Rail track extraction is essential for effective railway asset management and maintenance, especially in automated inspection and mapping workflows. This paper introduces a novel method for extracting rail tracks from classified 3D point clouds using a fully convolutional recurrent neural network that preserves full spatial resolution and is trained exclusively on synthetically generated data. This approach enhances per-pixel quality and is particularly suited for rail track extraction. The proposed method begins by rasterizing points corresponding to railroad tracks, then applies the neural network to reduce noise and yield a cleaner track representation suitable for vectorization [1]. Subsequent morphological operations further refine the resultant data, enabling accurate track centerline extraction. Next, the extracted centerlines undergo smoothing to eliminate residual irregularities [2, 3]. Finally, the algorithm transfers 3D information from lidar points onto 2D polylines and applies additional vertical smoothing. A single centerline for both tracks is found using the Dynamic Time Warping (DTW) algorithm [4]. The final outcome consists of rail top centerlines and track centerlines derived for rail pairs, with minimal manual intervention. Experimental validation confirms the effectiveness of this method in yielding high-quality rail track extraction.

This paper proposes a solution for constructing line features modeling each catenary curve present within a series of points representing multiple catenary curves. The solution can be applied to extract power lines from lidar point clouds, which can then be used in downstream applications like creating digital twin geospatial models and evaluating the encroachment of vegetation. This paper offers an example of how the results obtained by the proposed solution could be used to assess vegetation growth near transmission power lines based on freely available lidar data for the City of Utrecht, Netherlands [1].

Kriging models using five methods for calculating distance between locations on Earth’s surface are discussed. After reviewing statistical literature about kriging on a sphere, we discuss approaches for kriging on an ellipsoid, as well as a computationally intensive kernel convolution approach on an arbitrarily shaped three-dimensional body. Next, we propose computationally efficient kernel convolution algorithm. Then we explain how empirical Bayesian kriging interpolates data in a geographic coordinate system. The biggest computational and modeling advantage of EBK is that it divides data into subsets allowing for fast nonstationary data interpolation. We show by examples that empirical Bayesian kriging with chordal distances works well with both global and local data.

We described the key features of the pragmatic geostatistical methodology aiming at resolving the following drawbacks of classical geostatistical models: assuming that the data is the realization of a stationary process; assuming that the data values are distributed according to Gaussian distribution; describing the data with a single generating model; not accounting for the model uncertainty in prediction; and not supporting coincident data and individual measurement errors. Our variant of empirical Bayesian kriging (EBK) is a fast and reliable solution for both automatic and interactive data interpolation. It can be used for interpolation of very large datasets up to billions of points. The following features are discussed: the informative prior distribution construction and usage; automatic data transformation of the dependent variable into a Gaussian distribution; data subsetting and merging the estimated models; and interpolation over large areas on the earth's surface. We conducted one simulation experiment and two case studies using highly variable data to investigate the EBK predicting quality.

Simplification of polylines is used in many practical applications. However, in some applications, there is an expectation of having straight segments or even the ends of circular arcs of the resultant polyline being aligned to some preferred directions. For example, building footprints are usually aligned to the direction of streets and have orthogonal shapes. This paper extends the compression algorithms [1] to support a user-defined set of preferred directions. This paper also looks into using a graphics processing unit framework to improve the performance of the algorithm.

Using Bayesian bootstrap as the informative prior distribution is a key feature of the empirical Bayesian kriging method. We evaluate correctness of the method using two large simulation experiments. We also compare empirical Bayesian kriging performance with several popular geostatistical models implemented in R using two real datasets: the average annual precipitation in South Africa and the daytime land surface temperature satellite data. Results show that empirical Bayesian kriging performs better than other predictors, and increasingly so with data complexity.

There are many practical applications that require the simplification of polylines. Some of the goals are to reduce the amount of information, improve processing time, or simplify editing. Simplification is usually done by removing some of the vertices, making the resultant polyline go through a subset of the source polyline vertices. If the resultant polyline is required to pass through original vertices, it often results in extra segments, and all segments are likely to be shifted due to fixed endpoints. Therefore, such an approach does not necessarily produce a new polyline with the minimum number of vertices. Using an algorithm that finds the compressed polyline with the minimum number of vertices reduces the amount of memory required and the postprocessing time. However, even more important, when the resultant polylines are edited by an operator, the polylines with the minimum number of vertices decrease the operator time, which reduces the cost of processing the data. A viable solution to finding a polyline within a specified tolerance with the minimum number of vertices is described in this paper.

