Multi-Resolution Spatial Analysis Process (MRSAP)

The following example shows how pipeline processes are used to build image processing operations using Multi-Resolution Spatial Analysis Process (MRSAP). MRSAP is a PYXIS DGGS process built upon the zoom in and zoom out filter and the multi-resolution blur process and their ability to remove high frequency data from an image. 

PYXIS Multi Resolution Blur Process

A simple blurring filter was created by combining the Zoom Out and Zoom In filters, result in blurred data at the original image resolution. By zooming out multiple times before zooming back in, the Blur Filter is able to produce arbitrarily large blurs, since each additional step increases the area of the blur by a factor of three. This nonlinear effect means that the blur filter can very efficiently produce large blur effects when compared to the alternative approach of repeatedly applying a neighborhood filter.

Multi-Resolution Spatial Analysis Process

The MRSAP Filter recovers this high frequency data by subtracting the blurred image from the original source. Lower frequency channels can be extracted by taking the difference between subsequent blurs, and the lowest frequency channel is simply the last available blur. Note that MRSAP can be generalized to any number of blurring steps.

Sharpening Process

A simple image sharpening pipeline can be built by adding the image’s high frequency content back into the image. In the pipeline shown, MRSAP is used to extract the high frequency component of the image. Note that the addition process limits the range of output, so that cells that are sharpened above the upper limit are capped to that limit.

Image Fusion Process

Image fusion is the combination of images from different sensors to get new or more precise information about the subject of the images. 

For remote-sensing imagery there are two main features: spatial and spectral.  Combining processes within the PYXIS Pipelines provide a opportunities to complete both spectral and spatial fusion. The main effort is to prepare multiple images so that the different frequency components can be processed together. For the ISEA3H DGGS the main effort of up and down sampling between images of different resolutions is built into the grid structure.  Transforming the images into frequency components is also optimized.  In the process, some spatial-frequency information is lost and some artificial noise created. To best preserve the original information while minimizing the artificial noise, several methods were introduced, including subband filtering and wavelets.  

In the pipeline process shown below, high frequency data from each image is extracted using MRSAP.  One image is sharply focused on the foreground clock while the the second on the background clock.   Both clocks are in focus when the high frequency images are combined then fused with one low frequency image.