Planar quadrilateral (PQ) mesh generation is a key process in computer-aided design, particularly for architectural applications where the goal is to discretize a freeform surface using planar quad faces. The conjugate direction field (CDF) defined on the freeform surface plays a significant role in generating a PQ mesh, as it largely determines the PQ mesh layout. Conventionally, a CDF is obtained by solving a complex non-linear optimization problem that incorporates user preferences, i.e., aligning the CDF with user-specified strokes on the surface. This often requires a large number of iterations that are computationally expensive, preventing the interactive CDF design process for a desirable PQ mesh. To address this challenge, we propose a data-driven approach based on neural networks for controlled CDF generation. Our approach can effectively learn and fuse features from the freeform surface and the user strokes, and efficiently generate quality CDF respecting user guidance. To enable training and testing, we also present a dataset composed of 50000+ freeform surfaces with ground-truth CDFs, as well as a set of metrics for quantitative evaluation. The effectiveness and efficiency of our work are demonstrated by extensive experiments using testing data, architectural surfaces, and general 3D shapes.

Texture is fundamental to high-fidelity rendering of 3D digital assets, directly influencing scene detail and visual realism. Existing methods typically adopt 2D texture mapping, where texture images are either manually created or synthesized from exemplars. While advances in texture synthesis have improved 2D texture quality, 2D representations remain inadequate for modeling volumetric meso-structure textures with complex geometry. Methods targeting meso-structure textures often struggle to capture high-frequency details and lack real-time rendering capabilities, limiting their practical use. We propose MesoSplats, a neural implicit method for extracting and synthesizing meso-structure textures using 3D Gaussian splatting. Given the multi-view images containing the meso-structure geometric details, our approach supports texture extraction, synthesis, and real-time rendering. We introduce a mesh-Gaussian hybrid representation that decouples geometry into a coarse base mesh and embedded 3D Gaussians, guided by initial point cloud constraints to enhance reconstruction fidelity. Local implicit texture features are sampled from the base mesh surface and further refined through a proposed Consistency Tuning strategy, which enforces alignment between the reconstruction and sampling spaces. To boost texture synthesis quality, we incorporate a tileability-aware patch-matching algorithm alongside a smoothness regularization on the latent feature space to ensure spatial coherence. Extensive quantitative and qualitative experiments demonstrate the effectiveness of our method.

Weingarten surfaces are characterized by a functional relation between their principal curvatures. Such a specialty makes them suitable for building surface paneling in architectural applications, as the curvature relation implies approximate local congruence on the surface thus the molds for paneling can be largely reused. In this work, we aim at a novel task of Weingarten surface approximation. Given a surface mesh with arbitrary topology, we optimize its shape to make it as Weingarten as possible. We devise a curvature-based optimization approach based on the fact that the 2D principal curvature plots of a Weingarten surface comprise a group of 1D curves that encode the curvature relations. Our approach alternatively performs two steps. The first step transforms the principal curvature plots from a 2D region to 1D curves in order to explore the curvature relations. The second step deforms the shape such that its curvatures conform to the corresponding transformed curvature plots. We demonstrate the effectiveness of our work on a variety of shapes with different topologies. Hopefully our work would bring inspiration on the study of general Weingarten surfaces with arbitrary topology and curvature relation.

We present a lightweight system for reconstructing human geometry and appearance from sparse flashlight images. Our system produces detailed geometry including garment wrinkles and surface reflectance, which are exportable for direct rendering and relighting in traditional graphics pipelines. By capturing multi-view flashlight images using a consumer camera equipped with an co-located LED (e.g., a cell phone), we obtain view-specific shading cues that aid in the determination of surface orientation and help disambiguate between shading and material. To enable the reconstruction of geometry and appearance from sparse-view flashlight images, we integrate a pre-trained model into a differentiable physics-based rendering framework. As the learned image features from synthetic data cannot accurately reflect the shading features on real images, which is crucial for the high-quality reconstruction of geometry details and appearance, we propose to jointly optimize the image feature extractor with two MLPs for SDF and BRDF prediction using the differentiable physics-based rendering. Compared with existing methods for relightable human reconstruction, our system is able to produce high-fidelity 3D human models with more accurate geometry and appearance under the same condition. Our code and data are available at http://github.com/Jarvisss/Relightable_human_recon.

