Staircase Effect Research Articles

Directional Total Variation Regularized High-Resolution Prestack AVA Inversion

Prestack seismic inversion has emerged as a powerful technique for reconstructing parameters attribute to the subsurface properties and building the geophysical parameter models. However, the inversion algorithms always suffer from spatial blur and low resolution. Total variation (TV) regularization preserves the spatial variation boundary of data by highlighting the sparsity of the first-order difference, which is regarded as an important technical means for image restoration. However, when the data do not change along the spatial grid direction, TV regularization is prone to a staircase effect. In this article, a directional TV (DTV) method is proposed to conduct the prestack amplitude variation with offset/angle (AVO/AVA) inversion. The method consists of three essential steps: estimating the seismic slope attribute from the seismic data, introducing seismic slope attribute to the TV regularization to establish the objective function, and optimizing the objective function by the split-Bregman algorithm. Finally, the conventional and proposed methods are applied to the synthetic and the real seismic data. The comparison of different methods demonstrates that the proposed method is applicable to reveal the detailed subsurface models, alleviate the staircase effect or artifact substantially, and further upgrade the quality of prestack inversion results.

Improving the surface characteristics of additively manufactured parts: A review

Abstract Nowadays, the additive manufacturing process had significant attention due to its great advantages that are being used for developing products and producing prototypes. This technology overcomes the various drawbacks of existing techniques and it becomes the most efficient approach. In the industrial sector, this technology is most important for individual designing products and extended with different functions. The performance of additively manufactured parts, on the other hand, is largely influenced by their surface integrity and dimensional accuracy. The surface integrity is an important issue because the additively manufactured products are affected by staircase effects resulting from layer-by-layer manufacturing. The rapid prototyping contains multiple methods such as VAT Photopolymerization and Poor surface quality is caused by the staircase effect in all additive manufacturing processes so therefore, the various post-processing efforts and controlling different process parameters of additive manufacturing are necessary on the produced component for improving surface quality and reducing surface roughness. To focus on improving the finish of an additively manufactured part's surface, there are numerous methods presented. This research described the various existing approaches of surface finishing with various efficacies such as reduction of surface roughness value, mechanical strength, and dimensional accuracy. Current post-processing methods for improving the surface characteristics of additively manufactured parts are discussed, with a classification based on the processes' mechanisms.

High-Order Directional Total Variation for Seismic Noise Attenuation

High-amplitude noise could interfere with useful seismic signals, affecting our ability in processing and interpreting seismic data. Thus, attenuating seismic noise is an important task in seismic processing. Total variation (TV) has played an important role in many steps of seismic data processing but always neglected the seismic structural information. Directional TV (DTV), however, considers the structural direction of seismic events but tends to cause the staircasing effect on seismic records based on the first-order formulation. Here, we develop a high-order DTV (HDTV) method for seismic denoising. It considers the local structural direction of the seismic data and calculates the higher order derivatives of seismic images to avoid the staircasing effect. We design several synthetic models that are contaminated by various types of random noise to test the denoising ability. The denoising performance of our new method is compared with the first-order DTV, conventional high-order TV, and TV regularization methods from two aspects, i.e., the signal-to-noise ratio and the effective signal leakage degree. Then, the advantages of the proposed method are further validated via several field seismic data sets.

Special Issue on Tribology of Additive Manufacturing

Special Issue on Tribology of Additive Manufacturing

State of Art on Vapour Smoothing of Fused Deposition Modelling Components

Fused Deposition Modelling (FDM) is one of the additive manufacturing processes which can produce prototypes or functional components without the use of fixtures, and the lead time required is reduced drastically compared to traditional machining processes. The application of the FDM process in the biomedical and casting industries is limited by its poor surface roughness which is most generally caused by the staircase effect and chordal error of the 3D model. Owing to the drawbacks of mechanical based finishing techniques, researchers have come up with a new technique known as Vapour Smoothing (VS). In this work, past literature of the VS process of FDM components is reported and it has been seen that the VS process is giving a promising improvement in surface roughness of FDM components.

