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During the process of five-axis free-form milling, tool orientation and surface curvature of the workpiece have significant effects on tool wear. Five-axis milling experiments are carried out on 17-4PH stainless steel using a carbide ball end mill. The influence of tool orientation on the amount of wear, cutting force, and chip morphology of the ball end cutter was investigated. The results show that tool wear is slighter at a tool inclination angle of approximately 15°, reducing tool wear by up to 29.55% compared with other angles. The inclination angle also has great effects on the milling force and torque signals, a suitable tool inclination angle makes the milling force and torque signals smooth, and the standard deviation is only 0.94 N and 0.017 N·m, respectively. In addition, the chips can reflect the stability of the machining process to some extent. On this basis, different workpiece surfaces were selected to investigate the effect of workpiece surface characteristics on tool wear. The results show that more severe tool wear and higher milling force signals on curved surfaces occurred with smaller radii of curvature. An appropriate tool orientation in relation to the curvature of the workpiece surface can significantly reduce tool wear; concave surfaces are suitable for machining with small angle of inclination, e.g., 5° ~ 10°, whereas convex surfaces are suitable for machining with larger angle of inclination, e.g., 20° ~ 25°. [ABSTRACT FROM AUTHOR]

Multi-view stereo (MVS) can fulfill dense three-dimensional reconstruction from a collection of multi-view images. Although deep learning-based MVS has significantly enhanced the reconstruction performance, the reconstruction accuracy and completeness still require improvements to meet the need of real applications of three-dimensional content generation. So, a new MVS method, the curvature-guided multi-view stereo with transformers, is presented. By exploring inter-view relationships and measuring the size of the receptive field and feature information on the image surface using the surface curvature, the proposed method adapts to various candidate scales of curvatures to extract more detailed features adaptively for precise cost computation. Furthermore, a transformer-based feature-matching network is proposed to identify inter-view similarity better and enhance feature-matching accuracy. Additionally, a similarity measurement module based on feature matching integrates curvature and inter-view similarity measurement tightly to further improve reconstruction accuracy. Experiments on the DTU dataset and Tanks and Temples dataset validate the proposed method. [ABSTRACT FROM AUTHOR]

A model is proposed for the formation of the workpiece–tool contact zone in belt grinding of blades for gas turbine engines on CNC machine tools. The model takes account of fluctuation of the forces applied to the contact element; and the complex shape of the contact element and the workpiece. The Femlab modeling software employed permits assessment of the contact area and conclusions regarding the distribution of the belt pressure over the workpiece surface. [ABSTRACT FROM AUTHOR]

This paper explores the superior performance of quaternion multi-layer perceptron (QMLP) neural networks over real-valued multi-layer perceptron (MLP) neural networks, a phenomenon that has been empirically observed but not thoroughly investigated. The study utilizes loss surface visualization and projection techniques to examine quaternion-based optimization loss surfaces for the first time. The primary contribution of this research is the statistical evidence that QMLP models yield smoother loss surfaces than real-valued neural networks, which are measured and compared using a robust quantitative measure of loss surface "goodness" based on estimates of surface curvature. Extensive computational testing validates the effectiveness of these surface curvature estimates. The paper presents a comprehensive comparison of the average surface curvature of a tuned QMLP model and a tuned real-valued MLP model on both a regression task and a classification task. The results provide strong support for the improved optimization performance observed in QMLPs across various problem domains. [ABSTRACT FROM AUTHOR]

Polishing path optimization plays a crucial role in achieving high-quality and uniform surface polishing of free-form surfaces. To address the issue of uncontrollable ripple errors caused by uneven material removal in traditional contact polishing, this paper proposes an adaptive polishing path optimization method for uniform polishing of free-form surfaces based on footprint evolution. The presented approach considers the influence of curvature on footprint evolution and seeks to dynamically optimize the spacing between adjacent paths. This optimization ensures suitable overlap between neighboring footprints, ultimately leading to the achievement of uniform depth removal. Through modeling simulations and experimental comparisons involving different contact curvatures, it has been conclusively established that surface curvature plays a pivotal role in footprint evolution. Additionally, surface polishing experiments yielded results indicating a reduction in surface waviness within the central polishing area, decreasing from a root-mean-square value of 5.1766 to 4.1448 nm. These outcomes preliminary demonstrate the effectiveness of the proposed method. This study presents an efficient curvature adaptive path planning approach based on footprint evolution, offering new insights into achieving uniform polishing and suppressing waviness errors on free-form surfaces. [ABSTRACT FROM AUTHOR]

