ISO 16610-31:2025 幾何製品仕様 (GPS) — フィルタ — Part 31:堅牢なプロファイル フィルタ:ガウス回帰フィルタ | ページ 6

3.1

surface profile

line resulting from the intersection between a surface portion and an ideal plane

Note 1 to entry: The orientation of the ideal plane is usually perpendicular to the tangent plane of the surface portion.

Note 2 to entry: See ISO 17450-1:2011, 3.3 and 3.3.1, for the definition of an ideal plane.

[SOURCE:ISO 16610-1:2015, 3.1.2, modified — Note 2 to entry replaced.]

3.1.1

open profile

finite length surface profile (3.1) with two ends

Note 1 to entry: An open profile has a compact support, i.e. within a certain interval the height values of an open profile can be equal to any real number. Outside the interval, the height values of an open profile are set to zero.

[SOURCE:ISO 16610-1:2015, 3.7, modified — Note 1 to entry replaced.]

3.1.2

unbounded open profile

infinite length surface profile (3.1) without ends

Note 1 to entry: In this document, the term “unbounded” refers to the X-axis.

Note 2 to entry: The concept of the unbounded open profile is ideal and do not apply to real surface profiles.

3.1.3

closed profile

connected finite length surface profile (3.1) without ends

Note 1 to entry: A closed profile is a closed curve which is periodic with the finite period length L.

Note 2 to entry: A typical example of a closed profile is one from a roundness measurement.

[SOURCE:ISO 16610-1:2015, 3.8, modified — Note 1 to entry replaced and Note 2 to entry added.]

3.2

linear profile filter

profile filter which separates surface profiles (3.1) into large- and small-scale lateral components and is also a linear function

Note 1 to entry: If F is a function and X and Y are surface profiles, and if a and b are independent from X and Y, then F being a linear function implies F (a X + b Y) = a F(X) + b F(Y).

[SOURCE:ISO 16610-20:2015, 3.1, modified — In definition “profiles” replaced by “surface profiles” and “long wave” and “short wave” replaced by “large-scale lateral” and “small-scale lateral”; Note 1 to entry replaced.]

3.3

weighting function

function to calculate large-scale lateral components by convolution of the surface profile heights with this function

Note 1 to entry: The convolution (see ISO 16610-20:2015, 4.1) performs a weighted moving average of the surface profile heights. The weighting function, reflected at the X-axis, defines the weighting coefficients for the averaging process.

3.4

transmission characteristic of a filter

characteristic that indicates the amount by which the amplitude of a sinusoidal surface profile is attenuated as a function of its wavelength

Note 1 to entry: The transmission characteristic is the Fourier transformation of the weighting function (3.3) .

Note 2 to entry: [SOURCE: ISO 16610-20:2015, 3.4]

3.5

cut-off wavelength

wavelength of a sinusoidal surface profile of which 50 % of the amplitude is transmitted by the profile

Note 1 to entry: Linear profile filters are identified by the filter type and the cut-off wavelength value.

Note 2 to entry: The cut-off wavelength is the nesting index for linear profile filters.

[SOURCE:ISO 16610-20:2015, 3.5, modified — In Note 2 to entry “recommended” deleted.]

3.6

undulations per revolution

UPR

integer number of sinusoidal undulations contained in a closed profile (3.1.3)

Note 1 to entry: In this document, UPR is a frequency and is denoted by f.

3.7

cut-off frequency in undulations per revolution

f_c

frequency in UPR of a sinusoidal closed profile (3.1.3) of which 50 % of the amplitude is transmitted by the profile filter

3.8

robust profile filter

profile filter which separates surface profiles (3.1) into large- and small-scale lateral components and is insensitive against specific phenomena in the input data

Note 1 to entry: A robust profile filter is a nonlinear filter.

Note 2 to entry: See also ISO 16610-1:2015, 3.9.

Note 3 to entry: Outliers, scratches and steps are examples of specific phenomena. Further details can be found in ISO 16610-30:2015.

Note 4 to entry: In particular, the robust Gaussian regression filter (3.11) in accordance with this document reduces the influence of specific phenomena such as protruding dales and hills. Profile examples are given in Annex B.

3.9

biweight function of Beaton and Tukey

Note 1 to entry: The biweight function , the biweight function of Beaton and Tukey approaches zero.

Note 2 to entry: The biweight function of Beaton and Tukey is related to the influence function .

Note 3 to entry: See also ISO 16610-30:2015.

3.10

regression filter

profile filter which based on a local polynomial modelling of the large-scale lateral component of a surface profile (3.1)

3.11

robust Gaussian regression filter

regression filter (3.10) based on the Gaussian weighting function and the biweight function of Beaton and Tukey (3.9)