Local Window Size Research Articles

Efficient Estimation of Integrated Volatility Functionals via Multiscale Jacknife

We propose semi-parametrically efficient estimators for general integrated volatility functionals of multivariate semimartingale processes. It is known that a plug-in method that uses nonparametric estimates of spot volatilities induces high-order biases which need to be corrected to obey a central limit theorem. Such bias terms arise from boundary effects, the diffusive and jump movements of stochastic volatility, and the sampling error from the nonparametric spot volatility estimation. We propose a novel jackknife method for bias-correction. The jackknife estimator is simply formed as a linear combination of a few uncorrected estimators associated with different local window sizes used in the estimation of spot volatility. We show theoretically that our estimator is asymptotically mixed Gaussian, semi-parametrically efficient, and more robust to the choice of local windows. To facilitate the practical use, we introduce a simulation-based estimator of the asymptotic variance, so that our inference is derivative-free and, hence, is very convenient to implement.

Spine labeling in axial magnetic resonance imaging via integral kernels

This study investigates a fast integral-kernel algorithm for classifying (labeling) the vertebra and disc structures in axial magnetic resonance images (MRI). The method is based on a hierarchy of feature levels, where pixel classifications via non-linear probability product kernels (PPKs) are followed by classifications of 2D slices, individual 3D structures and groups of 3D structures. The algorithm further embeds geometric priors based on anatomical measurements of the spine. Our classifier requires evaluations of computationally expensive integrals at each pixel, and direct evaluations of such integrals would be prohibitively time consuming. We propose an efficient computation of kernel density estimates and PPK evaluations for large images and arbitrary local window sizes via integral kernels. Our method requires a single user click for a whole 3D MRI volume, runs nearly in real-time, and does not require an intensive external training. Comprehensive evaluations over T1-weighted axial lumbar spine data sets from 32 patients demonstrate a competitive structure classification accuracy of 99%, along with a 2D slice classification accuracy of 88%. To the best of our knowledge, such a structure classification accuracy has not been reached by the existing spine labeling algorithms. Furthermore, we believe our work is the first to use integral kernels in the context of medical images.

Stereo Matching by Filtering-Based Disparity Propagation.

Stereo matching is essential and fundamental in computer vision tasks. In this paper, a novel stereo matching algorithm based on disparity propagation using edge-aware filtering is proposed. By extracting disparity subsets for reliable points and customizing the cost volume, the initial disparity map is refined through filtering-based disparity propagation. Then, an edge-aware filter with low computational complexity is adopted to formulate the cost column, which makes the proposed method independent on the local window size. Experimental results demonstrate the effectiveness of the proposed scheme. Bad pixels in our output disparity map are considerably decreased. The proposed method greatly outperforms the adaptive support-weight approach and other conditional window-based local stereo matching algorithms.

Adaptive windowed range-constrained Otsu method using local information

An adaptive windowed range-constrained Otsu method using local information is proposed for improving the performance of image segmentation. First, the reason why traditional thresholding methods do not perform well in the segmentation of complicated images is analyzed. Therein, the influences of global and local thresholdings on the image segmentation are compared. Second, two methods that can adaptively change the size of the local window according to local information are proposed by us. The characteristics of the proposed methods are analyzed. Thereby, the information on the number of edge pixels in the local window of the binarized variance image is employed to adaptively change the local window size. Finally, the superiority of the proposed method over other methods such as the range-constrained Otsu, the active contour model, the double Otsu, the Bradley’s, and the distance-regularized level set evolution is demonstrated. It is validated by the experiments that the proposed method can keep more details and acquire much more satisfying area overlap measure as compared with the other conventional methods.

