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3.3.4 Adaptive Smoothing of Images with Local Weighted Regression

Mark Levenson

Statistical Engineering Division, CAML

David Bright

Surface and Microanalysis Science Division, CSTL

Jayaram Sethuraman

Department of Statistics, Florida State University

The dramatic increase in instrument sophistication and measurement capacity has made data in the form of images a common and fruitful part of scientific and engineering research. The field of image processing can roughly be broken up into three steps--data collection, image enhancement, and feature extraction. In each of these steps, statistical ideas and methodology can play an important role. In collaboration with visiting researcher Dr. Jayaram Sethuraman, we have developed an image enhancement procedure based on the ideas of local weighted polynomial regression.

The ideas of local regression have long been used in image processing, but such uses involve constant weighting in the regression fitting. Statisticians have extensively studied nonconstant weighting in the context of nonparametric regression. In particular, Cleveland (1979) suggested an iterative procedure, which down-weights suspected outliers based on residual estimates. Our procedure parallels that of Cleveland. An iteration of the procedure consists of the weighted least-squares fitting of polynomials to local neighborhoods of each pixel. The weight of a pixel in a fit is based on a gradient estimate from the previous iteration of the pixel relative to the central pixel. A pixel with a large gradient is down-weighted in the regression fit. The weighting function has a monotone property in which weights cannot increase along a direction from the central pixel. The degree of down-weighting is adaptive to the scale of the image using quantiles of local gradients.

The accompanying figure shows the results of the procedure applied to a microtomograph of a concrete sample, shown on the top of the page. The solid line in the plot on the bottom of page shows the intensity profile of the original image across the horizontal line shown in the image. The dashed line shows the intensities given by the procedure after three iterations. The small local variations in the original intensities are removed, yet the complete dynamic range of the peak intensity is maintained.


Figure 21: Processed Concrete Sample

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Date created: 7/20/2001
Last updated: 7/20/2001
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