This paper aims to explore the influence of surface curvature distribution on the mechanical properties of lattice structures. In this study, a series of typical structure types were designed to obtain lattice structures with different surface Gaussian curvatures, including BCC (body center cubic) configuration, cross-cube configuration, and diamond lattice structure. Then, the above-mentioned porous structural sample was formed by SLM (selective laser melting), and the relevant mechanical properties were obtained by simulation and experiment. In addition, a characteristic method to describe the surface curvature of discrete triangular plaques is proposed and used to calculate the curvature distribution of the designed lattice structure. The results show that the lattice structure with concentrated Gaussian curvature distribution on the surface has good mechanical properties. Especially, for the cross-cube structure, the elastic modulus of the traditional configuration lattice structure increases by 79%, and the elastic modulus of the stretched structure increases by 70% when the volume fraction increased from 10 to 15%. Meanwhile, the elastic modulus for the traditional structure and the stretched structure increases by 41% and 14%, respectively, when the volume fraction of the structure increases from 15 to 20%. It is noted that the influence of surface curvature distribution on mechanical properties is slightly inferior to the volume fraction, which provides a new idea for the quantitative evaluation and design of porous structural properties. In addition, the BCC structure with concentrated curvature distribution provides a new scheme for the protection device after the stress climb stage after the elastic stage. Furthermore, the influence of surface curvature on the mechanical properties of lattice structures described in this paper will provide new inspiration for lattice structures in the fields of biocompatibility and heat exchange. [ABSTRACT FROM AUTHOR]

In this paper, the grand canonical Monte Carlo (GCMC) method was used to explore the effects of four pore structures (disordered pore, wedge pore, carbon nanotube, and slit pore structures) and surface curvature of activated carbon on the adsorption and separation of CO2/N2. On the whole, carbon nanotubes have the greatest selectivity for CO2, followed by disordered pores, wedge pores, and slit pores. The effect of pore structure on the interaction energy of gas molecules is similar to that of selectivity, in which the fluid–solid potential energy between adsorbates and adsorbents plays an important role. Due to the different affinity between adsorbate molecules and activated carbon, CO2 with high affinity is more sensitive to the change of pore size. Therefore, under high pressure, the density of CO2 in the slit pore is greater than that in the wedge pore. However, N2 with poor affinity is limited by the surface area, resulting in the density of it in the wedge pore is always higher than that in the slit pore. Although the existence of non-six membered corannulene rings in activated carbon can't always cause the increase of specific surface area, the surface curvature of activated carbon caused by it can increase strong energetically adsorption sites. Hence, the surface curvature plays a positive role in the adsorption density, interaction energy, and CO2 selectivity. The discovery of CO2/N2 adsorption and separation at the molecular level is expected to provide valuable insights. [ABSTRACT FROM AUTHOR]

In this paper, the grand canonical Monte Carlo (GCMC) method was used to explore the effects of four pore structures (disordered pore, wedge pore, carbon nanotube, and slit pore structures) and surface curvature of activated carbon on the adsorption and separation of CO2/N2. On the whole, carbon nanotubes have the greatest selectivity for CO2, followed by disordered pores, wedge pores, and slit pores. The effect of pore structure on the interaction energy of gas molecules is similar to that of selectivity, in which the fluid–solid potential energy between adsorbates and adsorbents plays an important role. Due to the different affinity between adsorbate molecules and activated carbon, CO2 with high affinity is more sensitive to the change of pore size. Therefore, under high pressure, the density of CO2 in the slit pore is greater than that in the wedge pore. However, N2 with poor affinity is limited by the surface area, resulting in the density of it in the wedge pore is always higher than that in the slit pore. Although the existence of non-six membered corannulene rings in activated carbon can't always cause the increase of specific surface area, the surface curvature of activated carbon caused by it can increase strong energetically adsorption sites. Hence, the surface curvature plays a positive role in the adsorption density, interaction energy, and CO2 selectivity. The discovery of CO2/N2 adsorption and separation at the molecular level is expected to provide valuable insights. [ABSTRACT FROM AUTHOR]

