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Detection of edges and lines in multidimensional data is an important operation in a number of image processing applications. The multidimensional picture function is a sampling of the underlying reflectance function of the objects in the scene with the noise added to the true function values. Edges and lines refer to places in the image where there are jumps in the values of the function or its derivatives. The multidimensional greytone surface is expanded as a weighted sum of basis functions. Using multidimensional orthogonal polynomial basis functions, expressions are developed for the coefficients of the fitted quadrautic and cubic surfaces. The parameters of the fitted surfaces are obtained when there is a rotation in the coordinate system. Assuming the noise is Gaussian, statistical tests are devised for the detection of significant edges and lines. Direction isotropic properties of the fitted surfaces are described. For computational efficiency, recursive relations are obtained between the parameters of the fitted surfaces of successive neighborhoods. Furthermore, experimental results are presented by applying the developed theory to multiband Landsat-Imagery Data.