Decimation Steps Research Articles

A point cloud filtering method based on anisotropic error model

AbstractMany modelling applications require 3D meshes that should be generated from filtered/cleaned point clouds. This paper proposes a methodology for filtering of terrestrial laser scanner (TLS)‐derived point clouds, consisting of two main parts: an anisotropic point error model and the subsequent decimation steps for elimination of low‐quality points. The point error model can compute the positional quality of any point in the form of error ellipsoids. It is formulated as a function of the angular/mechanical stability, sensor‐to‐object distance, laser beam's incidence angle and surface reflectivity, which are the most dominant error sources. In a block of several co‐registered point clouds, some parts of the target object are sampled by multiple scans with different positional quality patterns. This situation results in redundant data. The proposed decimation steps removes this redundancy by selecting only the points with the highest positional quality. Finally, the Good, Bad, and the Better algorithm, based on the ray‐tracing concept, was developed to remove the remaining redundancy due to the Moiré effects. The resulting point cloud consists of only the points with the highest positional quality while reducing the number of points by factor 10. This novel approach resulted in final surface meshes that are accurate, contain predefined level of random errors and require almost no manual intervention.

Zero-site density matrix renormalization group and the optimal low-rank correction

A zero-site density matrix renormalization algorithm (DMRG0) is proposed to minimize the energy of matrix product states (MPS). Instead of the site tensors themselves, we propose to optimize sequentially the "message" tensors between neighbor sites, which contain the singular values of the bipartition. This leads to a local minimization step that is independent of the physical dimension of the site. Conceptually, it separates the optimization and decimation steps in DMRG. Furthermore, we introduce two new global perturbations based on the optimal low-rank correction to the current state, which are used to avoid local minima. They are determined variationally as the MPS closest to the one-step correction of the Lanczos or Jacobi-Davidson eigensolver, respectively. These perturbations mainly decrease the energy and are free of hand-tuned parameters. Compared to existing single-site enrichment proposals, our approach gives similar convergence ratios per sweep while the computations are cheaper by construction. Our methods may be useful in systems with many physical degrees of freedom per lattice site. We test our approach on the periodic Heisenberg spin chain for various spins, and on free electrons on the lattice.

Effect of the image resolution on the statistical descriptors of heterogeneous media

The characterization and reconstruction of heterogeneous materials, such as porous media and electrode materials, involve the application of image processing methods to data acquired by scanning electron microscopy or other microscopy techniques. Among them, binarization and decimation are critical in order to compute the correlation functions that characterize the microstructure of the above-mentioned materials. In this study, we present a theoretical analysis of the effects of the image-size reduction, due to the progressive and sequential decimation of the original image. Three different decimation procedures (random, bilinear, and bicubic) were implemented and their consequences on the discrete correlation functions (two-point, line-path, and pore-size distribution) and the coarseness (derived from the local volume fraction) are reported and analyzed. The chosen statistical descriptors (correlation functions and coarseness) are typically employed to characterize and reconstruct heterogeneous materials. A normalization for each of the correlation functions has been performed. When the loss of statistical information has not been significant for a decimated image, its normalized correlation function is forecast by the trend of the original image (reference function). In contrast, when the decimated image does not hold statistical evidence of the original one, the normalized correlation function diverts from the reference function. Moreover, the equally weighted sum of the average of the squared difference, between the discrete correlation functions of the decimated images and the reference functions, leads to a definition of an overall error. During the first stages of the gradual decimation, the error remains relatively small and independent of the decimation procedure. Above a threshold defined by the correlation length of the reference function, the error becomes a function of the number of decimation steps. At this stage, some statistical information is lost and the error becomes dependent on the decimation procedure. These results may help us to restrict the amount of information that one can afford to lose during a decimation process, in order to reduce the computational and memory cost, when one aims to diminish the time consumed by a characterization or reconstruction technique, yet maintaining the statistical quality of the digitized sample.

Nested cages

Many tasks in geometry processing and physical simulation benefit from multiresolution hierarchies. One important characteristic across a variety of applications is that coarser layers strictly encage finer layers, nesting one another. Existing techniques such as surface mesh decimation, voxelization, or contouring distance level sets do not provide sufficient control over the quality of the output surfaces while maintaining strict nesting. We propose a solution that enables use of application-specific decimation and quality metrics. The method constructs each next-coarsest level of the hierarchy, using a sequence of decimation, flow, and contact-aware optimization steps. From coarse to fine, each layer then fully encages the next while retaining a snug fit. The method is applicable to a wide variety of shapes of complex geometry and topology. We demonstrate the effectiveness of our nested cages not only for multigrid solvers, but also for conservative collision detection, domain discretization for elastic simulation, and cage-based geometric modeling.