Nowadays, 3D scenes are not merely static arrangements of objects. With the development of transformable modules, furniture objects can be translated, rotated, and even reshaped to achieve scenes with different functions (e.g., from a bedroom to a living room). Transformable domestic space, therefore, studies how a layout can change its function by reshaping and rearranging transformable modules, resulting in various transformable layouts. In practice, a rearrangement is dynamically conducted by reshaping/translating/rotating furniture objects with proper schedules, which can consume more time for designers than static scene design. Due to changes in objects' functions, potential transformable layouts may also be extensive, making it hard to explore desired layouts. We present a system for exploring transformable layouts. Given a single input scene consisting of transformable modules, our system first attempts to derive more layouts by reshaping and rearranging the modules. The derived scenes are organized into a graph-like hierarchy according to their functions, where edges represent functional evolutions (e.g., a living room can be reshaped to a bedroom), and nodes represent layouts that are dynamically transformable through translating/rotating/reshaping modules. The resulting hierarchy lets scene designers interactively explore possible scene variants and preview the animated rearrangement process. Experiments show that our system is efficient for generating transformable layouts, sensible for organizing functional hierarchies, and inspiring for providing ideas during interactions.

Effective removal of noises from raw point clouds while preserving geometric features is the key challenge for point cloud denoising. To address this problem, we propose a novel method that jointly optimizes the point positions and normals. To preserve geometric features, our formulation uses a generalized robust error metric to enforce piecewise smoothness of the normal vector field as well as consistency between point positions and normals. By varying the parameter of the error metric, we gradually increase its non-convexity to guide the optimization towards a desirable solution. By combining alternating minimization with a majorization-minimization strategy, we develop a numerical solver for the optimization which guarantees convergence. The effectiveness of our method is demonstrated by extensive comparisons with previous works.

Abstract The rapid development of the online apparel shopping industry demands innovative solutions for high‐quality digital apparel sample displays with virtual avatars. However, developing such displays is prohibitively expensive and prone to the well‐known “uncanny valley” effect, where a nearly human‐looking artifact arouses eeriness and repulsiveness, thus affecting the user experience. To effectively mitigate the “uncanny valley” effect and improve the overall authenticity of digital apparel sample displays, we present a novel photo‐realistic portrait generation framework. Our key idea is to employ transfer learning to learn an identity‐consistent mapping from the latent space of rendered portraits to that of real portraits. During the inference stage, the input portrait of an avatar can be directly transferred to a realistic portrait by changing its appearance style while maintaining the facial identity. To this end, we collect a new dataset, Daz‐Rendered‐Faces‐HQ (DRFHQ), specifically designed for rendering‐style portraits. We leverage this dataset to fine‐tune the StyleGAN2‐FFHQ generator, using our carefully crafted framework, which helps to preserve the geometric and color features relevant to facial identity. We evaluate our framework using portraits with diverse gender, age, and race variations. Qualitative and quantitative evaluations, along with ablation studies, highlight our method's advantages over state‐of‐the‐art approaches.

Outdoor scenes often involve large-scale geometry and complex unknown lighting conditions, making it difficult to decompose them into geometry, reflectance and illumination. Recently researchers made attempts to decompose outdoor scenes using Neural Radiance Fields (NeRF) and learning-based lighting and shadow representations. However, diverse lighting conditions and shadows in outdoor scenes are challenging for learning-based models. Moreover, existing methods may produce rough geometry and normal reconstruction and introduce notable shading artifacts when the scene is rendered under a novel illumination. To solve the above problems, we propose SOL-NeRF to decompose outdoor scenes with the help of a hybrid lighting representation and a signed distance field geometry reconstruction. We use a single Spherical Gaussian (SG) lobe to approximate the sun lighting, and a first-order Spherical Harmonic (SH) mixture to resemble the sky lighting. This hybrid representation is specifically designed for outdoor settings, and compactly models the outdoor lighting, ensuring robustness and efficiency. The shadow of the direct sun lighting can be obtained by casting the ray against the mesh extracted from the signed distance field, and the remaining shadow can be approximated by Ambient Occlusion (AO). Additionally, sun lighting color prior and a relaxed Manhattan-world assumption can be further applied to boost decomposition and relighting performance. When changing the lighting condition, our method can produce consistent relighting results with correct shadow effects. Experiments conducted on our hybrid lighting scheme and the entire decomposition pipeline show that our method achieves better reconstruction, decomposition, and relighting performance compared to previous methods both quantitatively and qualitatively.

