Non-uniform Sampling Distribution Research Articles

Exploring the concentration-dependent transport and the loss of rhodamine B, tartrazine, methylene blue, and amaranth dyes in common paperfluidic substrates

Understanding the fluid flow on paperfluidic substrates is crucial due to an increasing interest in affordable sensors for diagnosis, environmental testing, food testing, etc. Charged dyes are the most commonly used model analytes for characterizing the fluid flow in paperfluidic devices. Here, we propose a framework to quantify the concentration-dependent loss during transport of four charged dyes (e.g., rhodamine B, methylene blue, tartrazine and amaranth). At concentrations lower than a critical value (Cc), electrostatic interaction of the dye molecules with the filter paper retards the flow of cationic dyes rhodamine B and methylene blue, resulting in 75%–99% sample loss. We determined Cc to be 20 μM for rhodamine B and 5 mM for methylene blue. The large difference in their Cc values is explained by the molecular structures of these dyes. While anionic dyes (e.g., tartrazine and amaranth) are not retarded during flow on filter paper due to negligible electrostatic interaction with the substrate, they form strong coffee ring patterns in the detection zone when the dye concentration is below Cc. We introduced a new parameter called the ‘coffee ring index’ (CRI) to quantify the non-uniform sample distribution in the detection zone, and from this, determined Cc to be 250 μM for amaranth and 1.25 mM for tartrazine. Finally, we demonstrated that an increase in the dye viscosity by adding 30% glycerol can lower Cc of tartrazine from 1.25 mM to 100 μM. These results provide useful guidelines for the paperfluidics community to design more effective sensors.

Reconstruction algorithm for staggered synthetic aperture radar with modified second-order keystone transform

Staggered synthetic aperture radar (SAR), which operates with pulse repetition interval (PRI) variation, deals with the blind range problem caused by constant PRI in conventional high-resolution wide-swath SAR imaging. Due to the variation of PRI, there appear periodic loss of pulses and nonuniform sampling in azimuth. However, the exiting reconstruction methods mostly correct range curvature after resampling the nonuniform samplings into a uniform grid. It inevitably introduces the errors and thus affects the effectiveness of the correction. To solve the nonuniform sampling problem and eliminate the errors, our study proposes a reconstruction algorithm [reconstruction algorithm with modified second-order keystone transform (RMSKT)] with modified second-order keystone transform in staggered SAR mode. Moreover, to provide a priori knowledge required by the reconstruction, i.e., the nonuniform sampling distribution, which depends on PRI variation, our study first designs an optimal PRI variation scheme and optimizes the sequence parameters. With the designed PRIs sequence, the proposed RMSKT algorithm can achieve nonuniform range curvature correction and data reconstruction jointly. The proposed RMSKT algorithm shows significant improvements over the traditional reconstruction methods in terms of the peak-sidelobe ratio, the integral sidelobe ratio, and the azimuth ambiguity-to-signal ratio. Simulations and experiments on raw data generated in staggered mode are performed to verify the effectiveness of the proposed method.

Density Gain-Rate Peaks for Spectral Clustering

Clustering has been troubled by varying shapes of sample distributions, such as line and spiral shapes. Spectral clustering and density peak clustering are two feasible techniques to address this problem, and have attracted much attention from academic community. However, spectral clustering still cannot well handle some shapes of sample distributions in the space of extracted features, and density peak clustering encounters performance problems because it cannot mine the local structures of data and well deal with non-uniform distributions. In order to solve above problems, we propose the density gain-rate peak clustering (DGPC), a new type of density peak clustering method, and then embed it in spectral clustering for performance promotion. Firstly, in order to well handle non-uniform sample distributions, we propose density gain-rate for density peak clustering. Density gain-rate is based on the assumption that the density of a clustering center will be higher with the reduce of the radius. Even under non-uniform distributions, the cluster center in low density region will still have a significant density gain-rate thus can be detected. We combine density gain-rate in density peak clustering to construct DGPC method. Then in the framework of spectral clustering, we use our new density peak clustering to cluster the samples by their extracted features from a similarity graph of these samples, such as the neighbor-based similarity graph or the self-expressiveness similarity graph. Compared with the previous spectral clustering and density peak clustering, our method leads to better clustering performances on varying shapes of sample distributions. The experiment measures the performances of our clustering method and existing clustering methods by NMI and ACC on seven real-world datasets to illustrate the effectiveness of our method.

