Tracking linear deformable objects using slicing method

In this paper, an efficient novel method for tracking the linear deformable objects (LDOs) in real time is proposed. The method is developed based on recursively slicing a pointcloud into smaller pointclouds with sufficiently small variance. The performance of this method is investigated through a series of experiments with various camera resolutions in simulation when a robot end effector tracking an LDO using an RGBD camera, and in real word when the camera tracks a rope during a swing. The performance of the proposed method is compared with another state-of-the-art technique and the outcome is reported here.

CLASSIFICATION OF MULTIVARIATE SAMPLES USING PETUNIN ELLIPSES

The method of classification multivariate samples using Petunin ellipses is investigated in the paper. Several different types of samples were generated for testing. Based on the calculated accuracy of the criteria advantages and disadvantages of each of the linear and quadratic criteria and the specifics of the method as a whole were discovered. It has been found that both linear and quadratic criteria give high accuracy for samples with small variance. As the variance increases, the accuracy of the linear criterion remains high, the accuracy of the quadratic criterion decreases. Both criteria are resistant to sample noise.

MFPCA: Multiscale Functional Principal Component Analysis

We consider the problem of performing dimension reduction on heteroscedastic functional data where the variance is in different scales over entire domain. The aim of this paper is to propose a novel multiscale functional principal component analysis (MFPCA) approach to address such heteroscedastic issue. The key ideas of MFPCA are to partition the whole domain into several subdomains according to the scale of variance, and then to conduct the usual functional principal component analysis (FPCA) on each individual subdomain. Both theoretically and numerically, we show that MFPCA can capture features on areas of low variance without estimating high-order principal components, leading to overall improvement of performance on dimension reduction for heteroscedastic functional data. In contrast, traditional FPCA prioritizes optimizing performance on the subdomain of larger data variance and requires a practically prohibitive number of components to characterize data in the region bearing relatively small variance.

Nonparametric and parametric methods of spectral analysis

Spectral Analysis is one of the most important methods in signal processing. In practical application, it is critical to discuss the power spectral density estimation of finite data sampled from some stationary time series. A spectral estimator is expected to have good statistical properties such as consistency, high resolution and small variance. For one spectral estimation method, there exists a trade-off between high resolution and small variance. The paper provides a comparison of several popular spectral methods from both theoretical properties and practical applications. We first address several basic nonparametric methods, whose statistical characters are analysed. Then we explain the connections and differences between temporal windowing and lag windowing. Thereafter, the confidence intervals of both windows are given and used to evaluate the estimated results. Besides, several different parametric estimation methods of autoregressive time series are compared, and whose properties and effects are also introduced. Building on our understanding of these studies, we then apply parametric and nonparametric spectral estimation methods on the data of ocean surface wave height.