This paper reports the results from a direct numerical simulation of an initially turbulent boundary layer passing over a wall-mounted "speed bump" geometry. The speed bump, represented in the form of a Gaussian distribution profile, generates a favorable pressure gradient region over the upstream half of the geometry, followed by an adverse pressure gradient over the downstream half. The boundary layer approaching the bump undergoes strong acceleration in the favorable pressure gradient region before experiencing incipient or very weak separation within the adverse pressure gradient region. These types of flows have proved to be particularly challenging to predict using lower-fidelity simulation tools based on various turbulence modeling approaches and warrant the use of the highest fidelity simulation techniques. The present direct numerical simulation is performed using a flow solver developed exclusively for graphics processing units. Simulation results are utilized to examine the key phenomena present in the flowfield, such as relaminarization/stabilization in the strong acceleration region succeeded by retransition to turbulence near the onset of adverse pressure gradient, incipient/weak separation and development of internal layers, where the sense of streamwise pressure gradient changes at the foot, apex and tail of the bump. [ABSTRACT FROM AUTHOR]

Conformal Geometric Algebra (CGA) provides a unified representation of both geometric primitives and conformal transformations, and as such holds significant promise in the field of computer graphics. In this paper we implement a simple ray tracer in CGA with a Blinn–Phong lighting model, before putting it to use to examine ray intersections with surfaces generated from the direct interpolation of geometric primitives. General surfaces formed from these interpolations are rendered using analytic normals. In addition, special cases of point-pair interpolation, which might find use in graphics applications, are described and rendered. A closed form expression is found for the derivative of the square root of a scalar plus 4-vector element with respect to a scalar parameter. This square root derivative is used to construct an expression for the derivative of a pure-grade multivector projected to the blade manifold. The blade manifold projection provides an analytical method for finding the normal line to the interpolated surfaces and its use is shown in lighting calculations for the ray tracer and in generating vertex normals for exporting the evolved surfaces as polygonal meshes. [ABSTRACT FROM AUTHOR]

A mathematical model for synthesis of the initial tooth contour of a gear in terms of the reduced curvature of the working surfaces is proposed. The form of the initial tooth contour corresponding to high performance is determined for machining equipment. [ABSTRACT FROM AUTHOR]

Matching, clustering, and retrieving 3D CAD models of mechanical components based on their shape are useful for many CAD/CAM applications such as design reuse, variant process planning and group technology. Surfaces are the prominent elements of the B-Rep (Boundary Representation) CAD model, but the current methods of similarity assessment are not centered on the surfaces and lack an accurate description of their geometric features. In order to solve the problem of retrieval and clustering of B-Rep models more efficiently, the concept of "most crucial surface" is proposed and its corresponding characteristics are studied in detail. The contribution of our approach is that surfaces are the major shape determinants of the B-Rep model, and the distribution of Carosati curvatures is the optimum shape features of surfaces. First, the surface elements are extracted from the STEP (Standard for Exchange of Product Model) files of the B-rep models, and the distribution of minimum, Gauss and Carosati surface curvatures are converted into the shape feature space by the wavelet transform, the Fourier transform, and the grouping calculation. Thus we characterize the B-Rep model as a histogram with surfaces as bins, and then compare and cluster the B-Rep models by the bipartite matching algorithm or the earth mover's distance. The surface-based methods are evaluated with the four effectiveness indices in the clustering experiment of the NDR (National Design Reservoir) data, and the results indicated that the grouping method for the surface Carosati curvatures has a highly competent matching and clustering performance. [ABSTRACT FROM AUTHOR]

Size-controlled synthesis of two-dimensional (2D) catalysts with low stacking numbers and small nanoflake lengths is crucial for promoting the catalytic performance in diverse heterogeneous catalysis. Herein, we report a facile and general "surface curvature-confined synthesis" strategy to modulate the slab lengths and stacking numbers of 2D transition metal sulfides by controlling the strain induced by different surface curvature of supports. An efficient NiMo sulfide with shorter slab length (average 3.71 nm), less stacking number (1–2 layers) and more edge active sites is synthesized onto ZSM-5 zeolites with the average size of 100 nm, which shows superior kHDS value of dibenzothiophene (14.05 × 10−7 mol/(g·s)), enhanced stability up to 80 h, and high direct desulfurization selectivity (> 95%). This design concept is also proved to be generally applicable to modulate the slab lengths and stacking numbers of other 2D catalysts such as MoS2 and WS2 nanoflakes, which shows great potentials for developing more ultrasmall 2D catalysts with controlled sizes and excellent catalytic activities. [ABSTRACT FROM AUTHOR]

