Form filtering by splines

Krystek, Michael

doi:10.1016/0263-2241(96)00039-5

Cited by 105 publications

(52 citation statements)

References 2 publications

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“…The number of these parameters is equal to ( 1) n K + , where, recall, 1 n + is the number of coefficients of the n -th degree polynomial, while K is the number of subintervals of the interval P . Since ( ) s t is a function of class 1 n C − , in each of the 1 K − nodes within the interval P , we can formulate n equations for the derivatives from order 0 to order 1 n − for the polynomials adjacent to a given node.…”

Section: Consider An Intervalmentioning

confidence: 99%

“…In the paper by Krystek [1] and the respective standard [6] (with both considering the case of . It should be emphasized that the method of approximation of the function ( ) s t based on B-spline functions described by (8) is really crucial here, because the proof of property (20), which results in (21), significantly exploits the fact that the base function ˆ( ) n t β used for the approximation resembles the Gaussian function, as shown in (6).…”

Section: Comparing the Spline Filter With The Filter Based On B-splinmentioning

confidence: 99%

“…Many of them have good theoretical background. In [1,2], a variational approach was used. It assumes that the filtered profile minimizes a certain functional made up of two parts.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Separation Of Non-Periodic And Periodic 2D Profile Features Using B-Spline Functions

Janecki¹,

Cedro²,

Zwierzchowski³

2015

Metrology and Measurement Systems

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The form, waviness and roughness components of a measured profile are separated by means of digital filters. The aim of analysis was to develop an algorithm for one-dimensional filtering of profiles using approximation by means of B-splines. The theory of B-spline functions introduced by Schoenberg and extended by Unser et al. was used. Unlike the spline filter proposed by Krystek, which is described in ISO standards, the algorithm does not take into account the bending energy of a filtered profile in the functional whose minimization is the principle of the filter. Appropriate smoothness of a filtered profile is achieved by selecting an appropriate distance between nodes of the spline function. In this paper, we determine the Fourier transforms of the filter impulse response at different impulse positions, with respect to the nodes. We show that the filter cutoff length is equal to half of the node-to-node distance. The inclination of the filter frequency characteristic in the transition band can be adjusted by selecting an appropriate degree of the B-spline function. The paper includes examples of separation of 2D roughness, as well as separation of form and waviness of roundness profiles.

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Section: Consider An Intervalmentioning

confidence: 99%

Section: Comparing the Spline Filter With The Filter Based On B-splinmentioning

confidence: 99%

See 1 more Smart Citation

Separation Of Non-Periodic And Periodic 2D Profile Features Using B-Spline Functions

Janecki¹,

Cedro²,

Zwierzchowski³

2015

Metrology and Measurement Systems

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show abstract

“…The M-system was greatly enriched by incorporating advanced mathematical theories. The enhanced toolbox now contains the robust Gaussian regression filter [21,22], the spline filter [23] and the robust spline filter [24,25]. More recently, a method of Gaussian filtering for freeform surface was developed by solving the diffusion equation which overcomes geometrical distortion in the presence of non-zero Gaussian curvature [26].…”

Section: Introductionmentioning

confidence: 99%

Geometric computation theory for morphological filtering on freeform surfaces

2013

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Surfaces govern functional behaviours of geometrical products, especially high-precision and high-addedvalue products. Compared with the mean line-based filters, morphological filters, evolved from the traditional E-system, are relevant to functional performance of surfaces. The conventional implementation of morphological filters based on image-processing does not work for state-of-the-art surfaces, for example, freeform surfaces. A set of novel geometric computation theory is developed by applying the alpha shape to the computation. Divide and conquer optimization is employed to speed up the computational performance of the alpha-shape method and reduce memory usage. To release the dependence of the alpha-shape method on the Delaunay triangulation, a set of definitions and propositions for the search of contact points is presented and mathematically proved based on alpha shape theory, which are applicable to both circular and horizontal flat structuring elements. The developed methods are verified through experimentation.

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“…A fast algorithm of the higher order nonlinear Gaussian regression filter was introduced recently [4]. The linear spline filter was proposed by Krystek [5] as a complementary method for the standard Gaussian filter. Compared with the standard Gaussian filter, it has the advantages of no boundary effect and follows the form well.…”

Section: Introductionmentioning

confidence: 99%

A generalised linear and nonlinear spline filter

Zeng

Jiang

Scott

2011

Wear

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In this paper, a generalised spline filter, that has a unified description for both the linear spline filter and the nonlinear robust spline filter, is proposed. Based on the M-estimation theory, the general spline filter model can be solved by using an Iterated Reweighted Least Squared method which is also general for both the linear and nonlinear spline filter. The algorithm has been verified to be effective, efficient and fast.

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Form filtering by splines

Cited by 105 publications

References 2 publications

Separation Of Non-Periodic And Periodic 2D Profile Features Using B-Spline Functions

Separation Of Non-Periodic And Periodic 2D Profile Features Using B-Spline Functions

Geometric computation theory for morphological filtering on freeform surfaces

A generalised linear and nonlinear spline filter

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