Voxelization algorithms for geospatial applications: Computational methods for voxelating spatial datasets of 3D city models containing 3D surface, curve and point data models.
ABSTRACT: Voxel representations have been used for years in scientific computation and medical imaging. The main focus of our research is to provide easy access to methods for making large-scale voxel models of built environment for environmental modelling studies while ensuring they are spatially correct, meaning they correctly represent topological and semantic relations among objects. In this article, we present algorithms that generate voxels (volumetric pixels) out of point cloud, curve, or surface objects. The algorithms for voxelization of surfaces and curves are a customization of the topological voxelization approach ; we additionally provide an extension of this method for voxelization of point clouds. The developed software has the following advantages:•It provides easy management of connectivity levels in the resulting voxels.•It is not dependant on any external library except for primitive types and constructs; therefore, it is easy to integrate them in any application.•One of the algorithms is implemented in C++ and C for platform independence and efficiency.
Project description:Transcriptional profiling of mouse brain voxels from a single coronal slice of the mouse brain comparing each voxel to whole mouse brain RNA. Goal was to determine the gene expression profiles for the mouse genome in a coronal slice of the mouse brain. Keywords: Genetic modification Overall design: Two-condition experiment, Voxel vs. Whole Brain RNA. Biological replicates: 3 independent datasets from mouse brains, independently harvested. One voxel replicate per array.
Project description:<h4>Background</h4>Support vector machine (SVM) has been widely used as accurate and reliable method to decipher brain patterns from functional MRI (fMRI) data. Previous studies have not found a clear benefit for non-linear (polynomial kernel) SVM versus linear one. Here, a more effective non-linear SVM using radial basis function (RBF) kernel is compared with linear SVM. Different from traditional studies which focused either merely on the evaluation of different types of SVM or the voxel selection methods, we aimed to investigate the overall performance of linear and RBF SVM for fMRI classification together with voxel selection schemes on classification accuracy and time-consuming.<h4>Methodology/principal findings</h4>Six different voxel selection methods were employed to decide which voxels of fMRI data would be included in SVM classifiers with linear and RBF kernels in classifying 4-category objects. Then the overall performances of voxel selection and classification methods were compared. Results showed that: (1) Voxel selection had an important impact on the classification accuracy of the classifiers: in a relative low dimensional feature space, RBF SVM outperformed linear SVM significantly; in a relative high dimensional space, linear SVM performed better than its counterpart; (2) Considering the classification accuracy and time-consuming holistically, linear SVM with relative more voxels as features and RBF SVM with small set of voxels (after PCA) could achieve the better accuracy and cost shorter time.<h4>Conclusions/significance</h4>The present work provides the first empirical result of linear and RBF SVM in classification of fMRI data, combined with voxel selection methods. Based on the findings, if only classification accuracy was concerned, RBF SVM with appropriate small voxels and linear SVM with relative more voxels were two suggested solutions; if users concerned more about the computational time, RBF SVM with relative small set of voxels when part of the principal components were kept as features was a better choice.
Project description:BACKGROUND:3D segmentation is often a prerequisite for 3D object display and quantitative measurements. Yet existing voxel-based methods do not directly give information on the object surface or topology. As for spatially continuous approaches such as level-set, active contours and meshes, although providing surfaces and concise shape description, they are generally not suitable for multiple object segmentation and/or for objects with an irregular shape, which can hamper their adoption by bioimage analysts. RESULTS:We developed LimeSeg, a computationally efficient and spatially continuous 3D segmentation method. LimeSeg is easy-to-use and can process many and/or highly convoluted objects. Based on the concept of SURFace ELements ("Surfels"), LimeSeg resembles a highly coarse-grained simulation of a lipid membrane in which a set of particles, analogous to lipid molecules, are attracted to local image maxima. The particles are self-generating and self-destructing thus providing the ability for the membrane to evolve towards the contour of the objects of interest. The capabilities of LimeSeg: simultaneous segmentation of numerous non overlapping objects, segmentation of highly convoluted objects and robustness for big datasets are demonstrated on experimental use cases (epithelial cells, brain MRI and FIB-SEM dataset of cellular membrane system respectively). CONCLUSION:In conclusion, we implemented a new and efficient 3D surface reconstruction plugin adapted for various sources of images, which is deployed in the user-friendly and well-known ImageJ environment.