Optimal Path Planning Using Generalized Voronoi Graph and Multiple Potential Functions

In this article, we present a novel nonuniform sampling technique, based on the pipeline of rapidly exploring random tree (RRT), for efficiently computing high-quality collision-free paths while maintaining fast asymptotic convergence to the optimal solution. Our nonuniform sampling method focuses on the area where the optimal path may exist so that the path planning process can be further accelerated. First, the environment map is initialized with the generalized Voronoi graph and a heuristic path is calculated. Second, the heuristic path is discretized to construct the multiple potential functions (MPF), where the MPF provides a nonuniform sampling distribution for the path planner. As a meta-algorithm, our method is applicable to other RRT methods and helps to improve the performance of the underlying algorithm dramatically. We also prove the probabilistic completeness and the asymptotic optimality of our algorithm. The time cost and path length are selected to demonstrate the effectiveness of our algorithm. Through a series of simulation and real-world experiments, it is confirmed that the proposed algorithm achieves convincing performance compared with the state-of-the-art path planning algorithms.

Neural RRT*: Learning-Based Optimal Path Planning

Rapidly random-exploring tree (RRT) and its variants are very popular due to their ability to quickly and efficiently explore the state space. However, they suffer sensitivity to the initial solution and slow convergence to the optimal solution, which means that they consume a lot of memory and time to find the optimal path. It is critical to quickly find a short path in many applications such as the autonomous vehicle with limited power/fuel. To overcome these limitations, we propose a novel optimal path planning algorithm based on the convolutional neural network (CNN), namely the neural RRT* (NRRT*). The NRRT* utilizes a nonuniform sampling distribution generated from a CNN model. The model is trained using quantities of successful path planning cases. In this article, we use the A* algorithm to generate the training data set consisting of the map information and the optimal path. For a given task, the proposed CNN model can predict the probability distribution of the optimal path on the map, which is used to guide the sampling process. The time cost and memory usage of the planned path are selected as the metric to demonstrate the effectiveness and efficiency of the NRRT*. The simulation results reveal that the NRRT* can achieve convincing performance compared with the state-of-the-art path planning algorithms. Note to Practitioners —The motivation of this article stems from the need to develop a fast and efficient path planning algorithm for practical applications such as autonomous driving, warehouse robot, and countless others. Sampling-based algorithms are widely used in these areas due to their good scalability and high efficiency. However, the quality of the initial path is not guaranteed and it takes much time to converge to the optimal path. To quickly obtain a high-quality initial path and accelerate the convergence speed, we propose the NRRT*. It utilizes a nonuniform sampling distribution and achieves better performance. The NRRT* can be also applied to other sampling-based algorithms for improved results in different applications.

Construction of Projection Matrices Based on Non-Uniform Sampling Distribution for AoA Estimation

A Non-Uniform Sampling (NUS) methodology is presented, which improves the Angle of Arrival (AoA) estimation accuracy. The proposed sampling methodology is applied to extract the collected data efficiently and to reduce the possible dependency within rows/columns of the Covariance / Correlation Matrix (CM). The new sampled matrix approach is utilized to form such a projection matrix in order to provide better resolution of angles of arrival for closely incident signals on the antenna array receiver and to increase Degrees of Freedom (DOFs) compared to the classical criterion. The new direction-finding method based on the NUS methodology is called a Non-Uniform Projection Matrix (NUPM). A theoretical analysis is presented to demonstrate the advantage of the NUS methodology in terms of the obtained energy of the eigenvalues that are associated with the signal eigenvectors. It is proved that the proposed matrix sampling approach can provide better estimation resolution and detection of higher numbers of angles of arrival compared to the classical sampling method, without increasing array aperture size and the complexity of computations. A reduced-dimension process is applied to the NUPM in order to decrease the computational burden at the grid-scanning step. A computer simulation, including many scenarios, is implemented to justify the expected improvements of the NUS methodology compared to the classical approach. It is found that the new sampling distribution enhances noise immunity and increases DOFs compared to the conventional criterion. The performance of the NUPM method is compared with several AoA methods, including the Cramer-Rao Lower Bound (CRLB), and the obtained results verify the effectiveness and robustness of the proposed NUPM technique.

