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A divergence operator to quantify texture from multi‐spectral satellite images

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A divergence operator to measure the texture content in a multi‐spectral image is proposed. A multi‐spectral image is modelled as an n ‐dimensional vector field, ‘ n ' being the number of bands of the image. A pixel of the image is an n ‐dimensional vector in this field. It is demonstrated that the flux variations of the vector field are related to changes in texture in the image. A divergence operator measures the flux variation and, hence, texture. In order to save computer memory, speed up the divergence operator calculation and lessen the content of noise of the image, principal component transformation is applied to the bands of the image. The first three principal components are used to span the vector field. The partial derivatives involved in the divergence operator are written as weighted finite differences. To estimate these derivatives, cubes of three, five and seven voxels per side are considered. The cube is systematically displaced to cover the entire domain of the vector field. In each position of the cube, the divergence value is calculated using the weighted finite difference approximation. This value is written as a pixel in an output image file according to the Cartesian coordinates defined by the location of the cube. This image file depicts the texture variations of the multi‐spectral image. The relation flux variation versus coarseness of texture is discussed. Two examples, based on Landsat Thematic Mapper multi‐spectral and synthetic multi‐spectral images, are presented and analysed.
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Document Type: Research Article

Affiliations: Instituto de Geofísica‐UNAM, Cd. Universitaria, 04510 México DF, México

Publication date: 2006-07-10

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