Project description:The initial output of a time-resolved macromolecular crystallography experiment is a time-dependent series of difference electron density maps that displays the time-dependent changes in underlying structure as a reaction progresses. The goal is to interpret such data in terms of a small number of crystallographically refinable, time-independent structures, each associated with a reaction intermediate; to establish the pathways and rate coefficients by which these intermediates interconvert; and thereby to elucidate a chemical kinetic mechanism. One strategy toward achieving this goal is to use cluster analysis, a statistical method that groups objects based on their similarity. If the difference electron density at a particular voxel in the time-dependent difference electron density (TDED) maps is sensitive to the presence of one and only one intermediate, then its temporal evolution will exactly parallel the concentration profile of that intermediate with time. The rationale is therefore to cluster voxels with respect to the shapes of their TDEDs, so that each group or cluster of voxels corresponds to one structural intermediate. Clusters of voxels whose TDEDs reflect the presence of two or more specific intermediates can also be identified. From such groupings one can then infer the number of intermediates, obtain their time-independent difference density characteristics, and refine the structure of each intermediate. We review the principles of cluster analysis and clustering algorithms in a crystallographic context, and describe the application of the method to simulated and experimental time-resolved crystallographic data for the photocycle of photoactive yellow protein.
Project description:Mobile laser scanning (MLS) is a modern and powerful technology capable of obtaining massive point clouds of objects in a short period of time. Although this technology is nowadays being widely applied in urban cartography and 3D city modelling, it has some drawbacks that need to be avoided in order to strengthen it. One of the most important shortcomings of MLS data is concerned with the fact that it provides an unstructured dataset whose processing is very time-consuming. Consequently, there is a growing interest in developing algorithms for the automatic extraction of useful information from MLS point clouds. This work is focused on establishing a methodology and developing an algorithm to detect pole-like objects and classify them into several categories using MLS datasets. The developed procedure starts with the discretization of the point cloud by means of a voxelization, in order to simplify and reduce the processing time in the segmentation process. In turn, a heuristic segmentation algorithm was developed to detect pole-like objects in the MLS point cloud. Finally, two supervised classification algorithms, linear discriminant analysis and support vector machines, were used to distinguish between the different types of poles in the point cloud. The predictors are the principal component eigenvalues obtained from the Cartesian coordinates of the laser points, the range of the Z coordinate, and some shape-related indexes. The performance of the method was tested in an urban area with 123 poles of different categories. Very encouraging results were obtained, since the accuracy rate was over 90%.
Project description:Neuroimaging studies aim to analyze imaging data with complex spatial patterns in a large number of locations (called voxels) on a two-dimensional (2D) surface or in a 3D volume. Conventional analyses of imaging data include two sequential steps: spatially smoothing imaging data and then independently fitting a statistical model at each voxel. However, conventional analyses suffer from the same amount of smoothing throughout the whole image, the arbitrary choice of smoothing extent, and low statistical power in detecting spatial patterns. We propose a multiscale adaptive regression model (MARM) to integrate the propagation-separation (PS) approach (Polzehl and Spokoiny, 2000, 2006) with statistical modeling at each voxel for spatial and adaptive analysis of neuroimaging data from multiple subjects. MARM has three features: being spatial, being hierarchical, and being adaptive. We use a multiscale adaptive estimation and testing procedure (MAET) to utilize imaging observations from the neighboring voxels of the current voxel to adaptively calculate parameter estimates and test statistics. Theoretically, we establish consistency and asymptotic normality of the adaptive parameter estimates and the asymptotic distribution of the adaptive test statistics. Our simulation studies and real data analysis confirm that MARM significantly outperforms conventional analyses of imaging data.
Project description:A ubiquitous environment for road travel that uses wireless networks requires the minimization of data exchange between vehicles. An algorithm that can segment the ground in real time is necessary to obtain location data between vehicles simultaneously executing autonomous drive. This paper proposes a framework for segmenting the ground in real time using a sparse three-dimensional (3D) point cloud acquired from undulating terrain. A sparse 3D point cloud can be acquired by scanning the geography using light detection and ranging (LiDAR) sensors. For efficient ground segmentation, 3D point clouds are quantized in units of volume pixels (voxels) and overlapping data is eliminated. We reduce nonoverlapping voxels to two dimensions by implementing a lowermost heightmap. The ground area is determined on the basis of the number of voxels in each voxel group. We execute ground segmentation in real time by proposing an approach to minimize the comparison between neighboring voxels. Furthermore, we experimentally verify that ground segmentation can be executed at about 19.31 ms per frame.
