Monday, April 9, 2012

Digital Processing Using Convolutional Kernels

One of the advantages of a fully digital SEM such as the JEOL 5900 is the ability to use digital processing tools to manipulate images. This manipulation may simply be noise filtering. Image granularity may be removed by averaging longer per pixel or by increasing the probe spot-size (in cases where image is not degraded by increasing the probe diameter). Such noise can also be removed by frame averaging provided that there is no significant drift of the image field between subsequent frames. However, the digital format of the image allows the application of digital image processing techniques.

As an example, the above image of latex spheres can be processed using a Laplacian edge-detection kernel. Each pixel can be averaged with its nearest neighbors using a special weight to produce a second spatial derivative of the image. Such a spatial derivative will serve to emphasize the edges of structures and thus the Laplacian kernels act as image edge enhancement tools. An example of a Laplacian kernel is:

[0, -1, 0]
[-1, 4, -1]
[0, -1, 0]

This image is produced using a Laplacian kernel (but not the one above). Note that it acts to enhance the edges of structures. Isolated spheres now look like hollow rings, where spheres that were closely packed together with little secondary electron contrast between them somewhat merge together.

Other possibilities are the sharpening and smoothing kernels. These can be applied separately or together to a digital image. The final image combines both to make a sharper and cleaner image. Since these are convolutional filters, the more nearest neighbors used in filtering will reduce image graininess, but like all convolutional filters, will result in some blurring of the image as high frequency spectral information is lost. Custom kernels can also be made that combine sharpening, derivative and smoothing functions. In the case of SEM images where there is a fast and slow scanning direction, it is not uncommon to have different types of noise in the vertical and horizontal directions of the image. In such cases, novel asymmetric kernels can be of great utility.

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