I examined OpenCV filtering

at first

I investigated the filtering process provided by OpenCV

Operating environment

Python3,OpenCV

Simple smoothing (blurring / blurring) processing

Assuming that the original image has the following data (grayscale), simple smoothing (blurring) is performed.

Simple smoothing takes the simple average of a rectangle of multiple pixels surrounding each pixel as the value for that pixel. Here, since the size of the rectangle is (3 * 3), it is calculated as follows.

The total pixels are calculated as follows

import numpy as np
import cv2 as cv
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import matplotlib.cm as cm

black = [0x00, 0x00, 0x00]
white = [0xFF, 0xFF, 0xFF]

img = np.array([
                [black, black, black, black, black, black, black]
                ,[black, black, black, black, black, black, black]
                ,[black, black, white, white, white, black, black]
                ,[black, black, white, white, white, black, black]
                ,[black, black, white, white, white, black, black]
                ,[black, black, black, black, black, black, black]
                ,[black, black, black, black, black, black, black]                               
                ]
                , dtype=np.uint8)

#Grayscale
img = cv.cvtColor(img, cv.COLOR_RGB2GRAY)

#Graph drawing area
fig = plt.figure(figsize=(8, 3))
ax1 = fig.add_subplot(121, projection='3d')
ax2 = fig.add_subplot(122, projection='3d')

# X,Y
_x = np.arange(img.shape[1])
_y = np.arange(img.shape[0])
_xx, _yy = np.meshgrid(_x, _y)
x, y = _xx.ravel(), _yy.ravel()
width = depth = 1

#height
top = img.ravel()
bottom = np.zeros_like(top)

# 0-255 to 0.0-1.Definition of function to convert to 0(For grayscale display)
norm = colors.Normalize(0, 255)

#original
color_values = cm.gray(top.tolist())
ax1.bar3d(x, y, bottom, width, depth, top, color=color_values)
ax1.set_title('Original')

#Blur (kernel size 3*3)
blurImg = cv.blur(img, (3, 3))
top = blurImg.ravel()
color_values = cm.gray(norm(top.tolist()))
ax2.bar3d(x, y, bottom, width, depth, top, color=color_values)
ax2.set_title('Blur')

plt.show()

Median filtering

The median filter takes the median value of the rectangle that surrounds each pixel as the value for that pixel.

The total pixels are calculated as follows

#medianBlur (kernel size 3)*3)
mBlurImg = cv.medianBlur(img, 3)
top = mBlurImg.ravel()
color_values = cm.gray(norm(top.tolist()))
ax2.bar3d(x, y, bottom, width, depth, top, color=color_values)
ax2.set_title('medianBlur')

Gaussian filtering

The Gaussian filter multiplies the rectangle surrounding each pixel by a matrix called the Gaussian kernel and takes the sum as the value for that pixel. The 3 * 3 Gaussian kernel used here is as follows.

\begin{pmatrix}
1/16 & 2/16 & 1/16 \\
2/16 & 4/16 & 2/16 \\ 
1/16 & 2/16 & 1/16
\end{pmatrix}

PixelA is calculated as

import numpy as np

pixelA = np.array([[0, 0, 0]
                   ,[0, 255, 255]
                   ,[0, 255, 255]])
gaussKernel = np.array([[1/16, 2/16, 1/16]
                        ,[2/16, 4/16, 2/16]
                        ,[1/16, 2/16, 1/16]])
print(sum(sum(pixelA * gaussKernel))) 
#143  

The total pixels are calculated as follows

# GaussianBlur
gBlurImg = cv.GaussianBlur(img, (3, 3), 0, 0)
top = gBlurImg.ravel()
color_values = cm.gray(norm(top.tolist()))
ax2.bar3d(x, y, bottom, width, depth, top, color=color_values)
ax2.set_title('GaussianBlur')