Non-uniform Bins Research Articles

Multichannel Time-to-Digital Converters With Automatic Calibration in Xilinx Zynq-7000 FPGA Devices

This article proposes a weighted histogram calibration method and an automatic calibration architecture to implement high-linearity time-to-digital converters (TDCs) in low-cost Advanced RSIC Machine (ARM)-based system-on-chips (SoCs). The proposed method significantly reduces the nonlinearity introduced by nonuniform bins. It offers automatic calibration without manual interventions using ARM processors. Besides, our design is cost-effective in hardware consumption. We implemented and evaluated a 16-channel TDC system in a low-cost Zynq-7000 ARM-based SoC, in which the programable logic is equivalent to a 28 nm Artix-7 FPGA. The proposed TDC offers a resolution of 9.83 ps with good uniformity, achieving an averaged <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{DN}}{{\rm{L}}_{{\rm{pk}} - {\rm{pk}}}}$</tex-math></inline-formula> of 0.38 LSB, and an averaged <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\rm{IN}}{{\rm{L}}_{{\rm{pk}} - {\rm{pk}}}}$</tex-math></inline-formula> of 0.63 LSB.

Iris feature extraction through wavelet mel-frequency cepstrum coefficients

In this paper, a novel technique based on wavelet cepstrum feature is discussed for iris recognition system. The proposed method is based on the wavelet derived from the popular biorthogonal Cohen-Daubechies-Feauveau 9/7 filter bank. Moreover, being biorthogonal in nature it has superior frequency selectivity, symmetric, and better time-frequency localization. The suggested scheme deals with computing the two level detail coefficients from the normalized iris template. Then these detailed coefficients are then divided into non-uniform bins in a logarithmic manner. This helps in reducing the dimension of the wavelet coefficients followed by assigning non-uniform weights to the different frequency components. Then the discrete cosine transform of the same is computed, from which the energy feature is extracted. The proposed technique is experimentally validated with publicly available databases: CASIAv3, UBIRISv1, and IITD. The performance of the proposed approach is found be superior to that of the state-of-the-art methods.

An optimal FFT-based anisotropic power spectrum estimator

Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a moving line-of-sight, can be accelerated using Fast Fourier Transforms (FFTs) by decomposing the Legendre polynomials into products of Cartesian vectors. Here, we present a faster, optimal means of using FFTs for this measurement. We avoid redundancy present in the Cartesian decomposition by using a spherical harmonic decomposition of the Legendre polynomials. With this method, a given multipole of order ℓ requires only 2ℓ+1 FFTs rather than the (ℓ+1)(ℓ+2)/2 FFTs of the Cartesian approach. For the hexadecapole (ℓ = 4), this translates to 40% fewer FFTs, with increased savings for higher ℓ. The reduction in wall-clock time enables the calculation of finely-binned wedges in P(k,μ), obtained by computing multipoles up to a large ℓmax and combining them. This transformation has a number of advantages. We demonstrate that by using non-uniform bins in μ, we can isolate plane-of-sky (angular) systematics to a narrow bin at 0μ ≃ while eliminating the contamination from all other bins. We also show that the covariance matrix of clustering wedges binned uniformly in μ becomes ill-conditioned when combining multipoles up to large values of ℓmax, but that the problem can be avoided with non-uniform binning. As an example, we present results using ℓmax=16, for which our procedure requires a factor of 3.4 fewer FFTs than the Cartesian method, while removing the first μ bin leads only to a 7% increase in statistical error on f σ8, as compared to a 54% increase with ℓmax=4.

Image retrieval based on non-uniform bins of color histogram and dual tree complex wavelet transform

Traditional Content-Based Image Retrieval (CBIR) systems were developed for retrieving similar kinds of images from a whole image database based on the given query image. In this paper, the authors have proposed a hierarchical approach for designing a CBIR scheme based on the color and texture features of an image. Initially, a color based approach is adopted and the intermediate results produced by using these color features is appropriate to discard a significant number of non-relevant images from the database. The intermediate database will be the input for the second stage. At this stage, a texture based approach is adopted for retrieving images from the intermediate database. The color features are extracted by computing the statistical parameters of non-uniform quantized histograms of HSV color space while a rotation invariant multi-resolution texture based approach is accomplished on value(V) component of HSV color space for extracting texture features. These texture features are extracted based on the principal texture direction and by taking the energies from various sub-bands of a dual tree complex wavelet transform (DT-CWT). Furthermore, the proposed scheme is suitable to handle mirror images during the retrieval process. The presented scheme has reduced the processing cost due to the consideration of a hierarchical approach. The proposed scheme is tested on the two well-known Corel-1K and GHIM-10K image databases respectively and satisfactory results were achieved in terms of precision, recall and F-score. The proposed scheme is compared with some other existing state of art CBIR schemes and the experimental results validate the improvement over other schemes in most of the instances.

Balls into non-uniform bins

Balls-into-bins games for uniform bins are widely used to model randomised load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks. In this paper we consider scenarios in which non-uniform selection probabilities help to balance the load among the bins. While previous evaluations try to find strategies for identical bins, we investigate heterogeneous bins where the “capacities” of the bins might differ significantly. We look at the allocation of m balls into n bins of total capacity C where each ball has d random bin choices. For such heterogeneous environments we show that the maximum load remains bounded by lnln(n)/ln(d)+O(1)w.h.p. if the number of balls m equals the total capacity C. Further analytical and simulative results show better bounds and values for the maximum loads in special cases.

