Multi-scale freeform surface texture filtering using a mesh relaxation scheme

Abstract

Surface filtering algorithms using Fourier, Gaussian, wavelets … etc., are well-established for simple Euclidean geometries. However, these filtration techniques cannot be applied to today's complex freeform surfaces, which have non-Euclidean geometries, without distortion of the results. This paper proposes a new multi-scale filtering algorithm for freeform surfaces that are represented by triangular meshes based on a mesh relaxation scheme. The proposed algorithm is capable of decomposing a freeform surface into different scales and to separate surface roughness, waviness and form from each other as will be demonstrated throughout the paper. Results of applying the proposed algorithm to computer-generated as well as real surfaces are represented and compared with a lifting wavelet filtering algorithm.

Freeform texture representation and characterisation based on triangular mesh projection techniques

“…Moreover, many filtering and decomposition algorithms for freeform surfaces that are represented by triangular meshes were proposed. Those algorithms use different principles such as partial differential equations, lifting wavelets, mesh relaxation schemes, morphological operations and manifold harmonics, to filter any freeform surface or decompose it into its different scales and components [4][5][6][7][8][9][10]. The work carried out in this paper continues the previous work by investigating the two remaining blocks in figure 1, i.e., the texture representation and the parameter calculation.…”

“…After the decomposition of the surface and form removal process [4][5][6][7][8][9][10], the remaining residues that represent the surface texture have to be parameterised. The representation of these residues is very important for the calculation of the surface parameters.…”

“…After calculating a 2D planar domain for a 3D surface, the surface texture that is extracted from analysing, filtering and decomposing the 3D surface [4][5][6][7][8][9][10], has to be projected back into this 2D planar domain so that the surface parameters can be calculated. Traditionally, the surface texture is projected onto a 2D planar domain by subtracting the surface form from the original surface.…”

“…Consequently, surface texture characterisation has witnessed important shifts in the last decade or two; from profile measurements to areal measurements and from simple surfaces to complex freeform surfaces [1][2][3]. These shifts have triggered the need for new algorithms and techniques that can better describe, represent, measure and characterise the newly evolved complex freeform surfaces [4][5][6][7][8][9][10].…”

Hierarchical-information-based characterization of multiscale structured surfaces

“…This distortion issue is especially critical for MSS since the microstructures can be as small as several micrometres, which places limits on the available measurement technologies. Several methods [9,10] have been developed for characterization of MSSs but the accuracy is still a question.…”