Filling Path Planning and Polygon Operations for Wire Arc Additive Manufacturing Process

To improve the service life of hot forging die, the additive manufacturing algorithm and additive manufacturing device for die remanufacturing are developed. Firstly, a compound filling algorithm in which the inner zone is filled by linear scanning and the outer contour is filled by offsetting is developed in order to solve the problems encountered in filling path planning for wire arc additive manufacturing (WAAM) like staircase effect at marginal division, degenerated edge at outer contour, programming difficulty, and so forth. Meanwhile, the attitude control algorithm of welding gun is proposed to control the angle between welding gun and welding path so as to improve the welding forming quality. Secondly, the high-temperature and low-temperature wear resistances of Fe-based and Ni-based alloy are tested. The results show that Ni-based alloy has higher high-temperature wear resistance. Finally, a disabled crankshaft hot forging die is selected for application test and the results show that, using the techniques discussed in this paper, welding materials can be saved by more than 50% and machining cost can be saved by more than 60%. In addition, the surface of automatic-repaired die is smooth without oxidation, collapse, and other defects after forging 3000 times, which is much better than that of manual-repaired die.

Three-dimensional fractional total variation regularized tensor optimized model for image deblurring

Image deblurring is an important pre-processing step in image analysis. The research for efficient image deblurring methods is still a great challenge. Most of the currently used methods are based on integer-order derivatives, but they typically lead to texture elimination and staircase effects. To overcome these drawbacks, some researchers have proposed fractional-order derivative-based models. However, the existing fractional-order derivative-based models only exploit nonlocal smoothness of spatial dimensions and fail to consider the other dimensional information for three-dimensional (3D) images. To address this issue, we propose a three-dimensional fractional total variation (3DFTV) based-model for 3D image deblurring problem. In this paper, we mathematically formulate the proposed model under the tensor algebra. Furthermore, we develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to solve our model. Experimental results demonstrate the superiority of our model against comparing models in terms of quality metrics and visual effects.

Surface Texture Characterization of Metal Selective Laser Melted Part With Varying Surface Inclinations

Abstract Additive manufacturing offers the advantage of infinite freedom to design and fabricate complex parts at reduced lead-time. However, the surface quality of additively manufactured parts remains well behind the conventionally processed counterparts. This paper aims to systematically investigate the impact of varying surface inclination angles with respect to the build direction on the resultant surface textures. A bespoke metal truncheon artifact with inclination angles varying from 0 deg to 180 deg was built by selective laser melting. Focus variation microscopy was used to measure the topography of inclined surfaces with a tilt angle of up to 132 deg. The measurement data were then analyzed to characterize the staircase effect and the particles adherent to the artifact surface. Areal surface texture parameters, including height parameters, spatial parameters, functional parameters, and feature parameters, were explored to quantify the general surface topography, the staircase effect, and the particle features. The areal surface texture characterization and particle analysis reveal the resulted surface topographies are strongly correlated with the surface inclination angles.

An adaptive non-convex hybrid total variation regularization method for image reconstruction in electrical impedance tomography

The image reconstruction of conductivity distribution in electrical impedance tomography (EIT) is a seriously ill-posed inverse problem. To cope with the problem, it is recognized that the regularization method is an effective approach. In this paper, an adaptive non-convex hybrid total variation (ANHTV) regularization method is proposed to reconstruct the conductivity distribution in EIT. The iterative reweighted least squares algorithm and the iterative alternating direction method of multipliers algorithm are developed to solve the ANHTV-based inverse model in the image reconstruction. Besides, all the parameters utilized in the inverse model are adaptively selected. To validate the advantage of the proposed method, extensive numerical simulation and experimental work have been carried out. Also, qualitative and quantitative comparisons with two convex TV-based regularization methods are conducted. The results show that the proposed method is more advantageous in terms of staircase effect suppression, edge information preservation and noise resisting in the image reconstruction.