An improved solution of local window parameters setting for local singularity analysis based on Excel VBA batch processing technology

In this paper Excel VBA is used for batch calculation in Local Singularity Analysis (LSA), which is for the information extracting from different kinds of geoscience data. Capabilities and advantages of a new module called Batch Tool for Local Singularity Index Mapping (BTLSIM) are: (1) batch production of series of local singularity maps with different settings of local window size, shape and orientation parameters; (2) local parameter optimization based on statistical tests; and (3) provision of extra output layers describing how spatial changes induced by parameter optimization are related to spatial structure of the original input layers.

Removing smearing-effect artifacts in angle-domain common-image gathers from reverse time migration

Local plane-wave decomposition (LPWD) and local shift imaging condition (LSIC) methods for extracting angle-domain common-image gathers (ADCIGs) from prestack reverse time migration are based on the local plane-wave assumption, and both suffer from a trade-off in choosing the local window size. Small windows produce clean ADCIGs, but with low angle resolution, whereas large windows produce noisy ADCIGs, which include smearing-effect artifacts, but with high angle resolution. The cause of the smearing-effect artifacts in LPWD is the crosscorrelation of plane waves obtained by decomposition of the source and receiver wavefronts, at points that do not lie on the source wavefront excitation time trajectory. The cause of the smearing-effect artifacts in LSIC is the decomposition of curved events of offset-domain common-image gathers (ODCIGs) at incorrect depth points at zero offset. These artifacts can occur even if the migration velocity model is correct. Two methods were proposed to remove the artifacts. In the LPWD method, the smearing-effect artifacts were removed by decomposing and crosscorrelating the resulting source and receiver plane waves only at image points and excitation (image) times. In the LSIC method, the artifacts were removed by decomposing curved events in ODCIGs into planar events only at zero-offset target image points. Numerical tests with synthetic data revealed the success of the proposed methods.

PUMA-SPA: A Phase Unwrapping Method Based on PUMA and Second-Order Polynomial Approximation

This letter focuses on the phase unwrapping algorithm. A state-of-the-art phase unwrapping method called PUMA which is based on the max-flow/min-cut was proposed recently. The proposed method in this letter postprocesses the results of PUMA to improve the unwrapping results. A pointwise local second-order polynomial approximation method is considered to suppress the noise. We estimate the parameters of the polynomial by solving the overdetermined equations and get the solution with the Least Squares Error Fitting. The proposed algorithm synthesizes the unwrapping with the denoising method and is abbreviated as PUMA-SPA. In the denoising step, adaptive local window sizes are selected to compromise the fitting error and the suppression of noise. Experiments show that the proposed method can achieve better results than the method Congruence Operation and Least Squares Fitting (CO-LSF) proposed recently.

Color Image Segmentation Using IMOWT with 2D Histogram Grouping

In this paper, a novel algorithm based on 2D histogram Grouping for color Image Segmentation is proposed. The proposed method uses intermediate features of maximum overlap wavelet transform (IMOWT) as a pre-processing step. The coefficients derived from IMOWT are subjected to 2D histogram Grouping. This method is simple, fast and unsupervised. 2D histograms are used to obtain Grouping of color image. This Grouping output gives three segmentation maps which are fused together to get the final segmented output. This method produces good segmentation results when compared to the direct application of 2D Histogram Grouping. IMOWT is the efficient transform in which a set of wavelet features of the same size of various levels of resolutions and different local window sizes for different levels are used. IMOWT is efficient because of its time effectiveness, flexibility and translation invariance which are useful for good segmentation results.