Project description:Models of diffusion MRI within a voxel are useful for making inferences about the properties of the tissue and inferring fiber orientation distribution used by tractography algorithms. A useful model must fit the data accurately. However, evaluations of model-accuracy of commonly used models have not been published before. Here, we evaluate model-accuracy of the two main classes of diffusion MRI models. The diffusion tensor model (DTM) summarizes diffusion as a 3-dimensional Gaussian distribution. Sparse fascicle models (SFM) summarize the signal as a sum of signals originating from a collection of fascicles oriented in different directions. We use cross-validation to assess model-accuracy at different gradient amplitudes (b-values) throughout the white matter. Specifically, we fit each model to all the white matter voxels in one data set and then use the model to predict a second, independent data set. This is the first evaluation of model-accuracy of these models. In most of the white matter the DTM predicts the data more accurately than test-retest reliability; SFM model-accuracy is higher than test-retest reliability and also higher than the DTM model-accuracy, particularly for measurements with (a) a b-value above 1000 in locations containing fiber crossings, and (b) in the regions of the brain surrounding the optic radiations. The SFM also has better parameter-validity: it more accurately estimates the fiber orientation distribution function (fODF) in each voxel, which is useful for fiber tracking.
Project description:The aim of this paper is to develop a functional-mixed effects modeling (FMEM) framework for the joint analysis of high-dimensional imaging data in a large number of locations (called voxels) of a three-dimensional volume with a set of genetic markers and clinical covariates. Our FMEM is extremely useful for efficiently carrying out the candidate gene approaches in imaging genetic studies. FMEM consists of two novel components including a mixed effects model for modeling nonlinear genetic effects on imaging phenotypes by introducing the genetic random effects at each voxel and a jumping surface model for modeling the variance components of the genetic random effects and fixed effects as piecewise smooth functions of the voxels. Moreover, FMEM naturally accommodates the correlation structure of the genetic markers at each voxel, while the jumping surface model explicitly incorporates the intrinsically spatial smoothness of the imaging data. We propose a novel two-stage adaptive smoothing procedure to spatially estimate the piecewise smooth functions, particularly the irregular functional genetic variance components, while preserving their edges among different piecewise-smooth regions. We develop weighted likelihood ratio tests and derive their exact approximations to test the effect of the genetic markers across voxels. Simulation studies show that FMEM significantly outperforms voxel-wise approaches in terms of higher sensitivity and specificity to identify regions of interest for carrying out candidate genetic mapping in imaging genetic studies. Finally, FMEM is used to identify brain regions affected by three candidate genes including CR1, CD2AP, and PICALM, thereby hoping to shed light on the pathological interactions between these candidate genes and brain structure and function.
Project description:Volumetric models with known biases are shown to provide bounds for the uncertainty in estimations of volume for ecologically interesting objects, observed with a terrestrial laser scanner (TLS) instrument. Bounding cuboids, three-dimensional convex hull polygons, voxels, the Outer Hull Model and Square Based Columns (SBCs) are considered for their ability to estimate the volume of temperate and tropical trees, as well as geomorphological features such as bluffs and saltmarsh creeks. For temperate trees, supplementary geometric models are evaluated for their ability to bound the uncertainty in cylinder-based reconstructions, finding that coarser volumetric methods do not currently constrain volume meaningfully, but may be helpful with further refinement, or in hybridized models. Three-dimensional convex hull polygons consistently overestimate object volume, and SBCs consistently underestimate volume. Voxel estimations vary in their bias, due to the point density of the TLS data, and occlusion, particularly in trees. The response of the models to parametrization is analysed, observing unexpected trends in the SBC estimates for the drumlin dataset. Establishing that this result is due to the resolution of the TLS observations being insufficient to support the resolution of the geometric model, it is suggested that geometric models with predictable outcomes can also highlight data quality issues when they produce illogical results.