Indirect immunofluorescence image classification using texture descriptors

In this work we propose an ensemble of texture descriptors for HEp-2 cell classification. Our system is based on a “pyramidal application” of local binary patterns coupled with a method for handling nonuniform bins. This feature extraction approach is then combined with a support vector machine (SVM) classifier. We test our method on a recent contest dataset (the MIVIA HEp-2 images dataset) using different testing protocols. This dataset is very challenging since the images are characterized by high variability in illumination. Therefore, to obtain good results, it is essential to apply a preprocessing algorithm: we choose the histogram equalization. We found that the best results are obtained when the original intensity images are converted into grayscale images with ten discrete values. Since a training set is provided in the contest dataset, we use it for descriptor selection and for parameter settings. The system built by using the training data is then applied to the testing set. Experiments show that our method outperforms the winner of the recent contest at the 21st International Conference on Pattern Recognition 2012.Our descriptors and MATLAB code will be available at webpage http://www.dei.unipd.it/wdyn/?IDsezione=3314&IDgruppo_pass=124&preview=.

Note on non-uniform bin packing games

A non-uniform bin packing game is an N-person cooperative game, where the set N is defined by k bins of capacities b1,…,bk and n items of sizes a1,…,an. The objective function v of a coalition is the maximum total value of the items of that coalition which can be packed to the bins of that coalition. We investigate the taxation model of Faigle and Kern (1993) [2] and show that the 1/2-core is always nonempty for such bin packing games. If all items have size strictly larger than 1/3, we show that the 5/12-core is always non-empty. Finally, we investigate the limiting case k→∞, thereby extending the main result in Faigle and Kern (1998) [3] to the non-uniform case.

Fourier Transform-Based Scalable Image Quality Measure

We present a new image quality assessment (IQA) algorithm based on the phase and magnitude of the 2D (twodimensional) Discrete Fourier Transform (DFT). The basic idea is to compare the phase and magnitude of the reference and distorted images to compute the quality score. However, it is well known that the Human Visual Systems (HVSs) sensitivity to different frequency components is not the same. We accommodate this fact via a simple yet effective strategy of nonuniform binning of the frequency components. This process also leads to reduced space representation of the image thereby enabling the reduced-reference (RR) prospects of the proposed scheme. We employ linear regression to integrate the effects of the changes in phase and magnitude. In this way, the required weights are determined via proper training and hence more convincing and effective. Lastly, using the fact that phase usually conveys more information than magnitude, we use only the phase for RR quality assessment. This provides the crucial advantage of further reduction in the required amount of reference image information. The proposed method is therefore further scalable for RR scenarios. We report extensive experimental results using a total of 9 publicly available databases: 7 image (with a total of 3832 distorted images with diverse distortions) and 2 video databases (totally 228 distorted videos). These show that the proposed method is overall better than several of the existing fullreference (FR) algorithms and two RR algorithms. Additionally, there is a graceful degradation in prediction performance as the amount of reference image information is reduced thereby confirming its scalability prospects. To enable comparisons and future study, a Matlab implementation of the proposed algorithm is available at http://www.ntu.edu.sg/home/wslin/reduced_phase.rar.

Variable Binned Scatter Plots

The scatter plot is a well-known method of visualizing pairs of two continuous variables. Scatter plots are intuitive and easy-to-use, but often have a high degree of overlap which may occlude a significant portion of the data. To analyze a dense non-uniform data set, a recursive drill-down is required for detailed analysis. In this article, we propose variable binned scatter plots to allow the visualization of large amounts of data without overlapping. The basic idea is to use a non-uniform (variable) binning of the x and y dimensions and to plot all data points that are located within each bin into the corresponding squares. In the visualization, each data point is then represented by a small cell (pixel). Users are able to interact with individual data points for record level information. To analyze an interesting area of the scatter plot, the variable binned scatter plots with a refined scale for the subarea can be generated recursively as needed. Furthermore, we map a third attribute to color to obtain a visual clustering. We have applied variable binned scatter plots to solve real-world problems in the areas of credit card fraud and data center energy consumption to visualize their data distributions and cause-effect relationships among multiple attributes. A comparison of our methods with two recent scatter plot variants is included.

Doubly Smoothed EM Algorithm for Statistical Inverse Problems

Recent results on discretization effects in unfolding intensity function of an indirectly observed nonhomogeneous Poisson process show that a critical feasibility condition for the strong L2 consistency of the histogram sieve maximum likelihood estimates requires that the approximation error of the function of interest with step functions tend to 0 faster than the squared singular values of the discretized folding operator. This condition may not be fulfilled in some standard inverse problems like, for example, the deconvolution problem and the Wicksell problem discretized in a standard way. The condition may be satisfied, however, with suitably modified discrete operator and suitably constructed parametric sets for the discrete problems. Motivated by these results, an additional smoothing step is added to the EMS (expectation-maximization-smoothing) algorithm and an automatic procedure for the choice of a smoothing parameter is proposed. An application to the Wicksell problem is presented. In this context, the theory also suggests a special, nonuniform binning in the data space. A simulation study demonstrates that the new approach considerably reduces the L2 risk when compared to both the standard EMS algorithm and to a spectral procedure specially designed for the Wicksell problem. A priori knowledge of the value of the estimated function at 0 may further reduce the risk very significantly. Theoretical results on the strong L2 consistency and convergence rates are given.