The energy approach to the study of a hydroelastic system consisting of an elastic blood vessel, viscous fluid flow, and an aneurysm has been developed to evaluate the various energy components of the system: viscous flow dissipation energy and the stretching and bending energies of the aneurysm wall. To calculate the total energy of the system, we have developed a computing complex including commercial and free software and self-developed modules. The performance of the complex has been tested on model geometric configurations and configurations corresponding to blood vessels with cerebral aneurysms of real patients and reconstructed by angiographic images. The calculated values of the Willmore functional characterizing the shell bending energy are consistent with theoretical data. [ABSTRACT FROM AUTHOR]

In the milling process of automobile panel mold of hardened steel, the characteristic of free-form surface is one of the dominant factors for surface topography. In this paper, the trajectory of cutting edge is firstly modeled to analyze the residual height of the free-form surface in ball-end milling of hardened steel. Furthermore, the non-uniform rational B-splines (NURBS) surface reconstruction is utilized to generate the surface topography. Subsequently, the influences of surface curvature, lead angle, milling vibrations on the machined surface topography, and residual height are investigated, respectively. Finally, the accuracy of the surface topography and the roughness prediction model are validated by the milling experiments of free-form surface, where two-dimensional contour maps could be obtained. The simulation and experimental results demonstrate that the machined surface topography of hardened steel is fitted by means of NURBS surface reconstruction. In that manner, the effects of surface characteristics on the machined surface topography can be accurately predicted. [ABSTRACT FROM AUTHOR]

Vascular morphology characterization is useful for disease diagnosis, risk stratification, treatment planning, and prediction of treatment durability. To quantify the dynamic surface geometry of tubular-shaped anatomic structures, we propose a simple, rigorous Lagrangian cylindrical coordinate system to monitor well-defined surface points. Specifically, the proposed system enables quantification of surface curvature and cross-sectional eccentricity. Using idealized software phantom examples, we validate the method's ability to accurately quantify longitudinal and circumferential surface curvature, as well as eccentricity and orientation of eccentricity. We then apply the method to several medical imaging data sets of human vascular structures to exemplify the utility of this coordinate system for analyzing morphology and dynamic geometric changes in blood vessels throughout the body. Graphical abstract Pointwise longitudinal curvature of a thoracic aortic endograft surface for systole and diastole, with their absolute difference. [ABSTRACT FROM AUTHOR]

Tool orientation has an important effect on the surface quality of a free-form surface during ball end milling process, and the selection of tool orientation is important to ensure the surface quality. In this work, a series of milling experiments were performed by using a carbide ball end mill on a workpiece of TC17 titanium alloy. The purpose of this study was to determine the tool orientation producing optimal surface integrity. The results showed that the surface roughness in both directions was better when the rotational angle was within the range of 0°~90° and with a constant inclination angle. In addition, inclination angle had little effect on the roughness in the feed direction, whereas a much larger or smaller angle led to greater roughness in the step direction. The tool orientation strongly affected the surface morphology. Compressive residual stress was detected on all machined surfaces. The maximum surface residual stress was obtained when the rotational angle was 90°, and the surface residual stress decreased as the inclination angle increased. On this basis, four curved surface models with different curvatures were established according to the features of a blade, and the effects of inclination angle and cutter path orientation on surface integrity were studied. The results indicated that the surface roughness produced with an upward orientation varied more than that produced with a downward orientation for a steep curved surface; the value of the roughness was small for a horizontal orientation and when the machine surface was very smooth. The machined surface for a flat curved surface was smoother, and there were no obvious differences in surface morphology between the two cutter path orientations. For steep curved surfaces, the cutter path orientation had no obvious influence on the residual stress, and a greater value was obtained when the surface was much steeper. For flat curved surfaces, the residual stress had no obvious variation resulting from small changes of the inclination angle. [ABSTRACT FROM AUTHOR]

In this paper, a predictive model of milling stability, which considers the surface curvature and the lead angle of the milling cutter, is proposed for milling of the panel die with sculptured surface. Firstly, influences of the radius of curvature and lead angle of milling cutter on uncut chip thickness are analyzed by exploring the curvature characteristics of sculptured surface. Subsequently, influence of the curvature characteristics of sculptured surface on chatter stability lobes in milling process is investigated by utilizing the full-discretization method. This analysis implies that the milling stability decreases with the increase in the radius of the die surface's curvature; the milling stability decreases with the increase in lead angle. The experimental results demonstrate that the prediction of chatter stability lobes could match well with the measured results on the change trend, where the maximum relative percent error is less than 11.1 % in stable milling. It is further validated that this method can effectively predict the chatter stability lobes of the domain in ball end milling of sculptured surface of die. [ABSTRACT FROM AUTHOR]