Monte Carlo convolution for learning on non-uniformly sampled point clouds

Deep learning systems extensively use convolution operations to process input data. Though convolution is clearly defined for structured data such as 2D images or 3D volumes, this is not true for other data types such as sparse point clouds. Previous techniques have developed approximations to convolutions for restricted conditions. Unfortunately, their applicability is limited and cannot be used for general point clouds. We propose an efficient and effective method to learn convolutions for non-uniformly sampled point clouds, as they are obtained with modern acquisition techniques. Learning is enabled by four key novelties: first, representing the convolution kernel itself as a multilayer perceptron; second, phrasing convolution as a Monte Carlo integration problem, third, using this notion to combine information from multiple samplings at different levels; and fourth using Poisson disk sampling as a scalable means of hierarchical point cloud learning. The key idea across all these contributions is to guarantee adequate consideration of the underlying non-uniform sample distribution function from a Monte Carlo perspective. To make the proposed concepts applicable to real-world tasks, we furthermore propose an efficient implementation which significantly reduces the GPU memory required during the training process. By employing our method in hierarchical network architectures we can outperform most of the state-of-the-art networks on established point cloud segmentation, classification and normal estimation benchmarks. Furthermore, in contrast to most existing approaches, we also demonstrate the robustness of our method with respect to sampling variations, even when training with uniformly sampled data only. To support the direct application of these concepts, we provide a ready-to-use TensorFlow implementation of these layers at https://github.com/viscom-ulm/MCCNN.

Comprehensive simulation of metagenomic sequencing data with non‐uniform sampling distribution

BackgroundMetagenomic sequencing is a complex sampling procedure from unknown mixtures of many genomes. Having metagenome data with known genome compositions is essential for both benchmarking bioinformatics software and for investigating influences of various factors on the data. Compared to data from real microbiome samples or from defined microbial mock community, simulated data with proper computational models are better for the purpose as they provide more flexibility for controlling multiple factors.MethodsWe developed a non‐uniform metagenomic sequencing simulation system (nuMetaSim) that is capable of mimicking various factors in real metagenomic sequencing to reflect multiple properties of real data with customizable parameter settings.ResultsWe generated 9 comprehensive metagenomic datasets with different composition complexity from of 203 bacterial genomes and 2 archaeal genomes related with human intestine system.ConclusionThe data can serve as benchmarks for comparing performance of different methods at different situations, and the software package allows users to generate simulation data that can better reflect the specific properties in their scenarios.

A max-norm constrained minimization approach to 1-bit matrix completion

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrain...

Potential function methods: Efficient probabilistic approaches to model complex data distributions

Potential function methods are a family of non-parametric probabilistic techniques that estimate a probability density distribution of a class of interest as a sum of contributions from each single sample of the class. The resulting estimated overall probability distribution can be sectioned at different confidence levels, with isoprobability contours representing the boundaries of the class space at each confidence level. Boundaries of the class spaces can be very complex, capable of effectively describing non-normal and non-uniform sample distributions.

