Adv.Space Res. Vol. 14, No. 3, pp. O)177-(3)186, 1994 0273--1177/94 $6.00 + 0.00 Printed in Great Britain. All rights reserved. Copyright © 1993 COSPAR INVERSION TECHNIQUES FOR PROPORTION ESTIMATION OF MIXELS IN HIGH RE OLUTION SATELLITE IMAGE ANALYSIS Kohei Arai InformationScienceDepartmen~ Saga Un~ersity, lHonjo, Saga-city, Saga84~ Japan ABSTRACT A relationship between Instantaneous Field of View(IFOV) and spatial spectral variability is clarified. In accordance with improvement of IFOV, spatial spectral variability increased results in decreasing classification accuracy. Meanwhile, ratio of MIXELs which consist of plural classes decreases with improvement of IFOV. In such case, proportion estimation is more important to achieve high classification accuracy. The methods for proportion estimation are overviewed. Several examples are shown, in particular, for the estimation of cloud cover within a pixel and the method for checking a connectivity of road pieces in high resolution of satellite images. INTRODUCTION Spatial resolution of satellite based imaging sensors has been improved so far results in increasing spatial spectral variability. It causes decreasing classification accuracy, in general. Friedman(1965)/I/proposed a model for estimation classification accuracy as a function of variance of pixel value and range of pixel value for each class in spectral feature space. Arai(1985(1))/2/ clarified a relationship between IFOV and variance of pixel value. On the other hand, Crapper(1984) /3/proposed a model for representation of a relationship between IFOV and ratio of MIXELs. Arai(1985(2))/4/ refined his model to meet an experimental value. From these studies, a relationship between IFOV and classification accuracy becomes clear and these suggest that proportion estimation of heterogeneous regions is getting more important. Inversion techniques are applicable to estimate pixel proportion(hrai, 1991(I))/5/. In general, inversion techniques allows us to estimate causes by using results, if the results have a good characteristics or if some adequate constraints can be assumed between causes and results. If we assume the results are observation vector and mixing ratios of classes of interest are causes, proportion of MIXELs can be estimated. There are not so many methods for proportion estimation(Arai et al, 1990)/6/. This paper introduces several methods and also describes comparison among the methods(hrai et al, 1991/7/) followed by applicability to a knowledge base system for image classification(Arai et al, 1991(2)/8/). AN OVERVIEW OF THE METHODS FOR PROPORTION ESTIMATION From the view point of methodology, Teicher(1963)/9/suggested a mathematical possibility of proportion estimation then Horwitz et a1(1971)/10/proposed a proportion estimation method with inverse matrix then Nalepka et al (1972)/11/reported the method to NASA Contract Report. 8allum, C.R. (1972)/12/ proposed a best linear estimation of proportion of pixels while Boardman, J.W., (1989)/13/ proposed an inversion using singular value decomposition for imaging spectrometer data. For the application of the methods, Stinger R. et ai(1979) /14/studied proportion estimation of the pixels in the image of Mars surface. Hall, F.G. (1982)/15/showed an integrated method for acquiring global crop production information while Adams, J.B. et al (1986)/16/ proposed spectral mixture model for rock and soil types classification. Hapke, B. (1981)/17/showed an application of the method for bi-directional reflectance spectroscopy while Johnson,P.M. et al (1983)/18/ proposed a semiempirical method for analysis of the reflectance of binary mineral mixtures. PROPORTION ESTIMATION OF MIXED PIXELS(M1XELS) Let me assume that pixels consists of several classes with certain mixing ratios. Let an observed vector or feature vector be I with the dimensionality m, mixing ratio or proportion vector be B with (3)177