Abstract Logos are one of the most important graphic design forms that use an abstracted shape to clearly represent the spirit of a community. Among various styles of abstraction, a particular golden‐ratio design is frequently employed by designers to create a concise and regular logo. In this context, designers utilize a set of circular arcs with golden ratios (i.e., all arcs are taken from circles whose radii form a geometric series based on the golden ratio) as the design elements to manually approximate a target shape. This error‐prone process requires a large amount of time and effort, posing a significant challenge for design space exploration. In this work, we present a novel computational framework that can automatically generate golden ratio logo abstractions from an input image. Our framework is based on a set of carefully identified design principles and a constrained optimization formulation respecting these principles. We also propose a progressive approach that can efficiently solve the optimization problem, resulting in a sequence of abstractions that approximate the input at decreasing levels of detail. We evaluate our work by testing on images with different formats including real photos, clip arts, and line drawings. We also extensively validate the key components and compare our results with manual results by designers to demonstrate the effectiveness of our framework. Moreover, our framework can largely benefit design space exploration via easy specification of design parameters such as abstraction levels, golden circle sizes, etc.

Deep learning has been successfully used for tasks in the 2D image domain. Research on 3D computer vision and deep geometry learning has also attracted attention. Considerable achievements have been made regarding feature extraction and discrimination of 3D shapes. Following recent advances in deep generative models such as generative adversarial networks, effective generation of 3D shapes has become an active research topic. Unlike 2D images with a regular grid structure, 3D shapes have various representations, such as voxels, point clouds, meshes, and implicit functions. For deep learning of 3D shapes, shape representation has to be taken into account as there is no unified representation that can cover all tasks well. Factors such as the representativeness of geometry and topology often largely affect the quality of the generated 3D shapes. In this survey, we comprehensively review works on deep-learning-based 3D shape generation by classifying and discussing them in terms of the underlying shape representation and the architecture of the shape generator. The advantages and disadvantages of each class are further analyzed. We also consider the 3D shape datasets commonly used for shape generation. Finally, we present several potential research directions that hopefully can inspire future works on this topic.

Origami architecture (OA) is a fascinating papercraft that involves only a piece of paper with cuts and folds. Interesting geometric structures 'pop up' when the paper is opened. However, manually designing such a physically valid 2D paper pop-up plan is challenging since fold lines must jointly satisfy hard spatial constraints. Existing works on automatic OA-style paper pop-up design all focused on how to generate a pop-up structure that approximates a given target 3D model. This article presents the first OA-style paper pop-up design framework that takes 2D images instead of 3D models as input. Our work is inspired by the fact that artists often use 2D profiles to guide the design process, thus benefited from the high availability of 2D image resources. Due to the lack of 3D geometry information, we perform novel theoretic analysis to ensure the foldability and stability of the resultant design. Based on a novel graph representation of the paper pop-up plan, we further propose a practical optimization algorithm via mixed-integer programming that jointly optimizes the topology and geometry of the 2D plan. We also allow the user to interactively explore the design space by specifying constraints on fold lines. Finally, we evaluate our framework on various images with interesting 2D shapes. Experiments and comparisons exhibit both the efficacy and efficiency of our framework.

Redirected Walking (RDW) algorithms aim to impose several types of gains on users immersed in Virtual Reality and distort their walking paths in the real world, thus enabling them to explore a larger space. Since collision with physical boundaries is inevitable, a reset strategy needs to be provided to allow users to reset when they hit the boundary. However, most reset strategies are based on simple heuristics by choosing a seemingly suitable solution, which may not perform well in practice. In this article, we propose a novel optimization-based reset algorithm adaptive to different RDW algorithms. Inspired by the approach of finite element analysis, our algorithm splits the boundary of the physical world by a set of endpoints. Each endpoint is assigned a reset vector to represent the optimized reset direction when hitting the boundary. The reset vectors on the edge will be determined by the interpolation between two neighbouring endpoints. We conduct simulation-based experiments for three RDW algorithms with commonly used reset algorithms to compare with. The results demonstrate that the proposed algorithm significantly reduces the number of resets.

