Combining edge-gradient information to improve adaptive discontinuity-preserving smoothing of multispectral images

Abstract

A reported adaptive discontinuity-preserving smoothing technique was modified to improve the registration of interband edge features. With the unmodified technique, individual gray-scale images are convolved repeatedly with a small adaptive smoothing mask whose coefficients are a function of image gray-scale discontinuity, measured from edge gradients. After convergence, the image contains regions of uniform gray level separated by sharpened, steplike boundaries. However, adaptive smoothing of the individual bands of a multispectral image may cause relative displacements between corresponding sharpened steplike boundaries because of slight misregistrations and independent processing of each spectral band. In this study, a gradient-based adaptive smoothing technique was modified to include discontinuity information from all spectral band images. In contrast to independent smoothing, use of this modified technique aligns the interband boundaries. Several examples show adaptive smoothing of SPOT images for a threeband multispectral image and a combination of three multispectral and one panchromatic band images. In the latter, edge information from the higher resolution (10-m ground sample distance) panchromatic image somewhat improves the adaptive smoothing of the lower resolution (20-m ground sample distance) multispectral image. Preliminary results indicate that this modified adaptive smoothing technique improves the registration of edge boundaries between the multispectral image bands and may facilitate edge extraction Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the U.S. Government INTRODUCTION Adaptive edgeor discontinuity-preserving smoothing is an image enhancement technique that preserves image edges while smoothing or generalizing other image regions (Pratt, 1978). Several adaptive smoothing techniques have been used for low-level processing of raw image data to enhance the subsequent extraction of edge and region features (Nagao and Matsuyama, 1979, and Chen and Medioni, 1992.) Nagao and Matsuyama (1980) described adaptive edge-preserving smoothing (EPS) as a preprocessing technique for the segmentation of multispectral images, wherein each spectral band image was first smoothed to produce regions of constant intensity separated by sharpened, steplike edges. They observed boundary artifacts around larger uniform regions caused by slight misregistrations between the individual spectral band images and also by independently processing each image. However, simple modifications to another type of adaptive smoothing technique can reduce the boundary and edge artifacts that may result from misregistrations and from the independent processing of multiband images. This report describes modifications to the adaptive discontinuitypreserving smoothing (DPS) technique described by Chen and Medioni (1992) and Saint-Marc and Chen (1991). These modifications incorporate edge discontinuity information from several multispectral band images to make sharpened boundaries coregister. Several preliminary examples of adaptive smoothing of SPOT (SPOT Image Corporation, 1988) images are given for (1) a 20-m ground sample distance (GSD), three-band multispectral (XS) image (interpolated to 10 m), and (2) the combination of XS and 10-m GSD panchromatic (P) images. The latter example shows that the modified DPS technique creates sharpened edge boundaries in the lower resolution multispectral image that register with boundaries in higher resolution panchromatic images. Also there are examples that compare the EPS of Nagao and Matsuyama (1979,1980) with the DPS of Chen and Medioni (1992). METHODS The calculations for DPS described by Chen and Medioni (1992) include the repeated convolution of an image with a small smoothing mask whose coefficients are determined adaptively from a measure of edge discontinuities within the image subregion defined by the mask. For this specific technique, discontinuities are measured from gradient magnitude data. After many iterations and upon convergence, the image consists of regions of uniform amplitude, or gray level, separated by perfect steplike changes in gray level. Not only are small variations in gray level within regions smoothed, but image edges are sharpened as well. Also, they observed that edges were sharpened after a few iterations, but smoothing is extremely slow. This is advantageous because the sharpened edges can be detected readily with only simple edgedetection methods. The unmodified adaptive smoothing technique for a single-band image involves the repeated convolution of an image with a 3by 3-sample mask whose coefficients are a function of image discontinuities. Basically, these adaptive coefficients or smoothing weights will vary throughout the image as a function of image edge details in the subregion defined by the mask size. The larger the discontinuity, the smaller the smoothing coefficient and hence less smoothing of the discontinuity. In contrast, if the weights are fixed and equal, after many iterations all image discontinuities would be highly smoothed and eventually removed. As Chen & Medioni (1992) describe, the smoothing weights at each iteration t for each image pixel location x, y are determined from a continuity value, wt (x, y), that is a decreasing function /[. ] of the discontinuity dt (x, y). That is (1)