Distance Transform Research Articles

Solid analysis of micron-sized thin structures with BEM for steady-state heat conduction

Accurate thermal or mechanical analysis of thin structures has been a challenging task for various numerical methods, due to the exceeding closeness of the two neighboring surfaces. In this paper, the micron-sized interior-like thin structures for steady-state heat conduction is investigated with BEM. Three major difficulties would be encountered during solid analysis of thin structures with BEM: 1) degeneracy of the linear systems of equations; 2) evaluation of singular integrals over distorted elements; 3) evaluation of various orders of nearly singular integrals. To investigate the effect of singular and nearly singular integrals independently, the singularity subtraction technique (SST) and nonlinear distance transformation combined with adaptive subdivision method are employed to deal with singular and nearly singular integrals, respectively. Besides, a conformal mapping procedure aligned with sigmoidal transformation in angular direction is proposed to eliminate the near singularity derived from the distortion of element shape. Several challenging numerical examples with characteristic thickness h=10−3, including annular disk, hollow sphere and hollow torus examples, are solved with coarse meshes compared to original methods, and some meaningful conclusions have been obtained.

TSS & TSB: Tensor scale descriptors within circular sectors for fast shape retrieval

We propose two novel region-based descriptors for shape-based image retrieval and analysis, which are built upon an extended tensor scale based on the Euclidean Distance Transform (EDT). First the tensor scale algorithm is applied to extract local structure thickness, orientation, and anisotropy as represented by the largest ellipse within a homogeneous region centered at each image pixel. In this work, we extend the local orientation to 360°. Then, for the first proposed descriptor, named Tensor Scale Sector descriptor (TSS), the local distributions of relative orientations within circular sectors are used to compose a fixed-length feature vector for a region-based representation. For the second method, named Tensor Scale Band descriptor (TSB), we consider histograms of relative orientations for each circular concentric band to compose a fixed-length feature vector with linear time matching. Experimental results with MPEG-7 and MNIST datasets are presented to illustrate and validate the methods. TSS can achieve high retrieval values comparable to state-of-the-art methods, which usually rely on time-consuming correspondence optimization algorithms, but uses a simpler and faster distance function, while the even faster linear complexity of TSB leads to a suitable and better solution for very large shape collections.

Line Parameter based Word-Level Indic Script Identification System

In this paper, a line parameter based approach is presented to identify the handwritten scripts written in eight popular scripts. Since Optical Character Recognition (OCR) engines are usually script-dependent, automatic text recognition in multi-script environment requires a pre-processing module that helps identifying the scripts before processing the same through the respective OCR engine. The work becomes more challenging when it deals with handwritten document which is still a less explored research area. In this paper, a line parameter based approach is presented to identify the handwritten scripts written in eight popular scripts namely, Bangla, Devanagari, Gujarati, Gurumukhi, Manipuri, Oriya, Urdu, and Roman. A combination of Hough transform (HT) and Distance transform (DT) is used to extract the directional spatial features based on the line parameter. Experimentations are performed at word-level using multiple classifiers on a dataset of 12000 handwritten word images and Multi Layer Perceptron (MLP) classifier is found to be the best performing classifier showing an identification accuracy of 95.28%. The performance of the present technique is also compared with those of other state-of-the-art script identification methods on the same database. A combination of Hough transform (HT) and Distance transform (DT) is used to extract the directional spatial features based on the line parameter. Experimentation are performed at word-level on a total dataset of 12000 handwritten word images and Multi Layer Perceptron (MLP) classifier is found to be the best performing classifier showing an identification accuracy of 95.28%.

Feature based fuzzy inference system for segmentation of low-contrast infrared ship images

Segmentation of infrared ship target is important for sea surveillance system. However, as a result of the deficiencies of infrared images, the segmentation of infrared ship image becomes a challenge. For the purpose of addressing this problem, a feature based infrared ship image segmentation method utilizing the fuzzy inference system is proposed. Firstly, the intensity feature is extracted by applying unimodal threshold, which could preserve the low-contrast pixels in the infrared images. Secondly, the local spatial feature is extracted by employing saliency detection, region growing and morphology processing, which could express the shape of the target. Thirdly, the global spatial feature is extracted by utilizing partial region growing and weighted distance transformation, which could suppress the background. Then these features are fuzzified using accommodative ways and prior knowledge. And in light of the fuzzy rules based upon expert knowledge, these fuzzified features are integrated in fuzzy inference system. Finally, the complete target could be directly segmented from the output of the fuzzy inference system. Experimental results illustrate that the proposed method could effectively extract more intact targets from the low-contrast infrared ship images. Additionally, the proposed method outperforms some existed segmentation methods.