The curvature of surface topography is quantified in this study using a newly developed directional blanket covering curvature (DBCC) method. The novel method addresses a long-standing problem of a measurement of a local surface curvature at individual scales and directions. The curvature data are obtained using the first and second derivations of the quadratic polynomial fitted to the local surface profile extracted from the surface height image data at individual scale and direction. The range of scales is set between an instrument spatial resolution and 1/10 of the image shortest size. Using the surface curvature data, three parameters, i.e. curvature, peak and valley dimensions, are calculated as the slopes of lines fitted to data point subsets of log-log plots of surface areas (differences between dilated and eroded surface curvature matrices) against scales of calculation. The dimensions quantify directional changes in the overall curvature and the curvature of peaks and valleys at individual scales. The scale corresponds to the centre of the subset. A flat surface criterion based on the surface areas was also proposed. Using the criterion, a flat surface was identified in computer images of dome, corrugated plate and fractal surface. The DBCC method was applied to computer-generated fractal surfaces with increasing curvature complexity, sine waves with decreasing curvature at single scale and microscope images of isotropic (sandblasted) and anisotropic (ground) surfaces of titanium plates. Results showed that the method is accurate in the measurement of surface curvature and the detection of minute changes occurring in the curvature of real surfaces over a wide range of scales. [ABSTRACT FROM AUTHOR]

Complexity of sculptured surfaces has a great influence on multi-axis computer numerical control (CNC) machining performances such as processing efficiency, surface quality, and energy consumption. A term called surface machining complexity (SMC) is first presented to describe the complexity level of surface geometrical shape features, and its influence on CNC machining performance. Shape features of sculptured surfaces are classified into seven categories based on surface curvature. An innovative method for quantifying SMC using surface subdivision is proposed. Firstly, representation of sculptured surfaces is introduced. Then, three processes of surface subdivision are presented, which are surface discretization based on iso-parameter line sampling, rough partitioning based on surface shape categories, and region grouping based on two criteria. After that calculation, formulas of SMC including formulas of local SMC and global SMC are developed. The proposed formulas utilize three correction factors to describe the influences of surface size, cutter diameter, grouping order, and mode of different surface shape categories. Finally, the proposed method is applied to calculate SMC for a typical sculptured surface and multi-axis CNC machining experiments to demonstrate the ability of our method, which can form a foundation for further research. [ABSTRACT FROM AUTHOR]

Recovering three-dimensional (3D) points from image correspondences is an important and fundamental task in computer vision. Traditionally, the task is completed by triangulation whose accuracy has its limitation in some applications. In this paper, we present a framework that incorporates surface characteristics such as Gaussian and mean curvatures into 3D point reconstruction to enhance the reconstruction accuracy. A Gaussian and mean curvature estimation scheme suitable to the proposed framework is also introduced in this paper. Based on this estimation scheme and the proposed framework, the 3D point recovery from image correspondences is formulated as an optimization problem with the surface curvatures modeled as soft constraints. To analyze the performance of proposed 3D reconstruction approach, we generated some synthetic data, including the points on the surfaces of a plane, a cylinder and a sphere, to test the approach. The experimental results demonstrated that the proposed framework can indeed improve the accuracy of 3D point reconstruction. Some real-image data were also tested and the results also confirm this point. [ABSTRACT FROM AUTHOR]

The possibility of creating a vacuum in a membrane and maintaining the vacuum for many days during the osmotic membrane distillation (OMD) process has been experimentally shown. The limiting parameters of OMD with a vacuum have been evaluated as functions of external pressure, temperature, and temperature differential across the membrane. Equations and plots for calculation of the osmotic pressure and the temperature difference that stops the OMD process are presented. [ABSTRACT FROM AUTHOR]

An abdominal aortic aneurysm (AAA) carries one of the highest mortality rates among vascular diseases when it ruptures. To predict the role of surface curvature in rupture risk assessment, a discriminatory analysis of aneurysm geometry characterization was conducted. Data was obtained from 205 patient-specific computed tomography image sets corresponding to three AAA population subgroups: patients under surveillance, those that underwent elective repair of the aneurysm, and those with an emergent repair. Each AAA was reconstructed and their surface curvatures estimated using the biquintic Hermite finite element method. Local surface curvatures were processed into ten global curvature indices. Statistical analysis of the data revealed that the L2-norm of the Gaussian and Mean surface curvatures can be utilized as classifiers of the three AAA population subgroups. The application of statistical machine learning on the curvature features yielded 85.5% accuracy in classifying electively and emergent repaired AAAs, compared to a 68.9% accuracy obtained by using maximum aneurysm diameter alone. Such combination of non-invasive geometric quantification and statistical machine learning methods can be used in a clinical setting to assess the risk of rupture of aneurysms during regular patient follow-ups. [ABSTRACT FROM AUTHOR]

