A theoretical insight into morphological operations in surface measurement by introducing the slope transform

As one of the tools for surface analysis, morphological operations, although not as popular as linear convolution operations (e.g. the Gaussian filter), are really useful in mechanical surface reconstruction, surface filtration, functional simulation etc. By introducing the slope transform originally developed for signal processing into the field of surface metrology, an analytic capability is gained for morphological operations, paralleling that of the Fourier transform in the context of linear convolution. Using the slope transform, the tangential dilation is converted into the addition in the slope domain, just as by the Fourier transform, the convolution switches into the multiplication in the frequency domain. Under the theory of the slope transform, the slope and curvature changes of the structuring element to the operated surface can be obtained, offering a deeper understanding of morphological operations in surface measurement. The derivation of the analytical solutions to the tangential dilation of a sine wave and a disk by a disk are presented respectively. An example of the discretized tangential dilation of a sine wave by the disks with two different radii is illustrated to show the consistency and distinction between the tangential dilation and the classical dilation

From planar surfaces based on lattices to freeform surfaces based on triangular meshes: an advanced extension of the areal motif method

Surfaces are shifting from traditional planar surfaces to freeform surfaces with significantly reduced volume and weight and highly improved performance. The areal motif method is used to analyse the topographical features on planar surfaces which are important to surface function. However the areal motif analysis cannot be directly applied to freeform surfaces, usually described by the triangular mesh data structure. To overcome this obstacle, a feasible strategy is proposed to extend the motif method. Morphological operations are employed to separate the “texture” and “form” surface. The watershed segmentation is then applied to the “texture” height surface in which the connection of each vertex is defined by the triangular mesh. The tiny motif due to the over-segmentation is combined by pruning the peaks and pits in the Pfaltz graph

Regional Differences and Influencing Factors of Psychological Integration of Urban Floating Population in China

Based on the dynamic monitoring survey data of floating population in 2017, this paper analyzes the regional differences and influencing factors of psychological integration of urban floating population in China. The results show that: (1) The psychological integration of floating population is at a high level; (2) there are significant regional differences in the psychological integration of floating population. The psychological integration of Southeast coastal and a few Western cities is lower than the national average level, and the psychological integration of Northeast, Shandong, Sichuan and Chongqing is higher than the national average level; (3) the psychological integration of floating population has spatial agglomeration effect. In addition to Sichuan and Chongqing, hot spots are concentrated in the North and cold spots are concentrated in the Southeast. (4) Factors like owning real estate, employer status and high education level accelerate the psychological integration of floating population; the increase of income is not conducive to psychological integration, which is related to the sense of relative deprivation; participation in the “new rural cooperative medical system” has a restrictive effect on the psychological integration of floating population; The equalization of temporary residence permit/residence permit and basic public services is an important way to realize psychological integration. The rapid development of urban economy is conducive to the psychological integration of floating population. Inter provincial mobility has an inhibitory effect, and the effects of economic development level, family size and local residence time are not significant