833 research outputs found
Gap Filling of 3-D Microvascular Networks by Tensor Voting
We present a new algorithm which merges discontinuities in 3-D images of tubular structures presenting undesirable gaps. The application of the proposed method is mainly associated to large 3-D images of microvascular networks. In order to recover the real network topology, we need to ïŹll the gaps between the closest discontinuous vessels. The algorithm presented in this paper aims at achieving this goal. This algorithm is based on the skeletonization of the segmented network followed by a tensor voting method. It permits to merge the most common kinds of discontinuities found in microvascular networks. It is robust, easy to use, and relatively fast. The microvascular network images were obtained using synchrotron tomography imaging at the European Synchrotron Radiation Facility. These images exhibit samples of intracortical networks. Representative results are illustrated
A Phase Field Model for Continuous Clustering on Vector Fields
A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.
Hierarchical interpolative factorization for elliptic operators: differential equations
This paper introduces the hierarchical interpolative factorization for
elliptic partial differential equations (HIF-DE) in two (2D) and three
dimensions (3D). This factorization takes the form of an approximate
generalized LU/LDL decomposition that facilitates the efficient inversion of
the discretized operator. HIF-DE is based on the multifrontal method but uses
skeletonization on the separator fronts to sparsify the dense frontal matrices
and thus reduce the cost. We conjecture that this strategy yields linear
complexity in 2D and quasilinear complexity in 3D. Estimated linear complexity
in 3D can be achieved by skeletonizing the compressed fronts themselves, which
amounts geometrically to a recursive dimensional reduction scheme. Numerical
experiments support our claims and further demonstrate the performance of our
algorithm as a fast direct solver and preconditioner. MATLAB codes are freely
available.Comment: 37 pages, 13 figures, 12 tables; to appear, Comm. Pure Appl. Math.
arXiv admin note: substantial text overlap with arXiv:1307.266
Morphological operations in image processing and analysis
Morphological operations applied in image processing and analysis are becoming increasingly important in today\u27s technology. Morphological operations which are based on set theory, can extract object features by suitable shape (structuring elements). Morphological filters are combinations of morphological operations that transform an image into a quantitative description of its geometrical structure which based on structuring elements. Important applications of morphological operations are shape description, shape recognition, nonlinear filtering, industrial parts inspection, and medical image processing.
In this dissertation, basic morphological operations are reviewed, algorithms and theorems are presented for solving problems in distance transformation, skeletonization, recognition, and nonlinear filtering. A skeletonization algorithm using the maxima-tracking method is introduced to generate a connected skeleton. A modified algorithm is proposed to eliminate non-significant short branches. The back propagation morphology is introduced to reach the roots of morphological filters in only two-scan. The definitions and properties of back propagation morphology are discussed. The two-scan distance transformation is proposed to illustrate the advantage of this new definition.
G-spectrum (geometric spectrum) which based upon the cardinality of a set of non-overlapping segments in an image using morphological operations is presented to be a useful tool not only for shape description but also for shape recognition. The G-spectrum is proven to be translation-, rotation-, and scaling-invariant. The shape likeliness based on G-spectrum is defined as a measurement in shape recognition. Experimental results are also illustrated.
Soft morphological operations which are found to be less sensitive to additive noise and to small variations are the combinations of order statistic and morphological operations. Soft morphological operations commute with thresholding and obey threshold superposition. This threshold decomposition property allows gray-scale signals to be decomposed into binary signals which can be processed by only logic gates in parallel and then binary results can be combined to produce the equivalent output. Thus the implementation and analysis of function-processing soft morphological operations can be done by focusing only on the case of sets which not only are much easier to deal with because their definitions involve only counting the points instead of sorting numbers, but also allow logic gates implementation and parallel pipelined architecture leading to real-time implementation. In general, soft opening and closing are not idempotent operations, but under some constraints the soft opening and closing can be idempotent and the proof is given. The idempotence property gives us the idea of how to choose the structuring element sets and the value of index such that the soft morphological filters will reach the root signals without iterations. Finally, summary and future research of this dissertation are provided
Advanced Water Distribution Modeling and Management
Advanced Water Distribution Modeling and Management builds on Haestad Pressâ Water Distribution Modeling book. Addressing the modeling process from data collection to application, Advanced Water Distribution Modeling and Management adds extensive material from an international team of experts from both academia and consulting firms and includes topics such as: In-depth coverage of optimization techniques for model calibration, system design, and pump operations. Advanced water quality modeling topics including tank mixing, water quality solution algorithms, sampling techniques, tracer studies, tank design, and maintenance of adequate disinfectant residuals. Integration of SCADA systems with water distribution modeling for estimating model demands, initial conditions, and control settings; forecasting system operations; calibrating extended-period simulation models; streamlining water quality analysis; and estimating water loss during a main break. The essentials of transient analysis including the causes and sources of transients, as well as the potential effects of transients on water distribution systems. Application of GIS technology for skeletonization, demand allocation, and pipe break analysis; discussion of the technological issues that arise when integrating GIS and water distribution modeling; and the current state of the technology. Use of models to assess water system vulnerability and security, respond to emergencies in real-time, simulate contamination events, prioritize physical security improvements, and unravel past contamination events
ASKIT: Approximate Skeletonization Kernel-Independent Treecode in High Dimensions
We present a fast algorithm for kernel summation problems in high-dimensions.
These problems appear in computational physics, numerical approximation,
non-parametric statistics, and machine learning. In our context, the sums
depend on a kernel function that is a pair potential defined on a dataset of
points in a high-dimensional Euclidean space. A direct evaluation of the sum
scales quadratically with the number of points. Fast kernel summation methods
can reduce this cost to linear complexity, but the constants involved do not
scale well with the dimensionality of the dataset.
The main algorithmic components of fast kernel summation algorithms are the
separation of the kernel sum between near and far field (which is the basis for
pruning) and the efficient and accurate approximation of the far field.
We introduce novel methods for pruning and approximating the far field. Our
far field approximation requires only kernel evaluations and does not use
analytic expansions. Pruning is not done using bounding boxes but rather
combinatorially using a sparsified nearest-neighbor graph of the input. The
time complexity of our algorithm depends linearly on the ambient dimension. The
error in the algorithm depends on the low-rank approximability of the far
field, which in turn depends on the kernel function and on the intrinsic
dimensionality of the distribution of the points. The error of the far field
approximation does not depend on the ambient dimension.
We present the new algorithm along with experimental results that demonstrate
its performance. We report results for Gaussian kernel sums for 100 million
points in 64 dimensions, for one million points in 1000 dimensions, and for
problems in which the Gaussian kernel has a variable bandwidth. To the best of
our knowledge, all of these experiments are impossible or prohibitively
expensive with existing fast kernel summation methods.Comment: 22 pages, 6 figure
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