Spatial filtering & Frequency domain filtering (1)

1. Spatial filtering

A spatial filter consists of a small neighborhood window (odd edge length) that performs a predefined operation on pixels within a neighborhood (the linear case is the point multiplication sum), and the final result is assigned to the pixel at the center of the neighborhood.

The spatial filter can be divided into two kinds of smoothing spatial filter and sharpening space filter.

1) Smoothing Spatial filter has mean filter, median filter and so on, median filter is non-linear method, and has good effect on salt and pepper noise.

2) Sharpening the spatial filter has the First order differential, second derivative (see "Image local invariance characteristic and description" reading notes (3)--point and Edge detection), non-sharpening masking

The basic formula of one or two-order differential

Non-sharpening masking: Blur original image minus Blur image from original (result becomes template) add template to original

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a case of mixing two methods :

Need to enhance the detail of an image with a large noise and dark overall

Considering that the 1-order operator has better edge response than 2, and the 2-order operator has better response to detail than the 1-order (but it also brings a lot of noise), the original image is smoothed by 1-order (Sobel) sharpening, as a template (strong response to the edge, weak response to the flat area), and a 2-order (Laplace It is then multiplied with the template to enhance the detail, and finally the result is added to the original image and a power-law transform to get the enhanced images.

2. Using fuzzy sets to do gray-scale transformation and spatial filtering

Fuzzy set will not say, very basic, online a search a lot of

1) Grayscale Transformation

As an example of contrast enhancement, you first need to make a fuzzy rule :

IF a pixel is dark, then make it darker

IF One pixel is gray, then it is still gray

IF One pixel is bright, then make it lighter

Then you need to specify the membership function for the fuzzy variable within the fuzzy rule

Specify a standard output value for each fuzzy variable

such as VD = 0, vg = 127, VB = 255

This allows for a pixel to use the following formula to derive the fuzzy output

2) Spatial filtering

Take an example of a 3*3 neighborhood, where the neighborhood is shown in Figure 2-1

Figure 2-1. neighborhood, di = Zi-z5

Develop fuzzy rules :

IF D2 is 0 and D6 is 0 then Z5 is white

IF d6 is 0 and d8 is 0 then Z5 is white

IF D8 is 0 and D4 is 0 then Z5 is white

IF d4 is 0 and D2 is 0 then Z5 is white

ELSE Z5 is black

The membership function of fuzzy variable 0, white and black by ze, WH and BL respectively

standard output values of white and black are 255, 0

Output formulas similar to those introduced in grayscale transforms are calculated to get results