LAND USE CHANGE IN SUBURBAN AREA: A CASE OF MALANG CITY, EAST JAVA PROVINCE

The development of suburban areas of Malang City has developed an expansion of built-up areas between urban and suburban areas. There has been a great phenomenon that mostly occurs along the suburban areas where industrial activities took place. This study aims to determine what factors have influenced the land use change in the suburban areas of Malang City by employing “GeoDa” application. It is one of the Geographical Information System applications that particularly deals with statistical analysis. To achieve this purpose, the objectives are: delineating the study area, analyzing the characteristics of land use change, assessing and analyzing the variable influencing the land use change. The results have shown that the characteristics of land use change, such as population, distance, migration, and occupation transformation are directly proportional to the land use change. It has also been identified that the high level of density is only located in the surrounding areas of industries. From the assessed variables through the statistical model, population (X1), density (X2) and migration (X3) are found as the influencing factors of land use change.

Guest Editorial: Shape Analysis Beyond the Eikonal Equation

“Shape Analysis” is an interesting research area which contains many thought-provoking problems and mathematical challenges, especially at the representation level. Shape of an object is considered as the enclosing surface (the boundary) or the enclosed interior. One of the major challenges is to define representations of “shapes” that can be manipulated by image processing methods. This is an important need in practice because more often than not shapes need to be extracted or recovered from raw images; moreover, the process of recovering shapes from raw images highly benefits from prior knowledge of candidate shapes. One of the key means of shape representation is the Euclidean Distance Transform (EDT), which is governed by the Eikonal Equation. The values of the EDT at each interior point give the distance to the nearest boundary point. This distance notion is used in almost any problem that requires integrating shape and image information; e.g., a rich variety of shape guided image-processing or shape extraction tasks. Especially in the 1990s, the idea of embedding shapes as zeros of the signed EDT is highly popularized by the level-set framework and its fast implementation, leading to a booming research area in implicit shape representations. However, as challenging problems are developed, formulations that move beyond the classical Eikonal Equation emerged. This special issue consists of six papers each exploring an interesting direction moving beyond the Eikonal formulation in the field of Shape Analysis. The first two papers, “Analysis and Approximation of some Shape–from–Shading Models for non-Lambertian Surfaces” and “A Unified Variational Volume Registration Method based on Automatically Learned Brain Structures”, deal with two key applications that jointly involve shapes and images. In the first paper, Silvia Tozza and Maurizio Falcone present a unified mathematical formulation of some non-Lambertian models, which lead to more complex stationary nonlinear partial differential equations of Hamilton-Jacobi type which can be regarded as a generalization of the classical Eikonal Equation corresponding to the Lambertian case. In the second paper, Carl Lederman et al. present an active volume technique employing level sets of the distance function. Unlike the common practice, the level sets in their formulation are only utilized on their respective regions and not on the whole domain, making the computations feasible as the number of regions increases. The next four papers propose alternative distance notions or computations. They are briefly discussed as follows. In “Affine Invariant Distance Using Multiscale Analysis”, Luis Alvarez et al. present a distance transform for planar shapes that is invariant under any planar projection of the

Use of the Distance Transform for Integration of Local Measurements: Principle and Application in Chemical Engineering.

We propose an original methodology to integrate local measurement for nontrivial object shape. The method employs the distance transform of the object and least-square fitting of numerically computed weighting functions extracted from it. The method is exemplified in the field of chemical engineering by calculating the global metal concentration in catalyst grains from uneven metal distribution profiles. Applying the methodology on synthetic profiles with the help of a very simple deposition model allows us to evaluate the accuracy of the method. For high symmetry objects such as an infinite cylinder, relative errors on global concentration are lower than 1% for well-resolved profiles. For a less symmetrical object, a tetralobe, the best estimator gives a relative error below 5% at the cost of increased measurement time. Applicability on a real case is demonstrated on an aged hydrodemetallation catalyst. Sampling of catalyst grains at the inlet and outlet of the reactor allowed conclusions concerning different reactivity for the trapped metals.

