Application of the morphological alpha shape method to the extraction of topographical features from engineering surfaces

In contrast to the mean-line based filters, morphological filters are function oriented and more suitable for the functional prediction of component performance. This paper presents a novel morphological method based on the alpha shape for the extraction of topographical features from engineering surfaces. Compared to the traditional implementation of morphological filters, the alpha shape method is more efficient in performance for large structuring element. The resulting envelope follows the form of the surface all over such that the distortions caused the end effects are avoided. A series of measured surfaces from the automotive cylinder liner and the bioengineering femoral heads are analyzed using the morphological alpha shape method. The topographical features are successfully extracted, enabling further analysis to the components

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

Identifying and Characterizing Micro-machining Signatures on Freeform Surfaces Using Morphological Methods

Freeform surfaces are replacing traditional surfaces and have significantly reduced volume and weight and highly improved performance in modern complex optic systems, bio-systems and other disciplines [1]. These high-precision freeform components are enabled by state-of-the-art micro-machining technologies, compromising mechanical methods (diamond turning and polishing etc.), physical methods (laser beam and ion beam machining), and chemical methods (lithography, electro-chemical machining etc.). However, a fundamental pre-requisite to achieve the potential growth to these high-added value freeform components is to measure and characterize these components with the required accuracy such that their manufacturing quality can be controlled. The surface topography is a fingerprint of all process stages of the manufacturing process. Thus identifying and evaluating these topographical features on freeform surfaces left by production techniques are critically important in that they could present an indication of the manufacturing quality and offer feedback to the process control

Discrete algorithms for morphological filters in geometrical metrology

In geometrical metrology, morphological filters are useful tools for the surface texture analysis and functional prediction. Although they are generally accepted and regarded as the complement to mean-line based filters, they are not universally adopted in practice due to a number of fatal limitations in their implementations —they are restricted to planar surfaces, uniform sampled surfaces, time-consuming and suffered from end distortions and limited sizes of structuring elements. A novel morphological method is proposed based on the alpha shape with the advantages over traditional methods that it enables arbitrary large ball radii, and applies to freeform surfaces and non-uniform sampled surfaces. A practical algorithm is developed based on the theoretical link between the alpha hull and morphological envelopes. The performance bottleneck due to the costly 3D Delaunay triangulation is solved by the divide-and-conquer optimization. Aiming to overcome the deficits of the alpha shape method that the structuring element has to be circular and the computation relies on the Delaunay triangulation, a set of definitions, propositions and comments for searching contact points is proposed and mathematically proved based on alpha shape theory, followed by the construction of a recursive algorithm. The algorithm could precisely capture contact points without performing the Delaunay triangulation. By correlating the convex hull and morphological envelopes, the Graham scan algorithm, originally developed for the convex hull, is modified to compute morphological profile envelopes with an excellent performance achieved. The three novel methods along with the two traditional methods are compared and analyzed to evaluate their advantages and disadvantages. The end effects of morphological filtration on open surfaces are discussed and four end effect correction methods are explored. Case studies are presented to demonstrate the feasibility and capabilities of using the proposed discrete algorithms

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

DEVELOPMENT AND FUNCTIONS OF C-LOW-THRESHOLD MECHANORECEPTORS

Somatosensory neurons are essential for detecting diverse environmental stimuli, thus critical for survival of mammals. In order to achieve sensory modality specificity, many somatosensory subtypes emerge with various receptor and ion channel expression, as well as terminal morphologies. How the somatosensory system achieves such a high variety of neuronal subtypes is unknown. In this thesis, I used a newly discovered subtype, VGLUT3-expressing unmyelinated low-threshold mechanoreceptors (C-LTMRs), as a model to try to answer this question. C-LTMRs have been proposed to play a role in pleasant touch in humans or pain in mice. Previously, our lab has identified the Runt domain transcriptional factor Runx1 to be pivotal for the development of a cohort of sensory neurons such as pain related nociceptors, thermal receptors, as well as itch related pruriceptors. Here I found that Runx1 is also required to establish all known features associated with C-LTMRs. In search of the mechanism of how Runx1 controls C-LTMR development, I found that the zinc finger protein Zfp521 is predominantly expressed in C-LTMRs and its expression is Runx1 dependent. By generating and analyzing Zfp521 conditional knock out animals, I found Zfp521 is required for part of C-LTMR molecular identities and nerve terminal morphologies. Our studies suggest that Runx1 acts through Zfp521-dependent and Zfp521-independent pathways to specify C-LTMR identities. To study C-LTMR functions, we performed a series of behavioral analysis and found the loss of VGLUT3 and mechanosensitivities in C-LTMRs does not markedly affect acute or chronic mechanical pain measured from the hind paws, which argues against the proposed role of VGLUT3 in C-LTMRs in mediating mechanical pain in mice. In the future, we will continue to use our mutant mice to study physiological functions of C-LTMRs

Algorithms for morphological profile filters and their comparison

Morphological filters, regarded as the complement of mean-line based filters, are useful in the analysis of surface texture and the prediction of functional performance. The paper first recalls two existing algorithms, the naive algorithm and the motif combination algorithm, originally developed for the traditional envelope filter. With minor extension, they could be used to compute morphological filters. A recent novel approach based on the relationship between the alpha shape and morphological closing and opening operations is presented as well. Afterwards two novel algorithms are developed. By correlating the convex hull and morphological operations, the Graham scan algorithm, original developed for the convex hull is modified to compute the morphological envelopes. The alpha shape method depending on the Delaunay triangulation is costly and redundant for the computation for the alpha shape for a given radius. A recursive algorithm is proposed to solve this problem. A series of observations are presented for searching the contact points. Based on the proposed observations, the algorithm partitions the profile data into small segments and searches the contact points in a recursive manner. The paper proceeds to compare the five distinct algorithms in five aspects: algorithm verification, algorithm analysis, performance evaluation, end effects correction, and areal extension. By looking into these aspects, the merits and shortcomings of these algorithms are evaluated and compared

Effect of Tan-Sheep Rotational Grazing on Soil Erosion in Typical Steppe on the Loess Plateau of China

The effect of stocking rate on soil erosion has been at the forefront of water and soil conservation studies in recent years. By observing soil erosion caused by rainfall in typical steppe on the Loess Plateau in China, this research aimed to further explore the effect of stocking rate on soil erosion. The results showed that all the concerned indicators of soil erosion (runoff, runoff coefficient, soil loss, soil organic carbon loss, and soil total nitrogen and total phosphorus loss) had a significant (P \u3c 0.001) positive linear correlation with stocking rate alone, and precipitation alone, while the indicators of runoff and soil loss had a significant (P \u3c 0.01) negative linear correlation with typicalsteppe biomass (aboveground biomass, litter mass, and belowground biomass). Both stocking rate and precipitation had large significant (P \u3c 0.01) effects on soil erosion via changes in aboveground biomass, litter mass, and soil organic carbon