We present a framework for fast synthesizing indoor scenes, given a room geometry and a list of objects with learnt priors. Unlike existing data-driven solutions, which often learn priors by co-occurrence analysis and statistical model fitting, our method measures the strengths of spatial relations by tests for complete spatial randomness (CSR), and learns discrete priors based on samples with the ability to accurately represent exact layout patterns. With the learnt priors, our method achieves both acceleration and plausibility by partitioning the input objects into disjoint groups, followed by layout optimization using position-based dynamics (PBD) based on the Hausdorff metric. Experiments show that our framework is capable of measuring more reasonable relations among objects and simultaneously generating varied arrangements in seconds compared with the state-of-the-art works.

While recent researches on computational 3D scene synthesis have achieved impressive results, automatically synthesized scenes do not guarantee satisfaction of end users. On the other hand, manual scene modelling can always ensure high quality, but requires a cumbersome trial-and-error process. In this paper, we bridge the above gap by presenting a data-driven 3D scene synthesis framework that can intelligently infer objects to the scene by incorporating and simulating user preferences with minimum input. While the cursor is moved and clicked in the scene, our framework automatically selects and transforms suitable objects into scenes in real time. This is based on priors learnt from the dataset for placing different types of objects, and updated according to the current scene context. Through extensive experiments we demonstrate that our framework outperforms the state-of-the-art on result aesthetics, and enables effective and efficient user interactions.

3D spatial information is known to be beneficial to the semantic segmentation task. Most existing methods take 3D spatial data as an additional input, leading to a two-stream segmentation network that processes RGB and 3D spatial information separately. This solution greatly increases the inference time and severely limits its scope for real-time applications. To solve this problem, we propose Spatial information guided Convolution (S-Conv), which allows efficient RGB feature and 3D spatial information integration. S-Conv is competent to infer the sampling offset of the convolution kernel guided by the 3D spatial information, helping the convolutional layer adjust the receptive field and adapt to geometric transformations. S-Conv also incorporates geometric information into the feature learning process by generating spatially adaptive convolutional weights. The capability of perceiving geometry is largely enhanced without much affecting the amount of parameters and computational cost. Based on S-Conv, we further design a semantic segmentation network, called Spatial information Guided convolutional Network (SGNet), resulting in real-time inference and state-of-the-art performance on NYUDv2 and SUNRGBD datasets.

Humans have the ability to perceive kinetic depth effects , i.e., to perceived 3D shapes from 2D projections of rotating 3D objects. This process is based on a variety of visual cues such as lighting and shading effects. However, when such cues are weak or missing, perception can become faulty, as demonstrated by the famous silhouette illusion example of the spinning dancer . Inspired by this, we establish objective and subjective evaluation models of rotated 3D objects by taking their projected 2D images as input. We investigate five different cues: ambient luminance, shading, rotation speed, perspective, and color difference between the objects and background. In the objective evaluation model, we first apply 3D reconstruction algorithms to obtain an objective reconstruction quality metric, and then use quadratic stepwise regression analysis to determine weights of depth cues to represent the reconstruction quality. In the subjective evaluation model, we use a comprehensive user study to reveal correlations with reaction time and accuracy, rotation speed, and perspective. The two evaluation models are generally consistent, and potentially of benefit to inter-disciplinary research into visual perception and 3D reconstruction.

Abstract We present a novel anisotropic surface remeshing method that can efficiently eliminate obtuse angles. Unlike previous work that can only suppress obtuse angles with expensive resampling and Lloyd‐type iterations, our method relies on a simple yet efficient connectivity and geometry refinement, which can not only remove all the obtuse angles, but also preserves the original mesh connectivity as much as possible. Our method can be directly used as a post‐processing step for anisotropic meshes generated from existing algorithms to improve mesh quality. We evaluate our method by testing on a variety of meshes with different geometry and topology, and comparing with representative prior work. The results demonstrate the effectiveness and efficiency of our approach.