Feature extraction of kernel regress reconstruction for fault diagnosis based on self-organizing manifold learning

The feature space extracted from vibration signals with various faults is often nonlinear and of high dimension. Currently, nonlinear dimensionality reduction methods are available for extracting low-dimensional embeddings, such as manifold learning. However, these methods are all based on manual intervention, which have some shortages in stability, and suppressing the disturbance noise. To extract features automatically, a manifold learning method with self-organization mapping is introduced for the first time. Under the non-uniform sample distribution reconstructed by the phase space, the expectation maximization(EM) iteration algorithm is used to divide the local neighborhoods adaptively without manual intervention. After that, the local tangent space alignment(LTSA) algorithm is adopted to compress the high-dimensional phase space into a more truthful low-dimensional representation. Finally, the signal is reconstructed by the kernel regression. Several typical states include the Lorenz system, engine fault with piston pin defect, and bearing fault with outer-race defect are analyzed. Compared with the LTSA and continuous wavelet transform, the results show that the background noise can be fully restrained and the entire periodic repetition of impact components is well separated and identified. A new way to automatically and precisely extract the impulsive components from mechanical signals is proposed.

Differential domain analysis for non-uniform sampling

Sampling is a core component for many graphics applications including rendering, imaging, animation, and geometry processing. The efficacy of these applications often crucially depends upon the distribution quality of the underlying samples. While uniform sampling can be analyzed by using existing spatial and spectral methods, these cannot be easily extended to general non-uniform settings, such as adaptive, anisotropic, or non-Euclidean domains. We present new methods for analyzing non-uniform sample distributions. Our key insight is that standard Fourier analysis, which depends on samples' spatial locations, can be reformulated into an equivalent form that depends only on the distribution of their location differentials . We call this differential domain analysis. The main benefit of this reformulation is that it bridges the fundamental connection between the samples' spatial statistics and their spectral properties. In addition, it allows us to generalize our method with different computation kernels and differential measurements. Using this analysis, we can quantitatively measure the spatial and spectral properties of various non-uniform sample distributions, including adaptive, anisotropic, and non-Euclidean domains.

Frame theory in directional statistics

Distinguishing between uniform and non-uniform sample distributions is a common problem in directional data analysis; however for many tests, non-uniform distributions exist that fail uniformity rejection. To predict these distributions, we merge directional statistics with frame theory and find that probabilistic tight frames yield non-uniform distributions that minimize directional potentials, leading to failure of uniformity rejection for the Bingham test. Finally, we apply our results to model patterns found in granular rod experiments.

Nonlinear Dimensionality Reduction by Locally Linear Inlaying

High-dimensional data is involved in many fields of information processing. However, sometimes, the intrinsic structures of these data can be described by a few degrees of freedom. To discover these degrees of freedom or the low-dimensional nonlinear manifold underlying a high-dimensional space, many manifold learning algorithms have been proposed. Here we describe a novel algorithm, locally linear inlaying (LLI), which combines simple geometric intuitions and rigorously established optimality to compute the global embedding of a nonlinear manifold. Using a divide-and-conquer strategy, LLI gains some advantages in itself. First, its time complexity is linear in the number of data points, and hence LLI can be implemented efficiently. Second, LLI overcomes problems caused by the nonuniform sample distribution. Third, unlike existing algorithms such as isometric feature mapping (Isomap), local tangent space alignment (LTSA), and locally linear coordination (LLC), LLI is robust to noise. In addition, to evaluate the embedding results quantitatively, two criteria based on information theory and Kolmogorov complexity theory, respectively, are proposed. Furthermore, we demonstrated the efficiency and effectiveness of our proposal by synthetic and real-world data sets.