Texture of inclined up-facing surfaces in laser powder bed fusion of metals

Considerable surface texture is one of the typical drawbacks of laser powder bed fusion (LPBF). Especially up-facing inclined surfaces suffer from insufficient quality, due to the combination of the staircase effect (also called stair-stepping effect), attached powder particles and elevated edges (edge effect). In this work, the contribution of the edge effect to the topography of up-facing inclined surfaces is investigated in detail for the first time. Moreover, the effect of contour scanning was evaluated on up-facing surfaces over the whole range of inclinations, from horizontal to vertical. The edge effect was found to play a dominant role for surfaces with a low inclination angle, especially when contour scanning is used. A suitable scanning strategy can thus be determined for each surface inclination. In the present study, an optimization of scanning strategy allowed a significant improvement of the inclined surface quality. The arithmetical mean height of the roughness profile Ra could be reduced up to 52% for low inclinations, 20% for high inclinations and 32% for vertical walls.

Blind deconvolution using bilateral total variation regularization: a theoretical study and application

ABSTRACT Blind image deconvolution recovers a deblurred image and the blur kernel from a blurred image. From a mathematical point of view, this is a strongly ill-posed problem and several works have been proposed to address it. One successful approach proposed by Chan and Wong consists in using the total variation (TV) as a regularization for both the image and the kernel. These authors also introduced an Alternating Minimization (AM) algorithm in order to compute a physical solution. Unfortunately, Chan's approach suffers in particular from the ringing and staircasing effects produced by the TV regularization. To address these problems, we propose a new model based on Bilateral Total Variation (BTV) regularization of the image keeping the same regularization for the kernel. We prove the existence of a minimizer of a proposed variational problem in a suitable space using a relaxation process. We also propose an AM algorithm based on our model. The efficiency and robustness of our model are illustrated and compared with the TV method through numerical simulations.

Image denoising by a novel variable‐order total fractional variation model

The total variation model performs very well for removing noise while preserving edges. However, it gives a piecewise constant solution which often leads to the staircase effect, consequently small details such as textures are filtered out in the denoising process. Fractional‐order total variation method is one of the major approaches to overcome such drawbacks. Unlike their good quality of fractional order, all these methods use a fixed fractional order for the whole of the image. In this paper, a novel variable‐order total fractional variation model is proposed for image denoising, in which the order of fractional derivative will be allocated automatically for each pixel based on the context of the image. This kind of selection is able to capture the edges and texture of the image simultaneously. In this regard, we prove the existence and uniqueness of the presented model. The split Bregman method is adapted to solve the model. Finally, the results illustrate the efficiency of the proposed model that yielded good visual effects and a better signal‐to‐noise ratio.

A novel image denoising approach based on a non-convex constrained PDE: application to ultrasound images

In this paper, we are interested in the mathematical and simulation study of a new non-convex constrained PDE to remove the mixture of Gaussian–impulse noise densities. The model incorporates a non-convex data-fidelity term with a fractional constrained PDE. In addition, we adopt a non-smooth primal-dual algorithm to resolve the obtained proximal linearized minimization problem. The non-convex fidelity term is used to handle the high-frequency of the impulse noise component, while the fractional operator enables the efficient denoising of smooth areas, avoiding also the staircasing effect that appears on the relevant variational denoising models. Moreover, the proposed primal-dual algorithm helps in preserving fine structures and texture with good convergence rate. Numerical experiments, including ultrasound images, show that the proposed non-convex constrained PDE produces better denoising results compared to the state-of-the-art denoising models.