This paper addresses both the model selection (i.e., estimating the number of clusters K) and subspace clustering problems in a unified model. The real data always distribute on a union of low-dimensional sub-manifolds which are embedded in a high-dimensional ambient space. In this regard, the state-of-the-art subspace clustering approaches firstly learn the affinity among samples, followed by a spectral clustering to generate the segmentation. However, arguably, the intrinsic geometrical structures among samples are rarely considered in the optimization process. In this paper, we propose to simultaneously estimate K and segment the samples according to the local similarity relationships derived from the affinity matrix. Given the correlations among samples, we define a novel data structure termed the Triplet, each of which reflects a high relevance and locality among three samples which are aimed to be segmented into the same subspace. While the traditional pairwise distance can be close between inter-cluster samples lying on the intersection of two subspaces, the wrong assignments can be avoided by the hyper-correlation derived from the proposed triplets due to the complementarity of multiple constraints. Sequentially, we propose to greedily optimize a new model selection reward to estimate K according to the correlations between inter-cluster triplets. We simultaneously optimize a fusion reward based on the similarities between triplets and clusters to generate the final segmentation. Extensive experiments on the benchmark datasets demonstrate the effectiveness and robustness of the proposed approach.

With the explosion of visual information nowadays, millions of digital images are available to the users. How to efficiently explore a large set of images and retrieve useful information thus becomes extremely important. Unfortunately only some of the images can impress the user at first glance. Others that make little sense in human perception are often discarded, while still costing valuable time and space. Therefore, it is significant to identify these two kinds of images for relieving the load of online repositories and accelerating information retrieval process. However, most of the existing image properties, e.g., memorability and popularity, are based on repeated human interactions, which limit the research and application of evaluating image quality in terms of instantaneous impression. In this paper, we propose a novel image property, called impressiveness, that measures how images impress people with a short-term contact. This is based on an impression-driven model inspired by a number of important human perceptual cues. To achieve this, we first collect three datasets in various domains, which are labeled according to the instantaneous sensation of the annotators. Then we investigate the impressiveness property via six established human perceptual cues as well as the corresponding features from pixel to semantic levels. Sequentially, we verify the consistency of the impressiveness which can be quantitatively measured by multiple visual representations, and evaluate their latent relationships. Finally, we apply the proposed impressiveness property to rank the images for an efficient image recommendation system.

Abstract Designers always get good inspirations from fascinating geometric structures gifted by the nature. In the recent years, various computational design tools have been proposed to help generate cell packing structures on freeform surfaces, which consist of a packing of simple primitives, such as polygons, spheres, etc. In this work, we aim at computationally generating novel ellipsoid packing structures on freeform surfaces. We formulate the problem as a generalization of sphere packing structures in the sense that anisotropic ellipsoids are used instead of isotropic spheres to pack a given surface. This is done by defining an anisotropic metric based on local surface anisotropy encoded by principal curvatures and the corresponding directions. We propose an optimization framework that can optimize the shapes of individual ellipsoids and the spatial relation between neighboring ellipsoids to form a quality packing structure. A tailored anisotropic remeshing method is also employed to better initialize the optimization and ensure the quality of the result. Our framework is extensively evaluated by optimizing ellipsoid packing and generating appealing geometric structures on a variety of freeform surfaces.

Flat design is a modern style of graphics design that minimizes the number of design attributes required to convey 3D shapes. This approach suits design contexts requiring simplicity and efficiency, such as mobile computing devices. This `less-is-more' design inspiration has posed significant challenges in practice since it selects from a restricted range of design elements (e.g., color and resolution) to represent complex shapes. In this work, we investigate a means of computationally generating a specialized 2D flat representation - image formed by black-and-white patches - from 3D shapes. We present a novel framework that automatically abstracts 3D man-made shapes into 2D binary images at multiple scales. Based on a set of identified design principles related to the inference of geometry and structure, our framework jointly analyzes the input 3D shape and its counterpart 2D representation, followed by executing a carefully devised layout optimization algorithm. The robustness and effectiveness of our method are demonstrated by testing it on a wide variety of man-made shapes and comparing the results with baseline methods via a pilot user study. We further present two practical applications that are likely to benefit from our work.

Abstract Pixel art is a modern digital art in which high resolution images are abstracted into low resolution pixelated outputs using concise outlines and reduced color palettes. Creating pixel art is a labor intensive and skill‐demanding process due to the challenge of using limited pixels to represent complicated shapes. Not surprisingly, generating pixel art animation is even harder given the additional constraints imposed in the temporal domain. Although many powerful editors have been Designed to facilitate the creation of still pixel art images, the extension to pixel art animation remains an unexplored direction. Existing systems typically request users to craft individual pixels frame by frame, which is a tedious and error‐prone process. In this work, we present a novel animation framework tailored to pixel art images. Our system bases on conventional key‐frame animation framework and state‐of‐the‐art image warping techniques to generate an initial animation sequence. The system then jointly optimizes the prominent feature lines of individual frames respecting three metrics that capture the quality of the animation sequence in both spatial and temporal domains. We demonstrate our system by generating visually pleasing animations on a variety of pixel art images, which would otherwise be difficult by applying state‐of‐the‐art techniques due to severe artifacts.