Comparison of methods for extracting ADCIGs from RTM

Methods for extracting angle-domain common-image gathers (ADCIGs) during 2D reverse-time migration fall into three main categories; direction-vector-based methods, local-plane-wave decomposition methods, and local-shift imaging condition methods. The direction-vector-based methods, which use either amplitude gradients or phase gradients, cannot handle overlapping events because of an assumption of one propagation direction per imaging point per imaging time; however, the ADCIGs from the direction-vector-based methods have the highest angle resolution. A new direction-vector-based method using instantaneous phase gradients in space and time gives the same propagation directions and ADCIGs as those obtained by the Poynting vector or polarization vector based methods, where amplitudes are large. Angles calculated by the phase gradients have larger uncertainties at smaller amplitudes, but they do not significantly degrade the ADCIGs because they contribute only small amplitudes. The local-plane-wave decomposition and local-shift imaging condition methods, implemented either by a Fourier transform or by a slant stack transform, can handle overlapping events, and produce very similar angle gathers. ADCIGs from both methods depend on the local window size in which the transforms are done. In small local windows, both methods produce ADCIGs with low noise, but also with low angle resolution; in large windows, they have high angle resolution, but contain smeared artifacts.

Super-Resolution Method Based on Edge Feature for High Resolution Imaging

Super-resolution is recently one of the most attractive research themes. An image interpolation method using co-variance between neighboring pixels, so called New Edge-Directed Interpolation (NEDI), was proposed. It enables to interpolate pixels quantitatively regardless of edge features. However, in estimation of predictive coefficients and determination of NEDI’s local window size, edge features are not made consideration. So, NEDI cannot necessarily satisfy quality of picture. In order to overcome this problem, we propose a new intra-frame super-resolution method that window sizes and configurations are adaptively determined depending on edge strengths and orientations. Experimental simulation shows that the proposed method can interpolate pixels more clearly than NEDI for many kinds of edges.

Multiple-step local Wiener filter with proper stopping in wavelet domain

In this paper, we propose an adaptive multiple steps local Wiener filter image denoising algorithm in the wavelet domain. This algorithm can be considered as a discretized implementation of adaptive heat diffusion equation, and is carried out by multiple successive steps. The denoised output from one iteration is taken as the input to the next. The proper iteration number is determined by total denoising amount which is measured by noise variance. The selected local window sizes are also relatively stable. The experimental results show the effectiveness of the proposed method.

Multi-resolution decomposition in relation to characteristic scales and local window sizes using an operational wavelet algorithm

Data from an IKONOS image acquired over Dallas were used to demonstrate the use of an operational wavelet-based algorithm to examine the performance of different texture measures and window sizes at various resolutions in connection with characteristic scales. It was found that a 63 × 63 window was the optimal size, and energy measure produced the highest accuracy. Results from this study suggest that the choice of window size in wavelet-based classification affects the accuracy. Larger window sizes significantly improve the overall accuracy when using homogeneous samples. In the real-world situation, a larger window may not necessarily produce higher accuracy since a larger window tends to cover more land-use and land-cover classes and therefore may miss smaller regions of classes that could lead to poorer accuracy. On the other hand, a smaller window tends to be incomplete in its coverage of texture features that represent a complex class. The classification accuracy can be improved by using more combinations of sub-images at different scales. However, smaller sub-images at the last two levels may lower the classification accuracy. The characteristic scale of the most complex feature among all selected classes could be the optimal local window size necessary to achieve the highest accuracy.

Local indicators for categorical data: impacts of scaling decisions

When the geographic distribution of landscape pattern varies, global indices fail to capture the spatial nonstationarity within the dataset. Methods that measure landscape pattern at a spatially local scale are advantageous, as an index is computed at each point in the dataset. The geographic distribution of local indices is used to discover spatial trends. Local indicators for categorical data (LICD) can be used to statistically quantify local spatial patterns in binary geographic datasets. LICD, like other spatially local methods, are impacted by decisions relating to the spatial scale of the data, such as the data grain (p), and analysis parameters such as the size of the local neighbourhood (m). The goal of this article is to demonstrate how the choice of the m and p parameters impacts LICD analysis. We also briefly discuss the impacts spatial extent can have on analysis; specifically the local composition measure. An example using 2006 forest cover data for a region in British Columbia, Canada where mountain pine beetle mitigation and salvage harvesting has occurred is used to show the impacts of changing m and p. Selection of local window size (m = 3,5,7) impacts the prevalence and interpretation of significant results. Increasing data grain (p) had varying effects on significant LICD results. When implementing LICD the choice of m and p impacts results. Exploring multiple combinations of m and p will provide insight into selection of ideal parameters for analysis.