NMR Data Analysis: A Time-Domain Parametric Approach Using Adaptive Subband Decomposition

This paper presents a fast time-domain data analysis method for one- and two-dimensional Nuclear Magnetic Resonance (NMR) spectroscopy, assuming Lorentzian lineshapes, based on an adaptive spectral decomposition. The latter is achieved through successive filtering and decimation steps ending up in a decomposition tree. At each node of the tree, the parameters of the corresponding subband signal are estimated using some high-resolution method. The resulting estimation error is then processed through a stopping criterion which allows one to decide whether the decimation should be carried on or not. Thus the method leads to an automated selection of the decimation level and consequently to a signal-adaptive decomposition. Moreover, it enables one to reduce the processing time and makes the choice of usual free parameters easier, comparatively to the case where the whole signal is processed at once. The efficiency of the method is demonstrated using 1-D and 2-D <sup><i>13<i/><sup/>C NMR signals.

Near-Ideal M-ary LDGM Quantization with Recovery

For iterative mean-square error (MSE) quantizers with alphabet size M=2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</sup> using low-density generator-matrix (LDGM) code constructions, an efficient recovery algorithm is proposed, which adjusts the priors used in belief propagation (BP) to limit the impact of previous non-ideal decimation steps. Based on an analysis of the BP process under ideal or non-ideal decimation, the algorithm first estimates the conditional probability distributions describing the effect of non-ideal decimation, then adjusts the priors to make the distributions match the ideal situation. As shown in simulation results, the recovery algorithm can improve quantization performance greatly, reducing the shaping loss to as low as 0.012 dB, while the increase in computational complexity is modest thanks to the use of FFT techniques.

Sweep MRI with algebraic reconstruction

In the recently proposed technique Sweep Imaging with Fourier Transform (SWIFT), frequency-modulated radiofrequency pulses are used in concert with simultaneous acquisition to facilitate MRI of samples with very short transverse relaxation time. In the present work, sweep MRI is reviewed from a reconstruction perspective and several extensions and modifications of the current methodology are proposed. An algorithm for algebraic image reconstruction is derived from a comprehensive description of signal formation, including interleaved radiofrequency transmission and acquisition of arbitrary timing as well as the relevant filtering and decimation steps along the receiver chain. The new reconstruction approach readily permits several measures of optimising the signal sampling strategy as demonstrated in simulations and imaging experiments. Employing a variety of radiofrequency pulse envelopes, water and rubber phantoms as well as bone samples with transverse relaxation time in the order of 500 μsec were imaged at signal bandwidths of up to 96 kHz.

Stochastic renormalization group approach to random point processes. A fractal generalization of Poisson statistics

A generalization of the Shlesinger–Hughes stochastic renormalization method is suggested for random point processes. A decimation procedure is introduced in terms of two parameters: the probability α that a decimation step takes place and the probability β that during a decimation step a random dot is removed from the process. At each step a random number of dots are removed; by this procedure a chain of point processes is generated. The renormalized point process is a superposition of the intermediate processes attached to the different steps. For a statistical ensemble the fraction Lq of systems for which q decimation steps occur is a power function of the fraction ρq of points which survive q decimation steps Lq = (ρq)1−df where df=1−ln α/ln(1−β) is a fractal exponent smaller than unity, df&amp;lt;1. If the random points are initially independent then a complete analysis is possible. In this case explicit expressions for the renormalized Janossy densities, the joint densities, and the generating functional of the process are derived. Even though the initial process is made up of independent random points the points in the renormalized process are correlated. The probability of the number of points is a superposition of Poissonians corresponding to the different steps; however, it is generally non-Poissonian. It may be considered as a fractal generalization of Poisson statistics. All positive moments of the number of points exist and are finite and thus the corresponding probability does not have a long tail; the fractal features are displayed by the dependence of the probability on the initial average number of points λ: for λ→∞ the probability has an inverse power tail in λ modulated by a periodic function in ln λ with a period −ln(1−β). The new formalism is of interest for describing the lacunary structures corresponding to the final stages of chemical processes in low dimensional systems and for the statistics of rare events.