LEGO®, a popular brick-based toy construction system, provides an affordable and convenient way of fabricating geometric shapes. However, building arbitrary shapes using LEGO bricks with restrictive colors and sizes is not trivial. It requires careful design process to produce appealing, stable and constructable brick sculptures. In this work, we investigate the novel problem of constructing brick sculptures from pixel art images. In contrast to previous efforts that focus on 3D models, pixel art contains rich visual contents for generating engaging LEGO designs. On the other hand, the characteristics of pixel art and corresponding brick sculpture pose new challenges to the design process. We present Pixel2Brick, a novel computational framework to automatically construct brick sculptures from pixel art. This is based on implementing a set of design guidelines concerning the visual quality as well as the structural stability of built sculptures. We demonstrate the effectiveness of our framework with various brick sculptures (both real and virtual) generated from a variety of pixel art images. Experimental results show that our framework is efficient and gains significant improvements over state-of-the-arts.

Abstract Surface Ricci flow is a powerful tool to design Riemannian metrics by user defined curvatures. Discrete surface Ricci flow has been broadly applied for surface parameterization, shape analysis, and computational topology. Conventional discrete Ricci flow has limitations. For meshes with low quality triangulations, if high conformality is required, the flow may get stuck at the local optimum of the Ricci energy. If convergence to the global optimum is enforced, the conformality may be sacrificed. This work introduces a novel method to generalize the traditional discrete Ricci flow. The generalized Ricci flow is more flexible, more robust and conformal for meshes with low quality triangulations. Conventional method is based on circle packing, which requires two circles on an edge intersect each other at an acute angle. Generalized method allows the two circles either intersect or separate from each other. This greatly improves the flexibility and robustness of the method. Furthermore, the generalized Ricci flow preserves the convexity of the Ricci energy, this ensures the uniqueness of the global optimum. Therefore the algorithm won't get stuck at the local optimum. Generalized discrete Ricci flow algorithms are explained in details for triangle meshes with both Euclidean and hyperbolic background geometries. Its advantages are demonstrated by theoretic proofs and practical applications in graphics, especially surface parameterization.

This paper presents a novel skeleton-based method for deforming meshes (using an approximate skeleton, rather than a precise medial axis). The significant difference from previous skeleton-based methods is that the latter use the skeleton to control movement of vertices whereas we use it to control the simplices defining the model. By doing so, errors that occur near joints in other methods can be spread over the whole mesh, using an optimization process, resulting in smooth transitions near joints of the skeleton. By controlling simplices, our method has the advantage that no vertex weights need to be defined on the bones, which is a tedious requirement in previous skeleton-based methods. Our method can also easily be extended to control deformation by moving a few chosen line segments or vertices embedded in the object, rather than a skeleton.

Mesh parameterization is a fundamental technique in computer graphics. Our paper focuses on solving the problem of finding the best discrete conformal mapping that also minimizes area distortion. Firstly, we deduce an exact analytical differential formula to represent area distortion by curvature change in the discrete conformal mapping, giving a dynamic Poisson equation. Our result shows the curvature map is invertible. Furthermore, we give the explicit Jacobi matrix of the inverse curvature map. Secondly, we formulate the task of computing conformal parameterizations with least area distortions as a constrained nonlinear optimization problem in curvature space. We deduce explicit conditions for the optima. Thirdly, we give an energy form to measure the area distortions, and show it has a unique global minimum. We use this to design an efficient algorithm, called free boundary curvature diffusion, which is guaranteed to converge to the global minimum. This result proves the common belief that optimal parameterization with least area distortion has a unique solution and can be achieved by free boundary conformal mapping. Major theoretical results and practical algorithms are presented for optimal parameterization based on the inverse curvature map. Comparisons are conducted with existing methods and using different energies. Novel parameterization applications are also introduced.