Shape-based features for reliable action recognition using spectral regression discriminant analysis

This paper deals with the classification task of human activities in videos with learning using different image sequences as input methods. Image sequences of purely binary silhouette (or shape), that is Raw Silhouette Representation (RSR), distance transform (DT) images of RSR, edge images of RSR, Silhouette History Image (SHI) and Silhouette Energy Image (SEI), image sequences of Wavelet Transform (WT) are used for training and testing using spectral regression discriminant analysis. Hausdorff distance was used for similarity measures to match the embedded action trajectories. Then action classification is achieved in a K-nearest neighbour framework. Using these different input methods we achieved 100% for all the cases except WT cases. From the results, it is evident that SHI and SEI are effective input method in terms of time and space consumption.

Shape-based features for reliable action recognition using spectral regression discriminant analysis

This paper deals with the classification task of human activities in videos with learning using different image sequences as input methods. Image sequences of purely binary silhouette (or shape), that is Raw Silhouette Representation (RSR), distance transform (DT) images of RSR, edge images of RSR, Silhouette History Image (SHI) and Silhouette Energy Image (SEI), image sequences of Wavelet Transform (WT) are used for training and testing using spectral regression discriminant analysis. Hausdorff distance was used for similarity measures to match the embedded action trajectories. Then action classification is achieved in a K-nearest neighbour framework. Using these different input methods we achieved 100% for all the cases except WT cases. From the results, it is evident that SHI and SEI are effective input method in terms of time and space consumption.

Skeleton-based tracing of curved fibers from 3D X-ray microtomographic imaging

A skeleton-based fiber tracing algorithm is described and applied on a specific fibrous material, porous metal fiber sintered sheet (PMFSS), featuring high porosity and curved fibers. The skeleton segments are firstly categorized according to the connectivity of the skeleton paths. Spurious segments like fiber bonds are detected making extensive use of the distance transform (DT) values. Single fibers are then traced and reconstructed by consecutively choosing the connecting skeleton segment pairs that show the most similar orientations and radius. Moreover, to reduce the misconnection due to the tracing orders, a multilevel tracing strategy is proposed. The fibrous network is finally reconstructed by dilating single fibers according to the DT values. Based on the traced single fibers, various morphology information regarding fiber length, radius, orientation, and tortuosity are quantitatively analyzed and compared with our previous results (Wang et al., 2013). Moreover, the number of bonds per fibers are firstly accessed. The methodology described in this paper can be expanded to other fibrous materials with adapted parameters.

Social Distance and Knowledge Transformation: The Effects of Social Network Distance on Organizational Learning

Organizations are increasingly adopting technologies to promote knowledge sharing across boundaries of specialized groups. Yet, prior research beginning with March (1991) suggests that such knowledge-sharing technologies actually inhibit organizational learning by reducing solution diversity. This line of reasoning stems from the prior literature’s assumption that the knowledge shared will be transferred from one member to another perfectly and without distortion. We challenge this assumption and argue, instead, that knowledge is often altered or transformed when it is shared between members and that the degree of this transformation increases as the social distance between the knowledge sender and receiver increases. Because the implementation of knowledge-sharing technologies encourages learning between members across greater social distances, it increases knowledge transformation. Thus, knowledge-sharing technologies present a new opportunity to diversify solutions and lead to innovation.

Geodesic Distance Algorithm for Extracting the Ascending Aorta from 3D CT Images.

This paper presents a method for the automatic 3D segmentation of the ascending aorta from coronary computed tomography angiography (CCTA). The segmentation is performed in three steps. First, the initial seed points are selected by minimizing a newly proposed energy function across the Hough circles. Second, the ascending aorta is segmented by geodesic distance transformation. Third, the seed points are effectively transferred through the next axial slice by a novel transfer function. Experiments are performed using a database composed of 10 patients' CCTA images. For the experiment, the ground truths are annotated manually on the axial image slices by a medical expert. A comparative evaluation with state-of-the-art commercial aorta segmentation algorithms shows that our approach is computationally more efficient and accurate under the DSC (Dice Similarity Coefficient) measurements.

