filtering algorithm of image processing

First, learning experience:
When I learned the basic filtering algorithm principle, because the new contact is not very understanding how the algorithm is implemented, but after learning the morphology of the image, it is very simple to find the filtering algorithm. So it is suggested that beginners before learning the filtering algorithm, you can learn the image morphology, will achieve a multiplier effect.

Second, the understanding of the filter function:
Filter algorithm, can be understood as a filtering algorithm, as we filter products, the defective to remove, leaving only qualified products. In the image processing of the filtering algorithm, the object is to deal with the image, in addition to removing unwanted pixels in the image values (such as noise removal), but also to strengthen the image we need to study some content (such as edge extraction).

Third, filtering algorithm:
The algorithms described here are for image space filtering algorithms, where templates, which can be understood as structural elements in image morphology, are used to select the pixels in the image to be manipulated. Spatial filtering is divided into smoothing filter and sharpening filter according to its function. Smoothing Filter: can reduce or eliminate the high frequency components in the image, but does not affect the low frequency components, in the actual application can be used to eliminate the noise. Sharpening Filter: In contrast to smoothing filter, it can weaken or eliminate the low frequency component in the image, but does not affect the high frequency component, which can increase the contrast of image and the edge is obvious. The actual application can be used to enhance the blurred details or the edges of the target.

Spatial Enhancement Filtering Technology classification:

1. Linear Smoothing Filter

(1) box filter : Using the sum of the domain pixel values of a pixel as the filter result, the neighborhood is the image area covered by the template, at which point all the coefficients of the template are 1.

(2) neighborhood average : is a special generous box filter, with a pixel of the field average pixel value as the filter result, that a is the first situation.

where n (x, y) is the area of the image covered by the template age, and n is the size of the template.

(3) weighted average : At this time the template coefficient is not 1, but the specific coefficient. It is generally believed that the pixels from the center of the template should have a greater contribution to the filter results, so the coefficients closer to the template center can be obtained than the template periphery.

(4) Gauss average : is a special weighted average, except that the coefficients in the template are determined by the Gaussian distribution.

2. Linear Sharpening Filter

(1) Laplace operator
The Laplace operator is an isotropic second-order differential operator that uses the differential coefficients to determine the template coefficients and then convolution with the image to achieve sharpening filtering.

According to the Laplace definition:

Two second-order biasing along the x and Y directions are available with differential calculation:

Merge to:

When a template is a 8-neighborhood when a 4-neighborhood

  The sum of the coefficients of the above two templates is 0, which is to keep the mean value of the image after the template operation unchanged. The Laplace operator enhances the gray-scale discontinuous region in the image, but weakens the contrast of the gray-scale in the image, and the result is superimposed into the original image, which can get the amount of the image after Ruihua.

(2) High frequency lifting filter
The sharpening effect of the image can be obtained by overlaying the differential result of the image, or by deducting the image integral result.
Set the original image to F (x, Y), and the smoothed image is g (x, y):

Non-sharpening Mask: H (x, y) = f (x, Y)-g (x, Y)

Sharpen Image: {f (x, Y)-g (x, Y)} + f (x, Y)

High frequency boost filter: Multiplies the academician graph by one magnification factor A, minus the smoothed image

can be converted to:

When A=1, it is a non-sharpening mask;
When a=2, mask for non-sharpening.

3. Nonlinear Smoothing Filter

(1) Median filter: the corresponding pixel values under the template are sorted in ascending order, and the median value is selected as the result.

(2) Similar to median filtering, there are also maximum, minimum, midpoint filtering

The above four kinds of filtering is also known as percent filtering, percent filtering is based on the sorting of the template to work, also known as sequential statistical filtering.