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Digital Image Processing
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An Attempt to Observe Paths of Particle of Wind Flowing over Buildings Utilizing Simplified Aerial Photogrammetry
Wu Jianping
Department of Geography, East China Normal University,
Shanghai, China
Abstract
Decomposition of mixed pixels is an important way to improving Remote Sensing information representation. Many scientists have discussed the theories and methods about it. This paper describers fuzzy supervised and fuzzy unsupervised classification methods to decompose the mixed pixels. A Landsat TM subimage of a county is extracted for experiments and their accuracy are analyzed by area ratio which compares the area of every landuse in a region from fuzzy classification and from measure of aerial photograph.
Introduction
Mixed pixels exist extensively in scanning remote sensing image. It is estimated that NOAA image (1.1*1.1 km2) of meterological satellite have more than 90 percent mixed pixels in land part, MSS image (80*80 m2) of Landsat have about 70 percent, and TM image (30*30 m2) of Landsat have about 50 percent, even though the resolution of an image reaches 5*5 m2, there are more than 30 percent mixed pixels. If the mixture cannot be taken into consideration in using and processing remote sensing data, the expressive limitation will reduce the classification accuracy level and lead to the poor extraction of information.
Decomposition of mixed pixels is an important way to improving Remote Sensing information representation. Currently, there are two basic methods about it: 1) fuzzy classification method (1) 2) establishment of relation pattern between spectral response of a pixel and spectral response and area proportion of every elements in the pixels. (2)
Fuzzy Classification Method
In traditional classification, information is represented in a one-pixel -one - class method and its classification result is definite, i.e. a pixel belongs to a class. In fuzzy classification, a pixel is considered having different membership grades obtained from fuzzy classification indicate the area proportion of every cover classes in a mixed pixel. As the traditional method, the fuzzy classification can also be divided into fuzzy supervised and fuzzy unsupervised classification.
Fuzzy Supervised Classification
Sample pixels should be chosen for estimating fuzzy parameters before classification, different to conventional method, chosen sample need not be sufficiently homogeneous. Fuzzy mean can be expressed as
where n is the total number of sample pixels, fc is membership of a pixel to class c, xi is pixel value of sample pixels. Fuzzy covariance matrix can be expressed as
After the fuzzy parameters are determined, every pixel is classified according to its spectral value. To perform a fuzzy classification, the membership function must be defined for each class, in this work, the membership functions are defined based on maximum
likelihood classification algorithm with fuzzy and fuzzy covariance matrix replacing the conventional mean and covariance matrix. The following is the definition of membership function for cover class c:
N is the pixel vector dimension, m is number of predefined classes.
Fuzzy Unsupervised Classification
The fuzzy unsupervised classification can be performed in many methods, in this work, k-means clustering algorithm is adopted and is run using iteration as following:
- determine classification number k, 1
- give a initial membership matrix
- calculate fuzzy clustering where centers of every class
- calculate new membership matrix U(t+1) using formula
- if the criterion is satisfied, stop the iteration. Otherwise, repeat process 3 to 5. The criterion of ending iteration can choose
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