Automated detection of epileptic EEGs using a novel fusion feature and extreme learning machine

Automated seizure detection using EEG has gained increasing attraction in recent years and appeared more and more helpful in both diagnosis and treatment. How to design an appropriate feature extraction method and how to select an efficient classifier are recognized to be crucial in the successful realization. This paper first proposes a new Mahalanobis-similarity-based feature extraction method on the basis of the Mahalanobis distance and discrete wavelet transformation (DWT). Then in order to further improve the performance, this paper designs a fusion feature (MS-SE-FF) in the feature-fusion level, where the Mahalanobis-similarity-based feature characterizing the similarity between signals and the sample-entropy-based feature characterizing the complexity of signals are combined together. Finally, an automated seizure detection method FF-ELM-SD has been built, which is integrated between the novel fusion feature MS-SE-FF and extreme learning machine (ELM). Experimental results demonstrate that the proposed method FF-ELM-SD does a good job in the epileptic seizure detection while preserving the efficiency and simplicity.

Different Methods for Determining Porosity of Gas Diffusion Layer using X-ray Microtomography

Gas diffusion layer (GDL) is a crucial component in polymer electrode membrane fuel cells. Being highly porous, this layer facilitates transport of species from the flow field to the reaction sites and vice versa. One of the main characteristics of GDLs is porosity, which has been measured using a number of different methods including 3D X-ray microtomography (μ XCT). Despite the extensive use of this technique in investigating the properties of GDLs, there are variations in the results since the surface of the three dimensional volume used to obtain the bulk porosity of GDLs is difficult to quantify. In this paper, a robust surface identification method, referred to as “Rolling Ball”, is introduced to identify systematically the surface and hence porosity of GDLs from μ XCT datasets. In this method, the diameter of the GDL carbon fiber is used as the characteristic length in combination with a Distance Transform (DT) to robustly identify the surface topology. This method is then used to estimate porosity of four different samples of a highly porous GDL, SGL 25BA. The results between different samples show great consistency. A comparison with other methods is also performed, and variations in the bulk and in-plane porosity are observed. The main advantage of the proposed Rolling Ball method compared to prior methods used in the literature is that it uses the carbon fiber diameter to identify the surface results in a systematic fashion. This methodology can be easily applied to other highly porous media.

An Approach to Optimum Route and Site Selection of a Steam Gathering System for Geothermal Power Plants Using Multiple Weight Distance Transform

This article proposes a new approach to select the location for separators and routes for two phase flow pipelines in a geothermal steam gathering system. Multiple weight distance transform is presented and used to find the optimum location of site for a steam separator based on the flow capacity of geothermal wells. The routes are monotonic and the incline is slight in order to minimize the pressure drop and the slug flow conditions in the pipeline. A map with weighted distance for five wells shows the accessible area and the route from each well is calculated. The optimum site location reduces the total pipe length from all wells by 9%.

Automatic Liver Segmentation Based on Shape Constraints and Deformable Graph Cut in CT Images.

Liver segmentation is still a challenging task in medical image processing area due to the complexity of the liver's anatomy, low contrast with adjacent organs, and presence of pathologies. This investigation was used to develop and validate an automated method to segment livers in CT images. The proposed framework consists of three steps: 1) preprocessing; 2) initialization; and 3) segmentation. In the first step, a statistical shape model is constructed based on the principal component analysis and the input image is smoothed using curvature anisotropic diffusion filtering. In the second step, the mean shape model is moved using thresholding and Euclidean distance transformation to obtain a coarse position in a test image, and then the initial mesh is locally and iteratively deformed to the coarse boundary, which is constrained to stay close to a subspace of shapes describing the anatomical variability. Finally, in order to accurately detect the liver surface, deformable graph cut was proposed, which effectively integrates the properties and inter-relationship of the input images and initialized surface. The proposed method was evaluated on 50 CT scan images, which are publicly available in two databases Sliver07 and 3Dircadb. The experimental results showed that the proposed method was effective and accurate for detection of the liver surface.