Approaches for optimal automated individual tree crown detection in regenerating coniferous forests

Automated tree detection provides a means to acquire information on tree abundance and spatial distribution, both of which are critical for evaluating the status of regenerating forests. It is also often a precursor to automated tree delineation, which typically utilizes image data surrounding a detected crown point. However, obtaining consistently accurate detection results has proven difficult owing to errors associated with image scale. In this paper, four approaches that reduce this scale dependence are evaluated, including (1) determination of optimum global image smoothing to apply predetection, (2) determination of optimum local image smoothing to apply predetection, (3) determination of the optimal local window size for use in the detection algorithm, and (4) post-detection merging of initially defined crown segments. Each approach was applied to three datasets acquired by different sensors and with different regenerating forest conditions. A common local maximum tree detection algorithm was implemented for approaches 1–3, and a watershed segmentation algorithm was applied in approach 4. Detection accuracy was evaluated using standardized methods. The highest accuracies for each dataset were obtained with approaches based on local scale representations where the regenerating structure favored such approaches. However, more consistent accuracies across all datasets were obtained with the optimum global scale approach. Post-detection merging of adjacent crown segments produced the poorest results. Error sources and the advantages and disadvantages of each approach are discussed in terms of developing more operational methods for automated tree detection in regenerating forests.

Quantitative roughness of sputtered Fe-Cr superlattices

We obtained quantitative values of all significant parameters describing the roughness of Fe-Cr superlattices, both in the lateral and growth directions, by statistical analysis of energy-filtered transmis- sion electron microscopy images using cross section samples. These results are in good agreement with the complementary low-angle X-ray scattering measurements. The interface roughness of sputtered Fe-Cr superlattices was changed systematically by varying Ar-pressure during the growth and the number of the bilayers. By scaling local window size we obtained the dependence of the saturated roughness and its correlation lengths in both the lateral and growth directions. The roughness and its correlation lengths (lateral and perpendicular) increase with pressure. However correlation length in the lateral is constant with bilayer index for low-pressure sputtered samples

Performance analysis and optimal parameter selection for PYRAMID

Previously, we have proposed PYRAMID, a hierarchical, rule-based scheme for proximity effect correction in electron-beam lithography. In this paper we present a performance analysis of PYRAMID for a variety of different system parameters (resist thickness, substrate composition, etc.). We also discuss the optimal choice of two key correction parameters: global exposure block size and local exposure window size.

Interactive effects of local smoothing window size and fundamental frequency on shimmer calculation

Slow amplitude modulation of human voice was approximated by a sinusoidal wave. The theoretical effects of smoothing window size, F0, and modulation frequency on window amplitude average as well as calculated shimmer were mathematically derived. Subsequently, the theoretical predictions were tested using idealized and real voice signals from normal speakers. The theoretical and experimental results suggest that shimmer (when calculated using a smoothing window) is a function of window duration and modulation frequency. Window duration when defined as a constant number of pitch periods varies from speaker to speaker depending on their F0. It may not be desirable to use local smoothing windows with a constant number of cycles for shimmer computation, especially if voices with known low-frequency amplitude modulations but notably different fundamental frequencies are compared.

Nonparametric Bayes-risk estimation

Two nonparametric methods to estimate the Bayes risk using classified sample sets are described and compared. The first method uses the nearest neighbor error rate as an estimate to bound the Bayes risk. The second method estimates the Bayes decision regions by applying Parzen probability-density function estimates and counts errors made using these regions. This estimate is shown to be asymptotically consistent in mean square. The results of experiments with these estimators on simulated and empirical data imply that the estimators both have acceptable small-sample properties; however, small-sample convergence of both estimators depends strongly on the choice of metric and local area or window size in the measurement space.