Use of opencv3 6.2 low pass filter

frequency domain 、 The concept of frequency

The method of observing the frequency of the change of image intensity value is called frequency domain , The method of observing gray distribution to describe image features is called airspace .

Areas in the image where the gray intensity changes slowly Low frequency , And the area with fast change of intensity value produces High frequency , The frequency is divided into Vertical frequency （ Changes in the vertical direction ） and Horizontal frequency （ Changes in the horizontal direction ）.

It can be used The Fourier transform or cosine transform And other methods to display the frequency components of the image .

filter

Filtering is to selectively extract certain aspects of the image , You can enlarge some frequency bands in the image , At the same time, filter out operators of other frequency bands .

Filters can be divided into low pass filter and High pass filter , This section mainly introduces Block filter (box filter) and Gauss filter (gaussian filter).

Block filter

Block filter cv::blur You can replace the value of each function with the pixel neighborhood （ rectangular ） Average value .

The block filter uses the weighted accumulated value of the neighborhood pixels to replace the pixel value , So this filter is linear Of , And the block filter is a Mean filter , Because this example uses 5*5 The kernel of , Its kernel can be written as ：

1/25	1/25	1/25	1/25	1/25
1/25	1/25	1/25	1/25	1/25
1/25	1/25	1/25	1/25	1/25
1/25	1/25	1/25	1/25	1/25
1/25	1/25	1/25	1/25	1/25

Use a linear filter to move the kernel to the image On every pixel of , And multiply the corresponding pixel by the weight , Mathematically, it is called Convolution .

Gauss filter

Gauss filter cv::GaussianBlur It is also a linear filter , But unlike block filters , The weight of the Gaussian filter pixel is proportional to the distance from it to the central pixel , Normal distribution function . The formula of one-dimensional Gaussian function is ：

Parameters σ Determine the shape of Gaussian function curve ,σ The bigger it is , The flatter the function curve , That is, the smaller the weight of surrounding pixels ;σ The smaller it is , The steeper the function curve , That is, the greater the weight of surrounding pixels .

To create an image （ A two-dimensional space ） Apply two-dimensional Gaussian filter , Just apply a one-dimensional Gaussian filter on the horizontal line （ Filter the frequency in the horizontal direction ）, Then apply one-dimensional Gaussian filter on the longitudinal line （ Filter the frequency in the vertical direction ）. The principle is that Gaussian filter is a Separable filter , It can be divided into two one-dimensional filters .

Concrete realization

cv::Mat image = cv::imread("boldt.jpg");
cv::Mat boxblur, gaussianblur;
cv::blur(image,   // Original image 
         boxblur, // The image filtered by the block filter 
         cv::Size(5, 5)); // The size is 5*5 Filter for 
cv::GaussianBlur(image,          // Original image 
                 gaussianblur,   // The image after Gaussian filtering 
                 cv::Size(5, 5), // The size is 5*5 Filter for 
                 1.5,             // Parameters controlling the shape of Gaussian curve sigmaX,sigmaX The bigger it is , The smaller the proportion of nearby pixels 
                 0);             // Parameters controlling the shape of Gaussian curve sigmaY, If specified as 0 Or do not specify the default and sigmaX identical 
cv::imshow("image", image);
cv::imshow("boxblur", boxblur);
cv::imshow("gaussianblur", gaussianblur);

Effect display

cv::blur Use of functions

Function signature

CV_EXPORTS_W void blur( InputArray src, OutputArray dst,
                        Size ksize, Point anchor = Point(-1,-1),
                        int borderType = BORDER_DEFAULT );

The parameters are ： The input image , Output image , Filter size , Starting point （ The default is the middle point of the rectangle ）, Type of boundary （ General default ）.

cv::GaussianBlur Use of functions

Function signature

CV_EXPORTS_W void GaussianBlur( InputArray src, OutputArray dst, Size ksize,
                                double sigmaX, double sigmaY = 0,
                                int borderType = BORDER_DEFAULT );

The parameters are ： The input image , Output image , Filter size ,x Direction σ Parameters sigmaX,y Direction σ Parameters sigmaY, Type of boundary （ General default ）.

notes ： If only fill in sigmaX（ perhaps sigmaY Set to 0） It's fine too , Will default to sigmaY be equal to sigmaX. If sigmaX and sigmaY All set to 0, The function will determine the most suitable size by itself σ value .