Piecewise

About: Piecewise is a research topic. Over the lifetime, 21064 publications have been published within this topic receiving 432096 citations. The topic is also known as: piecewise-defined function & hybrid function.

On Detecting Edges

Abstract: An edge in an image corresponds to a discontinuity in the intensity surface of the underlying scene. It can be approximated by a piecewise straight curve composed of edgels, i.e., short, linear edge-elements, each characterized by a direction and a position. The approach to edgel-detection here, is to fit a series of one-dimensional surfaces to each window (kernel of the operator) and accept the surface-description which is adequate in the least squares sense and has the fewest parameters. (A one-dimensional surface is one which is constant along some direction.) The tanh is an adequate basis for the stepedge and its combinations are adequate for the roofedge and the line-edge. The proposed method of step-edgel detection is robust with respect to noise; for (step-size/?noise) ? 2.5, it has subpixel position localization (?position < ?) and an angular localization better than 10°; further, it is designed to be insensitive to smooth shading. These results are demonstrated by some simple analysis, statistical data, and edgelimages. Also included is a comparison of performance on a real image, with a typical operator (Difference-of-Gaussians). The results indicate that the proposed operator is superior with respect to detection, localization, and resolution.

Total-Variation-Regularized Low-Rank Matrix Factorization for Hyperspectral Image Restoration

Abstract: In this paper, we present a spatial spectral hyperspectral image (HSI) mixed-noise removal method named total variation (TV)-regularized low-rank matrix factorization (LRTV). In general, HSIs are not only assumed to lie in a low-rank subspace from the spectral perspective but also assumed to be piecewise smooth in the spatial dimension. The proposed method integrates the nuclear norm, TV regularization, and $L_1$ -norm together in a unified framework. The nuclear norm is used to exploit the spectral low-rank property, and the TV regularization is adopted to explore the spatial piecewise smooth structure of the HSI. At the same time, the sparse noise, which includes stripes, impulse noise, and dead pixels, is detected by the $L_1$ -norm regularization. To tradeoff the nuclear norm and TV regularization and to further remove the Gaussian noise of the HSI, we also restrict the rank of the clean image to be no larger than the number of endmembers. A number of experiments were conducted in both simulated and real data conditions to illustrate the performance of the proposed LRTV method for HSI restoration.

Regression trees with unbiased variable selection and interaction detection

Abstract: We propose an algorithm for regression tree construction called GUIDE. It is specifically designed to eliminate variable selection bias, a problem that can undermine the reliability of inferences from a tree structure. GUIDE controls bias by employing chi-square analysis of residuals and bootstrap calibration of signif- icance probabilities. This approach allows fast computation speed, natural ex- tension to data sets with categorical variables, and direct detection of local two- variable interactions. Previous algorithms are not unbiased and are insensitive to local interactions during split selection. The speed of GUIDE enables two further enhancements—complex modeling at the terminal nodes, such as polynomial or best simple linear models, and bagging. In an experiment with real data sets, the prediction mean square error of the piecewise constant GUIDE model is within ±20% of that of CART r � . Piecewise linear GUIDE models are more accurate; with bagging they can outperform the spline-based MARS r � method.