History of Long-Range Photography in Astronomy

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Slide 47

Convolution Matrix

The intensity of the image point located at the center of the matrix is replaced by the weighted average intensity of all the point located inside the matrix.

P1 P2 P3

P4 P5 P6

P7 P8 P9

P5 = (P1 + 2 * P2 + P3 + 2 * P4 + 4 * P5 + 2 * P6 + P7 + 2 * P8 + P9) / 16

The convoluted image is divided by the sum of the weighting coefficients: 16, 6, 8, and 2 respectively.

Slide 48

Median Filter

A variation on low-pass filtering and is better at eliminating noise.

Instead of replacing a pixel with the average of its neighbors, it is replaced with the median within the ensemble.

This filter is good for removing “hot” and “cold” pixels from an image.

Slide 49

High-Pass

A high-pass filter emphasizes fine detail in an image – exactly the opposite of what a low-pass filter does.

High-pass filters work exactly the same way, except that they use a different kernel.

High-pass filters can sharpen an image blurred by atmospheric seeing or poor focus.

Unfortunately, their effect on noise is also the opposite of a low-pass filter; noise becomes amplified.

Slide 50

Unsharp Masking

Unsharp masking is a variation of the high-pass filtering.

A low pass filter is first used to make a blurry copy of the original images.

This copy is subtracted from the original, suppressing large-scale features and leaving fine detail.

Unsharp masking is very effective for planetary imaging

Do not overdo high-pass filtering, since small, faint details can be greatly exaggerated. The result might not be a realistic view of the object.

An over processed image will look grainy and unnatural.

Slide 51

Deconvolution

Once we filter an image, we can undo the results through a process called deconvolution.

With deconvolution,instead of multiplying pixel data by a filter, we divide it.

Deconvolution can reduce the effects of atmospheric seeing and even defects created by poor optics.

Slide 52

Spatial Filtering Summary

Here are some guidelines I’ve found useful:

Low-pass filtering is good for picking faint nebulosity out of noisy images.

High-pass filtering and unsharp masking works well on lunar and planetary images.

Median filtering is good for reducing the noise in an image, particularly hot and cold pixels.

Deconvolution works well on high-resolution images.

After passing an image through a filtering algorith, try processing it with a stretching function.