A new nonlocal nonlinear diffusion equation for image denoising and data analysis

In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically detected parameter related to the local bounded variation and the local oscillating pattern of the noisy input signal. We provide a mathematical analysis of the existence of the solution of our nonlinear and nonlocal diffusion equation in the two dimensional case (images processing). Finally, we propose a numerical scheme with some numerical experiments which demonstrate the effectiveness of the new method

The determination of velocity fluctuations in shear flows by means of PTV

The present study considers the effects of some parameters in image acquisition and analysis procedures in connection with the use of the Particle Tracking Velocimetry (PTV) technique. The interest is focused towards flow fields with large velocity gradients as shear flows; in the paper, velocity measurements by PTV are performed in a turbulent channel flow upstream and downstream of a backward facing step at low Reynolds numbers. This is a flow field largely investigated in the past with available numerical and experimental to make comparison with. Among the possible parameters to be chosen in particle image acquisition and analysis, the following are considered - the concentration of seeding particles in the imaged region; - the spatial resolution of the image acquisition system; - the parameters used in the image analysis algorithm

A frame for a computer aided inspection planning system

Coordinate Measuring Machine (CMM) inspection planning is an activity performed by well-trained operators, but different measurement techniques, using the same data analysis algorithms yield in different measurement results. This is a well-recognized source of uncertainty in coordinate measurement. A CMM, provided with an automatic inspection planning (CAIP) system, permits to implement more accurate and efficient operating procedures and to fit higher quality assurance standards and tighter production timings. In this paper we present a frame of a CAIP system, able to deal with almost all the decisional stages of CMM inspection. Moreover, original approaches have been developed and presented in inspection feature selection, part set -up, probe configuration, and path planning

Impact of the Threshold on the Performance Verification of Computerized Tomography Scanners

Computerized tomography is an emerging technology for geometric inspection. Its capability of easily scanning internal and undercut surfaces, as well as micro components, makes it the only possible choice for several measurement tasks. However, traceability is still a relevant issue, due to the lack of well-established procedures for testing CT scanners: several international standards about the application of computerized tomography for geometric inspection are still under development. In this work, we will propose the results we obtained in the application of the VDI/VDE 2617 part 13 standard on two computerized tomography scanners. In particular, we will show the impact of the choice of the threshold on the results of the test

Optimal inspection strategy planning for geometric tolerance verification

"Two features characterize a good inspection system: it is accurate, and compared to the manufacturing cost, it is not expensive. Unfortunately, few measuring systems posses both these characteristics, i.e. low uncertainty comes with a cost. But also high uncertainty comes with a cost, because measuring systems with high uncertainty tend to generate more inspection errors, which come with a cost. In the case of geometric inspection, the geometric deviation is evaluated from a cloud of points sampled on a part. Therefore, not only the measuring device has to be selected, but also the sampling strategy has to be planned, i.e. the sampling point cloud size and where points should be located on the feature to inspect have to be decided. When the measuring device is already available, as it often happens in geometric measurement, where most instruments are flexible, an unwise strategy planning can be the largest uncertainty contributor. In this work, a model for the evaluation of the overall inspection cost is proposed. The optimization of the model can lead to an optimal inspection strategy in economic sense. However, the model itself is based on uncertainty evaluation, in order to assess the impact of measurement error on inspection cost. Therefore, two methodologies for evaluating the uncertainty will be proposed. These methodologies will be focused on the evaluation of the contribution of the sampling strategy to the uncertainty. Finally, few case studies dealing with the inspection planning for a Coordinate Measuring Machine will be proposed

Effect of filters on segmentation-free geometric verification by X-ray CT

A method has been proposed to verify geometric tolerances by X-ray computed tomography (XCT) without the need for image segmentation The method is based on the direct comparison of a part XCT image to a volumetric representation of its geometric tolerance. In previous works the method was directly applied to raw images. However, filters are commonly applied to XCT images. Usually, they mitigate noise or enhance details. In this work, we study if the segmentation-free verification benefits from the application of filters to XCT images. Standard filters a considered, e.g. Gaussian and non-local means

Robust Design of a Fixture Configuration in the Presence of form Deviations

During machining, the tool path is defined with respect to the workpiece reference frame. The workpiece's boundary surfaces have form deviations, and the geometry and the position of the locators are imperfect. The resulting misalignment produces geometrical errors in the features machined on the workpiece. The main purpose of this work is to investigate how the geometric errors of a machined surface are related to the main sources of the locator errors and to the form deviations of the workpiece. A mathematical framework is presented for an analysis of the relationship among the manufacturing errors, the part form deviations, and the locator errors

Performance improvement for optimization of the non-linear geometric fitting problem in manufacturing metrology

Product quality is a main concern today in manufacturing; it drives competition between companies. To ensure high quality, a dimensional inspection to verify the geometric properties of a product must be carried out. High-speed non-contact scanners help with this task, by both speeding up acquisition speed and increasing accuracy through a more complete description of the surface. The algorithms for the management of the measurement data play a critical role in ensuring both the measurement accuracy and speed of the device. One of the most fundamental parts of the algorithm is the procedure for fitting the substitute geometry to a cloud of points. This article addresses this challenge. Three relevant geometries are selected as case studies: a non-linear least-squares fitting of a circle, sphere and cylinder. These geometries are chosen in consideration of their common use in practice; for example the sphere is often adopted as a reference artifact for performance verification of a coordinate measuring machine (CMM) and a cylinder is the most relevant geometry for a pin-hole relation as an assembly feature to construct a complete functioning product. In this article, an improvement of the initial point guess for the Levenberg–Marquardt (LM) algorithm by employing a chaos optimization (CO) method is proposed. This causes a performance improvement in the optimization of a non-linear function fitting the three geometries. The results show that, with this combination, a higher quality of fitting results a smaller norm of the residuals can be obtained while preserving the computational cost. Fitting an 'incomplete-point-cloud', which is a situation where the point cloud does not cover a complete feature e.g. from half of the total part surface, is also investigated. Finally, a case study of fitting a hemisphere is presented

Comparison of chaos optimization functions for performance improvement of fitting of non-linear geometries

Fitting algorithms play an important role in the whole measuring cycle in order to derive a measurement result. They involve associating substitute geometry to a point cloud obtained by an instrument. This situation is more difficult in the case of non-linear geometry fitting since iterative method should be used. This article addresses this problem. Three geometries are selected as relevant case studies: circle, sphere and cylinder. This selection is based on their frequent use in real applications; for example, cylinder is a relevant geometry of an assembly feature such as pin-hole relationship, and spherical geometry is often found as reference geometry in high precision artifacts and mechanisms. In this article, the use of Chaos optimization (CO) to improve the initial solution to feed the iterative Levenberg–Marquardt (LM) algorithm to fit non-linear geometries is considered. A previous paper has shown the performance of this combination in improving the fitting of both complete and incomplete geometries. This article focuses on the comparison of the efficiency of different one-dimensional maps of CO. This study shows that, in general, logistic-map function provides the best solution compared to other types of one-dimensional functions. Finally, case studies on hemispheres and industrial cylinders fitting are presented