Summary of types and uses of various transform filters and noises

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First, the basic gray-scale transformation function

1.1 Image Inversion
Application scenario: enhances white or gray detail embedded in a dark area of an image, especially when the area of black is dominant in size.

1.2 Logarithmic transformations (against number transformations with opposite)
Procedure: Maps a low grayscale value with a narrower range in the input to a wide range of grayscale values in the output.
Useful: Used to extend the value of dark pixels in the image while compressing higher values of the gray level.
Feature: The dynamic range of an image with a large change in the value of the compressed pixel.
For example: The Fourier spectrum is processed, the low values in the spectrum are often not observed, and the details are richer after the logarithmic transformation.

1.3 Power conversion (AKA: Gamma Transform)
Procedure: Maps a narrow range of dark input values to a wider range of output values.
Useful: Gamma correction corrects power-law responses, which are often used to accurately display images on computer screens, and to enhance contrast and discernible detail.

1.4 Piecewise linear transformation function
Cons: Technical instructions require user input.
Advantages: The form can be arbitrarily complex.

1.4.1 Contrast stretch: Extend the dynamic range of an image

1.4.2 Grayscale Layering: Two-value images can be generated to study the motion of contrast agents

1.4.3 bit plane layering: the value of any pixel in the original image can be reconstructed by a similar binary pixel value corresponding to these bit planes, which can be used to compress a picture.

1.5 Histogram processing
1.5.1 Histogram equalization: Enhanced contrast, compensating for images that are visually indistinguishable from gray-level differences. Powerful as a self-adapting contrast enhancement tool.

1.5.2 Histogram matching (histogram-defined): The image you want to handle has a defined histogram shape. On the basis of histogram equalization, it is advantageous to solve the image that the pixel concentrates on the dark end of gray level.

1.5.3 local histogram processing: used to enhance the details of small areas by using a grayscale distribution in each pixel neighborhood in the image as the basis for designing the transformation function, which can be used to display the details that the global histogram equalization is not sufficient to affect.

1.5.4 Histogram statistics: can be used for image enhancement, can enhance the dark color area while keeping the bright areas as long as possible, flexibility is good.

Second, the basic spatial filtering
2.1 Smoothing Spatial Filter
2.1.1 Smoothing Linear filter (mean filter)
Output: A simple average of pixels contained within the neighborhood of a filter template, which replaces the value of each pixel in the image with the average grayscale in the neighborhood, and is a low-pass filter.
Results: Decrease the sharp change of image grayscale.
Application: Reduces noise and removes irrelevant details from the image.
Negative effects: blurred edges.

2.1.2 Statistical Sorting filter (nonlinear filter)
Example: Median filter
Procedure: Based on the ordering of the images contained in the image area defended by the filter, and then substituting the values of the central area with the values determined by the statistic sort results.
Use: Median filter can be a good solution to salt and pepper noise, that is, impulse noise.

2.2 Sharpening the spatial filter
2.2.1 Laplace operator (second-order differential)
Function: Emphasize the mutation of gray scale, can enhance the detail of the image

2.2.2 Non-sharpening masking and high-lift filtering
Principle: Subtract a non-sharpening (smooth) version of the original image
Background: Printing and publishing uses many years of image sharpening
High-lift filter: The result of the original image minus the blur graph is a template, the output is equal to the original and weighted template, when the weight of 1 to get non-sharpening masking, when the weight is greater than 10% for high-lift filter.

2.2.3 Gradient Sharpening (first order differential pair)
Meaning: The gradient indicates the direction of the maximum rate of change at that position.
Use: Industrial detection, auxiliary manual inspection of product defects, automatic detection of pre-treatment.

Three, the basic frequency filter
3.1.1 Ideal Low (high) pass filter
Characteristics: Ringing phenomenon, the actual can not be achieved
Usefulness: not practical, but it is useful to study the characteristics of a filter.

3.1.2 Butworth Low (high) pass filter
Features: No ringing phenomenon, thanks to the smooth transition between low and high frequencies, the second-order Butworth low-pass filter is a good choice.
Effect: Smoother than ideal low (high) pass filter, small edge distortion, high cutoff frequency, smoother distortion.

