' x can be any real number. The y values of the fuzzy function represent the weight of the corresponding feature value and have to satisfy the range of 0.0 <= y <= 1.0. Outside of the function's interval, defined by the smallest and the greatest x value, the y values of the interval borders are continued constantly. Such Fuzzy member functions can be generated by create_funct_1d_pairs.

If more than one set is defined, fuzzy_measure_pos / fuzzy_measure_pairs / fuzzy_measure_pairing yield the overall fuzzy weighting by the geometric middle of the weights of each set.

/* how to use a fuzzy function */
...
gen_measure_rectangle2 (50, 100, 0, 200, 100, 512, 512, 'nearest_neighbor', 
                        MeasureHandle) 
/* create a generalized fuzzy function to evaluate edge pairs 
 * (30% uncertainty). */
create_funct_1d_pairs ([0.7,1.0,1.3], [0.0,1.0,0.0], SizeFunction)
/* and transform it to expected size of 13.45 pixels */
transform_funct_1d (SizeFunction, [1.0,0.0,13.45,0.0], TransformedFunction)
set_fuzzy_measure (MeasureHandle, 'size', SizeFunction)

fuzzy_measure_pairs (Image, MeasureHandle, 1, 30, 0.5, 'all', RowEdgeFirst,
                     ColumnEdgeFirst, AmplitudeFirst, RowEdgeSecond, 
                     ColumnEdgeSecond, AmplitudeSecond, RowEdgeCenter,
                     ColumnEdgeCenter, FuzzyScore, IntraDistance, 
                     InterDistance)

set_fuzzy_measure is reentrant and processed without parallelization.

gen_measure_arc, gen_measure_rectangle2, create_funct_1d_pairs, transform_funct_1d

fuzzy_measure_pos, fuzzy_measure_pairs

set_fuzzy_measure_norm_pair

reset_fuzzy_measure

1D Metrology