Abstract
We consider a pixel in an image like a pixel in a remotely sensed image, corresponding to an area AF on the ground, in which there are several materials belonging to different categories. It is possible for us to determine the area covered by each material if we know the n-component (multi-spectral) measurement vector x representing the pixel and the n-component vectors xi representing each material included in the pixel. Here we assume that the vector x is a linear combination, that is, the weighted sum, of the vectors xi; x=Σaixi, where Σai=1. The weight ai is the proportion of the area covered by a material i in the whole area AF. To estimate ai is to solve for ai an equation system by x=Σaixi (i=1, 2, 3, …) when x and xi are given.
The vector xi representing each category is determined by training data selected from the image data to be processed. The vector xi does not necessarily represent the category to which the training data belong. In the present paper, we make a model for the difference between the true representative vector xi and the vector xi estimated from the training data taking the account of the variation of the diffuse reflectance of the terrain due to change in look angle.
The method proposed up to now is formulated as an algorithm using restricted least squares method. It is analytically shown to be highly probable that the method gives us very erroneous results owing to the difference. The computer simulation shows that it is the case for possible situations.
A new method for pixel decomposition is also proposed. The method uses least squares algorithm based on the application of the algorithm directly to the area instead of to the multi-spectral measurement vector as the conventional method does. The accuracy is theoretically shown to be significantly improved, and is also confirmed by computer simulation.