Continuous DLP-based ceramic 3D printing using a composite oxygen-rich film

The existing stereolithography-based ceramic 3D printing techniques are noncontinuous in a layer-by-layer method, which usually causes drawbacks of anisotropic mechanical properties, stair-casing effect, and the low fabrication rate. In this paper, a continuous DLP-based ceramic 3D printing is proposed to achieve the layerless ceramic manufacturing. In order to achieve this goal, a composite oxygen-rich film was designed with a microporous PET film and a PDMS coating to ensure a proper dead zone thickness according to the oxygen-controlled inhibition effect and low surface energy for releasing quickly from ceramic slurry. And a ceramic slurry with low viscosity was also prepared to match it. Then, the effects of influencing factors including the composite oxygen-rich film, ceramic slurry, and the print speed on the printing quality and geometrical overgrowth have been investigated. It shows that the geometrical overgrowth has a good linear relationship with this variable, the larger dead zone thickness, the higher solid content, and the low print speed, the larger the geometrical overgrowth. And the print speed does not worsen the surface quality. This proposed method can achieve the maximum speed of 143 mm/h and a surface roughness of 0.127 for a 40 vol% ceramic slurry. To demonstrate the utility of this system, parts of hollow structure, thin wall structure, and impeller structure have been successfully printed and sintered to ceramics with a condensed and porous structure. As a result, the proposed continuous DLP-based ceramic 3D printing technique provides a promising solution for ceramic 3D printing.

Fractional-order total variation algorithm with nonlocal self-similarity for image reconstruction

We propose the fractional-order total variation (TV) algorithm with nonlocal self-similarity for image reconstruction in compressed sensing to alleviate texture details deterioration and eliminate staircase artifacts, which results from the TV algorithms. The Grünwald–Letnikov fractional-order differential operators, which consider more neighboring image pixels and use four different directions to handle fractional-order gradients, are used to replace the integer-order differential operators. To suppress the staircase artifacts, modified nonlocal means operators are introduced into our method, which can contain prior image structural information and update the Lagrangian multipliers. An efficient augmented Lagrangian algorithm is used to solve the TV problem. Numerical results show that the algorithm achieves remarkable performance improvements at various sampling ratios. Compared with fractional-order TV-based projections onto convex sets, the maximum gains of peak signal-to-noise ratio and structural similarity index with all images are up to 2.52 dB and 0.0178, respectively, and the algorithm performs the better for preserving details and eliminating the staircase effect at the cost of taking more time.

Learning Convolutional Sparse Coding on Complex Domain for Interferometric Phase Restoration.

Interferometric phase restoration has been investigated for decades and most of the state-of-the-art methods have achieved promising performances for InSAR phase restoration. These methods generally follow the nonlocal filtering processing chain, aiming at circumventing the staircase effect and preserving the details of phase variations. In this article, we propose an alternative approach for InSAR phase restoration, that is, Complex Convolutional Sparse Coding (ComCSC) and its gradient regularized version. To the best of the authors' knowledge, this is the first time that we solve the InSAR phase restoration problem in a deconvolutional fashion. The proposed methods can not only suppress interferometric phase noise, but also avoid the staircase effect and preserve the details. Furthermore, they provide an insight into the elementary phase components for the interferometric phases. The experimental results on synthetic and realistic high- and medium-resolution data sets from TerraSAR-X StripMap and Sentinel-1 interferometric wide swath mode, respectively, show that our method outperforms those previous state-of-the-art methods based on nonlocal InSAR filters, particularly the state-of-the-art method: InSAR-BM3D. The source code of this article will be made publicly available for reproducible research inside the community.

