11MaximumLikelyhoodandFuzzySetClassificationLectureNotes

11MaximumLikelyhoodandFuzzySetClassificationLectureNotes -...

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1 Geo 4037c Digital Image Analysis Maximum Likelihood and Fuzzy Set Classification Maximum Likelyhood Classifier This technique is slower than the other techniques, but can produce superior results. It is used when you know from ancillary sources approximately how much of the image lies in each class. Advantages of the Maximum Likelihood Classifier Many pixels lie somewhere between two classes in spectral space. For instance, mixed pixels or mixels on the land water boundary do not have the spectral characteristics of land or water, or forest, but rather, somewhere inbetween. A decision must be made; which class to assign mixels to. The decision is often arbitrary, but we can use probabilities to weigh the decision rule. Suppose an image is 15% water, 40% forest, 35% urban and 10% fields. We want to assign mixels by prior probabilities, so that 15% of the mixels go to water, 40% go to forest, 35% go to urban and 10% go to fields. Disadvantages of the Maximum Likelihood Classifier This classifier uses both the means and variance of the training field vectors to assign pixels to classes. It predicts how many pixels in class X have a BV of 13 in Band Z. It assumes that the training field data is normally distributed, and that the histogram is unimodal, or has a single, not multiple peak. Therefore when using the maximum likelihood classifier, it is necessary to have gaussian distributions in the training fields. This means that examination of the histograms of the training fields must be undertaken. If the histogram has more than one peak, the training field is not suitable for maximum likelihood classification. How the maximum likelihood classifier works Each pixel has a mean vector in multidimensional spectral space. A pixel vector is classified as a particular class only if the probability of belonging to that class is greater than the probability of belonging to any other class. The program examines the mean vector and variance within each training field, and also, the probability that a pixel belongs to a particular class. This technique is computationally complex, especially for thematic mapper data, with six spectral dimensions. The results are not necessarily superior, but the best fit is found for each pixel. Running the program using the defaults assumes the probability of a pixel belonging to any one class is equal; it assumes water, forest, fields and urban each comprise 25% of the image. The strength of the classifier is that it allows the assignment of prior probabilities for each class. So if we know in advance that water is 10% of the image, only the closest 10% of mixels
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2 that somewhat resemble water should be classed as water, using a Bayesian decision rule. ASSUME PIXEL HAS A VALUE OF 13
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This note was uploaded on 12/21/2010 for the course GIS 4037c taught by Professor Roberts during the Fall '10 term at FAU.

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11MaximumLikelyhoodandFuzzySetClassificationLectureNotes -...

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