Steady-state free plane surface waves are investigated in the nonlinear formulation by means of the narrow streak method. The second-order differential equation derived can readily be integrated numerically. The first approximation of the equation is integrated. The next approximation leads to a nonlinear first-order differential equation which is traditional to the problem considered and whose coefficients have a simple physical meaning. [ABSTRACT FROM AUTHOR]

It is believed that left ventricular (LV) regional shape is indicative of LV regional function, and cardiac pathologies are often associated with regional alterations in ventricular shape. In this article, we present a set of procedures for evaluating regional LV surface shape from anatomically accurate models reconstructed from cardiac magnetic resonance (MR) images. LV surface curvatures are computed using local surface fitting method, which enables us to assess regional LV shape and its variation. Comparisons are made between normal and diseased hearts. It is illustrated that LV surface curvatures at different regions of the normal heart are higher than those of the diseased heart. Also, the normal heart experiences a larger change in regional curvedness during contraction than the diseased heart. It is believed that with a wide range of dataset being evaluated, this approach will provide a new and efficient way of quantifying LV regional function. [ABSTRACT FROM AUTHOR]

We investigated the propagation and transformation of laser beams and the formation of caustics in particular directions, including optical axes of crystals. We found a direct connection between the particular directions and the curvature of wave surfaces that is determined by the symmetry and optical properties of the crystals. We demonstrated that caustics in particular directions are characterized by a degree of the curvature degeneracy and are described by particular solutions of the corresponding nonlinear equations. [ABSTRACT FROM AUTHOR]

Quantification of heart valve leaflet deformation during the cardiac cycle is essential in understanding normal and pathological valvular function, as well as in the design of replacement heart valves. Due to the technical complexities involved, little work to date has been performed on dynamic valve leaflet motion. We have developed a novel experimental method utilizing a noncontacting structured laser-light projection technique to investigate dynamic leaflet motion. Using a simulated circulatory loop, a matrix of 150–200 laser light points were projected over the entire leaflet surface. To obtain unobstructed views of the leaflet surface, a stereo system of high-resolution boroscopes was used to track the light points at discrete temporal points during the cardiac cycle. The leaflet surface at each temporal point was reconstructed in three dimensions, and fit using our biquintic hermite finite element approach (Smith et al., Ann. Biomed. Eng. 26:598–611, 2001). To demonstrate our approach, we utilized a bovine pericardial bioprosthetic heart valve, which revealed regions of complex flexural deformation and substantially different shapes during the opening and closing phases. In conclusion, the current method has high spatial and temporal resolution and can reconstruct the entire surface of the cusp simultaneously. Because it is completely noncontacting, this approach is applicable to studies of fatigue and bioreactor technology for tissue engineered heart valves. © 2001 Biomedical Engineering Society. PAC01: 8719Hh, 8780-y, 4262Be, 8719St [ABSTRACT FROM AUTHOR]

The computational problems in segmenting range data into surface patches based on the invariant surface properties, i.e., mean curvature H and Gaussian curvature K, are investigated. The goal is to obtain reliable HK surface maps. Two commonly encountered problems are: firstly the noise effect in computing derivative estimates, and secondly the smoothing across discontinuities. Here, the segmentation is formulated as finding minimization solutions of energy functionals involving discontinuities. A two-stage approach to the goal is presented: stage (1) from a range image to curvature images and stage (2) from the curvature images to the HK maps. In both stages, solutions are found through minimizing energy functionals that measure the degree of bias of a solution from two constraints: the closeness of the solution to the data, and the smoothness of the solution controlled by predetermined discontinuities. Propagation across discontinuities is prevented during minimization, which preserves the original surface shapes. Experimental results are given for a variety of test images. [ABSTRACT FROM AUTHOR]

An interference method for measuring the refractive index and surface curvature of cylindrical microlenses is considered. The method consists in probing microlenses by a dynamic interference pattern with a localization of order of several to tens micrometers corresponding to the period of the interference fringes. Basic analytical expressions for evaluation of the curvature radius and refractive index of the probed portion of the microlens are presented. [ABSTRACT FROM AUTHOR]