Efficient Directional Gaussian Smoothers

Abstract

Linear and nonlinear filters, including morphological operators, play a significant role in the processing of remote sensing imagery. In particular, smoothing filters have been extensively used for noise removal and image restoration. In applications where linear and shift-invariant filters can be effectively employed, filtering is computationally efficient if implemented in transform domains. Nevertheless, in remote sensing applications, it is essential that smoothing filters be capable of handling missing and erroneous data without loss of information. In such cases, filtering requires the involvement of logical operations in order to determine which pixels should be used for processing, and thus takes the form of a nonlinear operator. Hence, transform-based methods cannot be used. Still, in applications where large volumes of data need to be processed, it is greatly desired that fast filtering algorithms are used. This letter introduces a computationally efficient spatial-domain-based implementation which is partially separable and steerable. The technique is general, and its efficiency has been demonstrated on weather radar data. It is shown that the proposed filtering approach is significantly faster compared to a recently introduced separable filter implementation.