Surface accuracy optimization of mechanical parts with multiple circular holes for additive manufacturing based on triangular fuzzy number

Surface accuracy directly affects the surface quality and performance of mechanical parts. Circular hole, especially spatial non-planar hole set is the typical feature and working surface of mechanical parts. Compared with traditional machining methods, additive manufacturing (AM) technology can decrease the surface accuracy errors of circular holes during fabrication. However, an accuracy error may still exist on the surface of circular holes fabricated by AM due to the influence of staircase effect. This study proposes a surface accuracy optimization approach for mechanical parts with multiple circular holes for AM based on triangular fuzzy number (TFN). First, the feature lines on the manifold mesh are extracted using the dihedral angle method and normal tensor voting to detect the circular holes. Second, the optimal AM part build orientation is determined using the genetic algorithm to optimize the surface accuracy of the circular holes by minimizing the weighted volumetric error of the part. Third, the corresponding weights of the circular holes are calculated with the TFN analytic hierarchy process in accordance with the surface accuracy requirements. Lastly, an improved adaptive slicing algorithm is utilized to reduce the entire build time while maintaining the forming surface accuracy of the circular holes using digital twins via virtual printing. The effectiveness of the proposed approach is experimentally validated using two mechanical models.

Scalable image decomposition

Image decomposition, which separates a given input image into structure and texture images, has been used for various applications in the fields of computer graphics and image processing. Most previous image decomposition algorithms and applications start with high-quality images, but it requires numerous steps to separate and edit the high-resolution structure and texture images from the low-resolution input counterparts. This paper proposes a simple but effective end-to-end deep neural image decomposition network, which is called ”scalable image decomposition”, by decomposing and upscaling structure and texture images from the degraded input image at the same time. We train the deep neural network to automatically estimate high-resolution structure and texture from the low-resolution input image by designing a shared feature extractor, and structure and texture upscaling networks which have a powerful capability to establish and distinguish a complex mapping between the low-resolution input image and high-quality structure and texture, while preserving more contextual information without any prior information regarding the low-resolution input image. Quantitative and qualitative analyses of the proposed scalable image decomposition network validate that the proposed method is stable and robust against blurring and staircase effects by separating texture and structure upscaling networks in real-time. The predicted upscaled structure and texture images can be used to a variety of applications, such as image abstraction, detail enhancement, and pencil sketching.

Colour image segmentation based on a convex K‐means approach

Image segmentation is a fundamental and challenging task in image processing and computer vision. The colour image segmentation is attracting more attention as the colour image provides more information than the grey image. A variational model based on a convex K-means approach to segment colour images is proposed. The proposed variational method uses a combination of l1 and l2 regularizers to maintain edge information of objects in images while overcoming the staircase effect. Meanwhile, our one-stage strategy is an improved version based on the smoothing and thresholding strategy, which contributes to improving the accuracy of segmentation. The proposed method performs the following steps. First, the colour set which can be determined by human or the K-means method is specified. Second, a variational model to obtain the most appropriate colour for each pixel from the colour set via convex relaxation and lifting is used. The Chambolle–Pock algorithm and simplex projection are applied to solve the variational model effectively. Experimental results and comparison analysis demonstrate the effectiveness and robustness of the method.

Geodesic Distance Field-Based Process Planning for Five-Axis Machining of Complicated Parts

Abstract A critical task in multi-pass process planning for the five-axis machining of complicated parts is to determine the intermediate surfaces for rough machining. Traditionally, the intermediate surfaces are simply parallel Z-level planes, and the machining is of the simplest three-axis type. However, for complicated parts, this so-called Z-level method lacks flexibility and causes isolated islands on layers, which require extraneous air movements by the tool. Moreover, the in-process workpiece machined according to the Z-level method suffers from the staircase effect, which often induces unstable dynamic problems on the tool-spindle system. In this paper, we propose a new method of planning a five-axis machining process for a complicated freeform solid part. In our method, the intermediate surfaces are no longer planar but curved, and they are intrinsically influenced by the convex hull of the part. The powerful algebraic tool of geodesic distance field is utilized to generate the desired intermediate surfaces, for which collision-free five-axis machining tool paths are then planned. In addition, we propose a novel idea of alternating between the roughing and finishing machining operations, which helps improve the stiffness of the in-process workpiece. Ample physical cutting experiments are performed, and the experimental results convincingly confirm the advantages of our method.