291.

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Page 60

In the case of a k-band feature space, if the unit vector (where T denotes the matrix transpose) of each transformed axis i is obtained, the projection pi of the jth pixel with original vector (i.e. formed by the pixel values in each band), , on new coordinate i is calculated by:

(2.1)

where c is a constant required in order to ensure that the resulting pi is always positive. Equation (2.1) is the basic relationship in coordinate transform theory for calculating the new mapping location of the points. Readers should refer to Mather (1999a) for further elaboration.

Crist and Cicone (1984b) modified the Tasselled Cap transform to deal with six-band Landsat TM images (the thermal infrared band, conventionally numbered 6, is excluded). They transform the six-dimensional TM feature space into three new coordinates axes called ‘brightness’, ‘greenness’ and ‘wetness’. The first two axes are similar to the first two MSS Tasselled Cap axes, as described above. The third axis, ‘wetness’, was constructed according to the variation in water reflectance, and was defined using the TM mid-IR bands.

The advantages of the Tasselled Cap transform are:

1 The dimensionality of the feature space is reduced, making the classification problem less complex.

2 The axes of the feature space represent specific concepts (brightness, greenness and wetness) that can be considered to be defined externally to the specific data set under study.

The principal disadvantages of the transform are:

1 The Tasselled Cap axes may not be well defined for a particular problem if the coefficients are not properly calculated (Jackson, 1983).

2 There can be no assurance that significant information is not omitted by the transformation of the six-band Landsat TM data set to a set of three Tasselled Cap axes.

3 The method has been widely used only for Landsat TM and MSS data.

2.1.2 Principal components analysis

Principal components analysis (PCA) is another general tool for coordinate transformation and data reduction in remote sensing image processing. However, unlike the Tasselled Cap, the new axes formed by PCA are not specified by the user’s prior definition of the transformation matrix, but are derived from the variance-covariance or correlation matrix computed

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Classification Methods for Remotely Sensed Data
Classification Methods for Remotely Sensed Data, Second Edition
ISBN: 1420090720
EAN: 2147483647
Year: 2001
Pages: 354

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