The task of finding the optimal compression of a polyline with straight-line segments and arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. Optimal compression algorithms find the best solution using the dynamic programming approach, which requires a significant amount of arc fitting. This paper describes an improvement to the dynamic programming approach by reducing the amount of arc fitting necessary to find the optimal solution. Instead of processing from the second to the last vertices in the dynamic programming approach, the algorithm proceeds forward and skips as many steps as possible without affecting the inference in any way. Such a modification extends the practical application of the algorithm to polylines having arcs with a large number of vertices.

We discuss how the kernel convolution approach can be used to accurately approximate the spatial covariance model on a sphere using spherical distances between points. A detailed derivation of the required formulas is provided. The proposed covariance model approximation can be used for non-stationary spatial prediction and simulation in the case when the dataset is large and the covariance model can be estimated separately in the data subsets.

The task of approximating points with circular arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. However, the development of algorithms that perform a significant amount of circular arcs fitting require an efficient way of fitting circular arcs with complexity O(1). The elegant solution to this task based on an eigenvector problem for a square nonsymmetrical matrix is described in [1]. For the compression algorithm described in [2], it is necessary to solve this task when two points on the arc are known. This paper describes a different approach to efficiently fitting the arcs and solves the task when one or two points are known.

One of the most efficient ways to produce unconditional simulations is with the kernel convolution using fast Fourier transform (FFT) [1]. However, when data is located on a surface, this approach is not efficient because data needs to be processed in a three-dimensional enclosing box. This paper describes a novel approach based on integer transformation to reduce the volume of the enclosing box.

One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However, points on the arbitrary surface can be generated randomly using uniform distribution to replace a regular grid. This paper will describe a nonstationary kernel convolution approach for data on arbitrary surfaces.

We discuss two flexible and fast empirical Bayesian kriging models: (1) intrinsic random function of order zero and one and (2) kriging with local data transformation to a Gaussian distribution. In the case of large datasets, all calculations are made in the data subsets, and predictions are made using weighted sums of predictions from different subsets, possibly overlapping. The methodology is illustrated using 1.35 billion samples collected using LiDAR technology.

This paper proposes a new flexible non-parametric data transformation to Gaussian distribution. This option is often required because kriging is the best predictor under squared-error minimization criterion only if the data follow multivariate Gaussian distribution, while environmental data are often best described by skewed distributions with non-negative values and a heavy right tail. We assume that the modeling random field is the result of some nonlinear transformation of a Gaussian random field. In this case, the researchers commonly use a certain parametric monotone (for example, power or logarithmic) or variants of normal score transformation. We discuss drawbacks of these methods and propose a new flexible non-parametric transformation. We compare the performance of simple kriging with the proposed data transformation to several other data transformation methods, including transformation based on a mixture of Gaussian kernels and multiplicative skewing with several base distributions. Our method is flexible, and it can be used for automatic data transformation, for example, in black-box kriging models in emergency situations.

Classifying a set of objects into clusters can be done in numerous ways, producing different results. They can be visually compared using contingency tables [27], mosaicplots [13], fluctuation diagrams [15], tableplots [20] , (modified) parallel coordinates plots [28], Parallel Sets plots [18] or circos diagrams [19]. Unfortunately the interpretability of all these graphical displays decreases rapidly with the numbers of categories and clusterings. In his famous book A Semiology of Graphics [5] Bertin writes “the discovery of an ordered concept appears as the ultimate point in logical simplification since it permits reducing to a single instant the assimilation of series which previously required many instants of study”. Or in more everyday language, if you use good orderings you can see results immediately that with other orderings might take a lot of effort. This is also related to the idea of effect ordering [12], that data should be organised to reflect the effect you want to observe. This paper presents an efficient algorithm based on Bertin's idea and concepts related to Kendall's t [17], which finds informative joint orders for two or more nominal classification variables. We also show how these orderings improve the various displays and how groups of corresponding categories can be detected using a top-down partitioning algorithm. Different clusterings based on data on the environmental performance of cars sold in Germany are used for illustration. All presented methods are available in the R package extracat which is used to compute the optimized orderings for the example dataset.

We discuss features of local polynomial interpolation (LPI), focusing on the problem with unstable solutions of the LPI system of linear equations. We develop a new diagnostic based on condition number values. Also, a variant of Tikhonov regularization is proposed, which allows the production of continuous predictions and prediction standard errors nearly everywhere in the data domain. This variant of LPI can be used in the presence of barriers defined by polylines. LPI model is a good candidate for real time automatic mapping of the data regularly collected from the environmental monitoring networks. We illustrate the LPI usage with both simulated data and real data.