Non-uniform surface sampling techniques for three-dimensional object inspection

While the uniform sampling method is quite popular for point- wise measurement of manufactured parts, we present three novel sam- pling strategies that emphasize 3D non-uniform inspection capability. They are direct and indirect adaptive sampling and local adjustment sampling. The adaptive sampling strategy is based on a recursive sur- face subdivision process that applies two different approaches. One uses the direct triangular patch subdivision while the other uses the in- direct sectional adaptive approach. The direct adaptive sampling ap- proach can distribute points more closely around edges, corners, and vertices as found on the class of machined products. The indirect adap- tive sampling techniques extend optimum 2D sampling methods to 3D applications. The modified 2D adaptive sampling techniques are used sequentially twice; first, the critical cross sections are optimally selected, and then each section is optimally sampled to develop an accurate geo- metric description using a small number of sampling points. Beyond the practical application value of a technique to inspect curved surface ob- jects, this kind of technique is also of value in understanding the principle of optimum sampling in a 3D sense. The local adjustment sampling strat- egy uses a set of predefined starting points and then finds the local optimum position of each nodal point. This method approximates the object by moving the points toward object edges and corners. The pre- defined starting points sets include uniform and non-uniform sampling distribution generated by the direct adaptive sampling approach. The results show that the initial point sets, when preprocessed by the adap- tive sampling using triangular patches, are moved the shortest distance to edges and corners for global optimum approximation, again showing this method's superiority. The performance comparisons of applying uni- form sampling and adaptive sampling are made based on the MSE mean square error value between the real object surfaces and their approximating surfaces. The adaptive sampling methods exhibit better performance than the uniform sampling methods in reducing the MSE values with fewer sample points. In addition to the performance advan- tage over uniform sampling, the non-uniform sampling techniques we propose also proved to be integratable with view planning for the inspec- tion of products by different manufacturing processes. © 2008 Society of

Fast image classification using a sequence of visual fixations

Based on human retinal sampling distributions and eye movements, a sequential resolution image preprocessor is developed. Combined with a nearest neighbor classifier, this preprocessor provides an efficient image classification method, the sequential resolution nearest neighbor (SRNN) classifier. The human eye has a typical fixation sequence that exploits the nonuniform sampling distribution of its retina. If the retinal resolution is not sufficient to identify an object, the eye moves in such a way that the projection of the object falls onto a retinal region with a higher sampling density. Similarly, the SRNN classifier uses a sequence of increasing resolutions until a final class decision is made. Experimental results on texture segmentation show that the preprocessor used in the SRNN classifier is considerably faster than traditional multiresolution algorithms which use all the available resolution levels to analyze the input data.

Factors Affecting the Analysis of Growth Patterns of Large Mammals

Growth of large mammals under natural conditions often is studied by regressing the mass of collected individuals against their estimated ages; however, this practice might lead to biased estimates of growth. Monte Carlo simulations were used to assess effects of nonuniform sample distribution and of imprecise and erroneous age determination on estimates of growth for male white-tailed deer ( Odocoileus virginianus ) using the Richards sigmoid growth equation. Effects of errors in age determination and sample distribution also were evaluated over a range of values of growth parameters, and biases were compared between estimates obtained from Richards, Gompertz, and von Bertalanffy equations. Variation in birth dates of individuals tended to increase the variance, but not the bias of growth estimates. Assigning individuals to the wrong year class resulted in biased estimates of all three growth parameters, with the shape parameter m being affected most. This bias was most pronounced when the sampling distribution was nonuniform and was not consistent for growth curves of different shapes. It appears that little confidence should be placed in estimates of m from data that may contain animals assigned incorrect ages. Asymptotic mass ( W ∞) and growth period ( T ) were relatively insensitive to this effect; however, a nonuniform sample distribution increased the bias of these estimates. For our data, estimates of W ∞ and T obtained from the Richards equation were less biased than estimates obtained from Gompertz or von Bertalanffy equations.

A transformation method for the reconstruction of functions from nonuniformly spaced samples

The reconstruction of functions from their samples at nonuniformly distributed locations is an important task for many applications. This paper presents a sampling theory which extends the uniform sampling theory of Whittaker et al. [11] to include nonuniform sample distributions. This extension is similar to the analysis of Papoulis [15], who considered reconstructions of functions that had been sampled at positions deviating slightly from a uniform sequence. Instead of treating the sample sequence as deviating from a uniform sequence, we show that a more general result can be obtained by treating the sample sequence as the result of applying a coordinate transformation to the uniform sequence. It is shown that the class of functions reconstructible in this manner generally include nonband-limited functions. The two-dimensional uniform sampling theory of Petersen and Middle ton [16] can be similarly extended as is shown in this paper. A practical algorithm for performing reconstructions of two-dimensional functions from nonuniformly spaced samples is described, as well as examples illustrating the performance of the algorithm.