3.1.3 Gaussian low (high) pass filter
Features: no ringing.
Usefulness: Any type of artificial defect is unacceptable (medical imaging)

3.1.4 passivation template, high-lift filter and high-frequency accent filter
Usefulness: X-ray, first high frequency emphasis, then histogram equalization.

3.1.5 Homomorphic filtering
Principle: The image is divided into the product of irradiation component and reflection component.
Useful: Enhance the image, sharpen the reflection component (edge information) of the image, such as PET scan.

3.1.6 Selective filtering Band-stop filter and band-pass filter.
Function: Handles the development of small areas of frequency bands and rectangular regions. Trap Filter
Principle: Reject or pass a pre-defined neighborhood on the center of the frequency rectangle.
Application: Selectively modifies the local area of the discrete Fourier transform.
Pros: Direct DFT processing, without padding required. Interactive processing does not result in a winding error.
Purpose: To solve Moire ripple.

Four, the important noise probability density function
4.1. Gaussian noise
Features: Mathematical ease of handling.

4.2 Rayleigh Noise
Features: The basic shape is deformed to the right and is suitable for the approximate skew histogram.

4.3 Irish (gamma) noise
Features: The denominator of the density distribution function is the gamma function.

4.4 Exponential Noise
Feature: Density distribution follows exponential function.

4.5 Uniform Noise
Features: uniform density.

4.6 Impulse noise (bipolar pulse noise aka salt and pepper Noise)
Features: The only type of noise that can cause degradation, visually distinguishable.

Five, Space filter reduction noise
5.1 Mean value filter
5.1.1 arithmetic mean-value filter
Results: The results are blurred and the noise is reduced.
Suitable for: Gaussian or even random noise.

5.1.2 Geometric mean filter
Result: Fewer image details are lost than arithmetic mean filters.
Applicable: More suitable for Gaussian or even random noise.

5.1.3 Harmonic mean filter
Results: Good for salt noise (white), but not for pepper noise (black), good at dealing with other noises like Gaussian noise.

5.1.4 Inverse harmonic mean-value filter
Results: It is suitable to reduce or eliminate the effect of salt and pepper noise in practice, when the Q value is positive, the noise of pepper is eliminated, when the Q value is negative, the filter eliminates salt noise. However, these two types of noise cannot be eliminated at the same time.
Application: Impulse noise.
Cons: It is important to know whether the noise is noise or dark noise.

5.2 Statistical Sorting filter
5.2.1 Mid-value filter
Suitable for: presence of unipolar or bipolar pulse noise.

5.2.2 Max-Value Filter
Function: Find the most bright spot in the image, can reduce the pepper noise.

5.2.2 Minimum Value Filter
Function: Useful for the darkest point, can reduce salt noise.

5.2.3 Midpoint Filter
Function: Combined with statistical sorting and averaging, it works well for random distributed noises, such as Gaussian noise or uniform noise.

5.2.4 Modified alpha mean filter
Function: Useful in situations involving a variety of noises, such as Gaussian noise and salt and pepper noise mixing.

5.3 Adaptive Filter
5.3.1 Adaptive Local Noise reduction filter
Function: To prevent meaningless results due to lack of knowledge of image noise variance, the additive Gaussian noise determined by mean and variance is applied.

5.3.1 Adaptive Median filter
Function: Handles more probability of impulse noise while smoothing non-impulse noise while preserving detail, reducing distortion such as object boundary coarsening or thinning.

5.4 Frequency Domain filter eliminates periodic noise
5.4.1 Band Resistance Filter
Application: Noise elimination in the general position of the noise component in the frequency domain near a known application

5.4.2 Band-pass filter
Note: You cannot use band-pass filters directly on a single image, which eliminates too much image detail.
Useful: Masks The result of the selected band and helps to mask the noise pattern.

5.4.3 Trap Filter
Principle: Blocks the frequency within the neighborhood of the pre-defined center frequency.
Function: eliminates periodic noise.

5.4.4 Best Trap Filter
function: To solve the situation where there are many interference components.

Summary of types and uses of various transform filters and noises

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