Viewpoint-independent 3D object segmentation for randomly stacked objects using optical object detection

This work proposes a novel approach to segmenting randomly stacked objects in unstructured 3D point clouds, which are acquired by a random-speckle 3D imaging system for the purpose of automated object detection and reconstruction. An innovative algorithm is proposed; it is based on a novel concept of 3D watershed segmentation and the strategies for resolving over-segmentation and under-segmentation problems. Acquired 3D point clouds are first transformed into a corresponding orthogonally projected depth map along the optical imaging axis of the 3D sensor. A 3D watershed algorithm based on the process of distance transformation is then performed to detect the boundary, called the edge dam, between stacked objects and thereby to segment point clouds individually belonging to two stacked objects. Most importantly, an object-matching algorithm is developed to solve the over- and under-segmentation problems that may arise during the watershed segmentation. The feasibility and effectiveness of the method are confirmed experimentally. The results reveal that the proposed method is a fast and effective scheme for the detection and reconstruction of a 3D object in a random stack of such objects. In the experiments, the precision of the segmentation exceeds 95% and the recall exceeds 80%.

Extraction of microcracks in rock images based on heuristic graph searching and application

In this paper, we propose a new method, based on a graph searching technique, for microcrack extraction from scanning electron microscopic images of rocks. This method mainly focuses on how to detect the crack and extract it, and then quantify some basic geometrical features. The crack can be detected automatically with the aid of two endpoints of the crack. The algorithm involves the following process: the A⁎ graph searching technique is first used to find a path throughout the crack region, defined by the initial two endpoints; the pixels of the path will be used as the seeds for the region growing method to restore the primary crack area; then, an automatic filling holes’ operation is used to remove the possible holes in the region growing result; the medial axis and distance transformation of the crack area are acquired, and then the final crack is rebuilt by painting disks along a medial axis without branches. The crack result is separated without interaction. In the remaining parts, the crack features are quantified, such as the length, width, angle and area, and error analysis shows that the error percentage of the proposed approach reduces to a low level with actual width increases, and results of some example images are illustrated. The algorithm is efficient and can also be used for image detection of other linear structural objects.

A unified framework for isotropic meshing based on narrow-band Euclidean distance transformation

In this paper, we propose a simple-yet-effective method for isotropic meshing relying on Euclidean distance transformation based centroidal Voronoi tessellation (CVT). Our approach improves the performance and robustness of computing CVT on curved domains while simultaneously providing high-quality output meshes. While conventional extrinsic methods compute CVTs in the entire volume bounded by the input model, we restrict the computation to a 3D shell of user-controlled thickness. Taking voxels which contain surface samples as sites, we compute the exact Euclidean distance transform on the GPU. Our algorithm is parallel and memory-efficient, and can construct the shell space for resolutions up to 20483 at interactive speed. The 3D centroidal Voronoi tessellation and restricted Voronoi diagrams are also computed efficiently on the GPU. Since the shell space can bridge holes and gaps smaller than a certain tolerance, and tolerate non-manifold edges and degenerate triangles, our algorithm can handle models with such defects, which typically cause conventional remeshing methods to fail. Our method can process implicit surfaces, polyhedral surfaces, and point clouds in a unified framework. Computational results show that our GPU-based isotropic meshing algorithm produces results comparable to state-of- the-art techniques, but is significantly faster than conventional CPU-based implementations.

Precise Euclidean distance transforms in 3D from voxel coverage representation

Distance transforms (DTs) are, usually, defined on a binary image as a mapping from each background element to the distance between its centre and the centre of the closest object element. However, due to discretization effects, such DTs have limited precision, including reduced rotational and translational invariance. We show in this paper that a significant improvement in performance of Euclidean DTs can be achieved if voxel coverage values are utilized and the position of an object boundary is estimated with sub-voxel precision. We propose two algorithms of linear time complexity for estimating Euclidean DT with sub-voxel precision. The evaluation confirms that both algorithms provide 4–14 times increased accuracy compared to what is achievable from a binary object representation.