Convolution Filters

Spatial and Frequency Transformations

Fourier transforms  are ubiquitous in data analysis and are an important tool in image processing.  Fast Fourier Transforms, Discrete  Fourier Transforms, and Multi Resolution Spatial Analysis Process on the ISEA3H DGGS are included in the PYXIS DGGS SDK. 

Fast Fourier Transform

The PYXIS Fourier Transform is a powerful tool in image processing which essentially maps data from the ISEA3H spatial domain into the frequency domain. It can be used in a large number of applications, including spectral analysis, blurring and image compression. The PYXIS FFT applies Fouriers to arbitrarily sized regions of the ISEA3H DGGS using a rhombus are to map the hexagonal structure to the rectilinear structure of a traditional FFT. 

Discrete Fourier Transform

The PYXIS Discrete Fourier Transform used the hexagonal tessellation of the ISEA3H directly.  As this shape is not “rectangular” in the same way that the diamond FFT shape is, a unique cell traversal has been developed to extract cell values that preserve the information that would be transformed by a conventional DFT.