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

Cathepsins and Parkinson’s disease: insights from Mendelian randomization analyses

BackgroundParkinson’s disease (PD), the second most prevalent neurodegenerative condition, has a multifaceted etiology. Cathepsin-cysteine proteases situated within lysosomes participate in a range of physiological and pathological processes, including the degradation of harmful proteins. Prior research has pointed towards a potential link between cathepsins and PD; however, the precise causal relationship between the cathepsin family and PD remains unclear.MethodsThis study employed univariate and multivariate Mendelian randomization (MR) analyses to explore the causal relationship between the nine cathepsins and Parkinson’s disease (PD) risk. For the primary analysis, genome-wide association study (GWAS) summary statistics for the plasma levels of the nine cathepsins and PD was obtained from the INTERVAL study and the International Parkinson’s Disease Genomics Consortium. GWAS for PD replication analysis were obtained from the FinnGen consortium, and a meta-analysis was performed for the primary and replication analyses to evaluate the association between genetically predicted cathepsin plasma levels and PD risk. After identifying significant MR estimates, genetic co-localization analyses were conducted to determine whether shared or distinct causal variants influenced both cathepsins and PD.ResultsElevated cathepsin B levels were associated with a decreased risk of PD in univariate MR analysis (odds ratio [OR] = 0.890, 95% confidence interval [CI]: 0.831–0.954, pFDR = 0.009). However, there was no indication that PD affected cathepsin B levels (OR = 0.965, 95% CI: 0.858–1.087, p = 0.852). In addition, after adjusting for the remaining cathepsins, cathepsin B levels independently and significantly contributed to the reduced risk of PD in multivariate MR analysis (OR = 0.887, 95% CI: 0.823–0.957, p = 0.002). The results of the replication MR analysis with the FinnGen GWAS for PD (OR = 0.921, 95% CI: 0.860–0.987, p = 0.020) and meta-analysis (OR = 0.905, 95% CI: 0.862–0.951, p < 0.001) were consistent with those of the primary analysis. Colocalization analysis did not provide any evidence of a shared causal variant between cathepsins and PD (PP.H4.abf = 0.005).ConclusionThis genetic investigation supports the hypothesis that cathepsin B exerts a protective effect against PD. The quantification of cathepsin B levels could potentially serve as a predictive biomarker for susceptibility to PD, providing new insights into the pathomechanisms of the disease and possible interventions