We describe a multivariate version of areal interpolation where both the primary and the secondary cokriging variables can be binomial, negative binomial, or Gaussian. For all data types, we describe model fitting and model diagnostics. Areal kriging can be used as an alternative for traditional choropleth maps because it can better represent the data variability and “hot spots” that are difficult to recognize when the raw data are displayed. Gaussian areal interpolation is the basis for understanding models for count data, and the Gaussian model can be useful for interpolation of air and soil contamination collected in populated places but the exact sample location is unknown. Poisson kriging of count data collected in points and polygons was recently discussed in geostatistical literature. To account for overdispersion in the Poisson process, we extend this model to the negative binomial distribution. Binomial kriging is helpful for interpolation and reaggregation of epidemiological and social data. We show examples of Gaussian, overdispersed Poisson and binomial areal kriging and cokriging interpolation using environmental and epidemiological data. All case studies are prepared using the beta version of ArcGIS Geostatistical Analyst 10.1. The mathematical details of the models described in the main text are provided in the appendix.

Geographic information system (GIS) users often need to disaggregate and reaggregate data collected in polygons, but classical kriging models only allow for data collected in points. We discuss our implementation of areal interpolation, a kriging-based disaggregation technique, in the Geostatistical Analyst extension of ArcGIS 10.1 for Gaussian, binomial, and overdispersed Poisson data. All methods allow for surfaces of prediction standard errors. We also allow for the use of a secondary cokriging variable, which can be any of the three above-mentioned distributions. Our areal interpolation model overcomes several computational problems, such as how to handle polygons of vastly different sizes and how to analyze polygons that are overlapping or disjoint.For Gaussian data averaged over polygons, the output is a surface predicting the value at each individual location. Gaussian polygonal data may arise when continuous point measurements are averaged to polygons in order to protect privacy or reduce overhead, and the original point data is discarded. For polygons containing Poisson counts, the output is a surface predicting the density of counts at each location in the data domain. Our model allows for overdispersed counts and for different observation times between polygons. The output for binomial data is a surface predicting the underlying risk at each location of seeing an individual with a certain trait. Each polygon of the input data must contain a count and a population value. The latter indicates the number of individuals sampled, and the former indicates the number of sampled individuals with a certain trait.Once a prediction surface has been created, predictions can be aggregated back to a new set of polygons. This allows for the collection of data over one set of polygons and the prediction for a different set of polygons. We discuss diagnostic options for determining how well the data fits a model, and we demonstrate areal interpolation with three case studies.

In acute myeloid leukemia (AML), nonrandom clonal chromosome aberrations are detectable in ∼55% of adult cases. Translocation t(8;21)(q22;q22) resulting in the 5′RUNX1/3′RUNX1T1 fusion gene occurs in ∼8% of AML cases. Also, ins(8;21) and ins(21;8) have been described that show a broad heterogeneity at the molecular level with inserted fragment sizes ranging from 2.4 to 44 Mb. Microarray‐based comparative genomic hybridization (arrayCGH) in 49 intermediate‐risk AML and RT‐PCR‐based screening in 532 AML cases allowed the detection of ins(21;8)/ins(8;21) in three cases; arrayCGH and subsequent RT‐PCR revealed an ∼0.5 Mb sized inserted fragment generating the 5′RUNX1/3′RUNX1T1 fusion gene in one case with a submicroscopic ins(21;8)(q22;q22q22) whereas the other two cases were identified by banding analysis and RT‐PCR, respectively. Gene expression profiling (GEP) and a detailed review of the literature highlighted similar biological features of AML cases with ins(21;8)/ins(8;21) and t(8;21)(q22;q22). Our study demonstrates the potential of high‐resolution array‐based analysis and GEP and provides further evidence that AML with insertions generating the 5′RUNX1/3′RUNX1T1 fusion not only biologically resemble the t(8;21)(q22;q22) AML subgroup, but might also share its prognostically favorable clinical behavior. Thus, similar treatment options should be considered in these patients. © 2010 Wiley‐Liss, Inc.

Poor quality, inaccurate or inadequate data can lead to inappropriate assumptions, misleading results, bias and ultimately poor policy and decision making. Finding errors and cleaning data is a time consuming process and requires domain knowledge. This work presents a modified technique – called Interactive Tableplot – for visualizing data and supporting the incorporation of user’s domain knowledge so that erroneous cases are easily revealed. Tableplot is implemented in the software Gauguin (Gribov et al. 2006) that provides techniques for the interactive visual exploration of multivariate datasets.