Smoothing

Smoothing is a method to restore image from degradation by noise. Perform preprocess to remove the noise, then the image can be analyzed properly.

The method by using local operator

　The method by using local operator convolution is a most basic calculation to remove noise.

Simple Average

Local Average Filter

　Average pixels in specified window. Eos can perform by using mrcImageSmoothing (-m 2), or mrcImageConvolution with suitable kernel.

Local Weighted Average Filter

　Local Average Filter deals uniformly pixels in specified window. Against it, this filter greatly affects pixels near the centre. You can perform by using mrcImageConvolution with suitable kernel. 　In Addition, it supports convolution of Gaussian Function. In this case, generally use a Windowing Function as ±2σ ~±3σ.

Smoothing without lack of Image quality(edge, line)

Median Filter

　This is a filter which treats a medium value in specified window as the representative value. It is non linear filter. mrcImageSmoothing supports it.

　Merit: Edge doesn't become almost dull. Good at removing the salt-and-pepper noise (Poisson noise). 　Demerit: It needs to spend many time. The calculation is nonlinear.

Variable weighted averaging method

　This purpose is relaxation of noise by adaptively changing weight of weighted average in local region depending on each density pattern.

Sub local region splitting method

　This is a method that splits a local region to multiple local region, and selects a most uniform subregion, and performs smoothing at the region.

Lee-Sigma Filter

　This is a method which treats the mean about local region without data over specified range ±Kσ (Unique point) as a representative value. mrcImageSmoothing supports it.

　Merit: Edge doesn't become almost dull. Good at removing the salt-and-pepper noise (Poisson noise). 　Demerit: It needs to spend many time. The calculation is nonlinear.

Bilateral Filter

　This is used for smoothing preserving edge, and the Point Spread Function(PSF) on region that has great difference among its densities is reduced. mrcImageSmoothing supports it.

Relaxation

　This method treats grayscale level as probability, and get a suitable solution by repeating calculation finally.

Smoothing by process at frequency regions

Low-Pass Filter

　Noise(e.g. Gaussian Noise) has intensity to same extent for each frequency component in a spatial frequency. Against it, generally a signal has large intensity at low frequency component, and has small intensity at high frequency component. For it, there is this filter that improves the SN ratio by reducing the high frequency component.

Merit: comparatively high speed. Linear calculation.
Demerit: Edge become sometimes dull.