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Digital image processing in Python 3 - part I: digital image filters

See on LiaScript:

https://liascript.github.io/course/?https://raw.githubusercontent.com/HueblerPatricia/LiaScriptTUBAF/main/DigitalImageFilters.md

Goals and fields of application

goals fields
reduce noise satellite pictures
make details stand out aerial photos
CT / X-ray imaging

What do we want to do?

  • prepare image for further processing
  • improve image for human user --{{0}}-- First of all let's make clear, what we use filter methods for. Basically there are two possibilities for that: In the first one, we want to change a picture in that way, that a computer is able to do further work on it. In the second one, which we want to deal with, our goal is to improve the image for a human user. That means, we want to make special parts of the picture more or better visible.

Preparations

Import necessary modules

import numpy as np                #working with arrays
import matplotlib.pyplot as plt   #plot an image

@Pyodide.eval

--{{0}}-- First we need to bind in some Python modules.

What are the modules for?

module content
NumPy work with arrays, matrices, vectors etc.
Matplotlib.Pyplot plotting images and referred settings

Create a simple picture

Colorful - rgb

--{{0}}-- For a colorful image we need, of course, some colors. Let's define them.

red       = [255,0  ,0  ]
green     = [0  ,255,0  ]
blue      = [0  ,0  ,255]
brown     = [145,111,124]
purple    = [255,0  ,255]
yellow    = [255,255,0  ]
orange    = [255,212,45 ]
white     = [255,255,255]
turquoise = [0  ,255,255]
black     = [0  ,0  ,0  ]

@Pyodide.eval

Creating our picture

--{{0}}-- Now we create an array with 3 color layers. You can take this example, play with the colors or be more creative.

def rotateList(lst, rot):

    '''Rotates a given list

    Parameters
    ----------
    lst : list
        list with entries of any data type
    rot : integer
        number of entries for the list to be rotated

    Returns
    -------
    list
        the rotated list
    '''
    l2 = lst[rot:] + lst[:rot]
    return l2

#the picture's side length
pictSize = 120

# a list with predefined colors from above
# create list because we want to "play" with the colors
colorList = [yellow, white, red, orange, purple]

pictSize = pictSize//len(colorList)
squareLen = pictSize
pictSize *= len(colorList)
#create array with 3 color layers for r, g and b
pictarray = np.zeros([pictSize, pictSize, 3], dtype=np.uint8)

lsta = 0
lstp = squareLen
for lines in range(0,len(colorList)):
    csta = 0
    cstp = squareLen
    for col in range(0,len(colorList)):
        pictarray[lsta:lstp,csta:cstp] = colorList[col]
        csta += squareLen
        cstp += squareLen
    lsta += squareLen
    lstp += squareLen
    colorList = rotateList(colorList,-2)

@Pyodide.eval

Colorful squares

plt.figure(dpi=180)
plt.imshow(pict)
plt.show()

Normally you could use the commands above, but again we are in LiaScript, so use the lines below!

fig, ax = plt.subplots()
plt.imshow(pictarray)
plt.show()

plot(fig)

@Pyodide.eval

Shades of gray

--{{0}}-- You may do all following computations with all three color layers or you may convert your picture into grayscale.

Normally you would have another ready implemented function for this and could use the following code:

from skimage.color import rgb2gray

gray = rgb2gray(pictarray)

#plt.imshow(gray, cmap = plt.get_cmap('gray'))
#plt.show()

But LiaScript doesn't know the module "skimage", so let's write our own function "rgb2gray". Anyway, for understanding that is the better way.

Change to grayscale yourself

def rgb2gray(rgb):

    '''Converts an rgb pixel into grayscale

    Parameters
    ----------
    rgb : array
        a pixel with 3 color layers

    Returns
    -------
    float
        the grayscale value for the given rgb
    '''

    r, g, b = rgb[:,:,0], rgb[:,:,1], rgb[:,:,2]
    gray = 0.2989 * r + 0.5870 * g + 0.1140 * b
    return gray

@Pyodide.eval

Remark: You may also change the weights for the 3 colors. Those above were taken from Wikipedia (https://de.wikipedia.org/wiki/Grauwert).

Now the computation:

gray = rgb2gray(pictarray)

@Pyodide.eval

Look at "gray"

fig, ax = plt.subplots()
plt.imshow(gray, cmap = plt.get_cmap('gray'))
plt.show()
plot(fig)

@Pyodide.eval

A new picture

In a few slides we will come to deal with linear image filters. Do you want to continue with the square picture? Then just skip the next slide and go on! Otherwise we will take an example picture from the Python modules.

First opportunity: import

Remark: Don't do this if your internet connection is not the best! Otherwise it will take a high amount of time.

--{{0}}-- We have to bind in another module. If you already know that process will take too long, skip this slide and try the second opportunity. If you do this, the picture will be rgb.

from scipy import misc

gray = misc.face(gray = True)

@Pyodide.eval

{{1}}


Second opportunity: use a ready definition

--{{1}}-- Here is an array that is already filled with the picture's grayscale values. This definition should be much faster, but the image is of a lower resolution.

gray = np.array([
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	0x16, 0x16, 0x32, 0x4F, 0x5F, 0x6F, 0x7C, 0x80, 0x7F, 0x84, 0x84, 0x8A,
	0x8E, 0x93, 0x8F, 0x8D, 0x8A, 0x8A, 0x86, 0x86, 0x80, 0x8D, 0x94, 0x86,
	0x75, 0x8D, 0xCA, 0xC0, 0xA3, 0xAA, 0xC3, 0xC7, 0xB9, 0x8D, 0x7C, 0xA4,
	0xB1, 0xB8, 0xBF, 0xC2, 0xC5, 0xAF, 0x52, 0x79, 0x94, 0x8A, 0x56, 0x26,
	0x16, 0x41, 0x58, 0x4C, 0x18, 0x18, 0x19, 0x1A, 0x49, 0x5F, 0x6D, 0x83,
	0x6C, 0x64, 0x7F, 0x82, 0x85, 0x90, 0x96, 0x9E, 0x92, 0x83, 0x5D, 0x58,
	0x63, 0x77, 0x62, 0x78, 0x7E, 0x7D, 0x7E, 0x5A, 0x79, 0x79, 0x79, 0x7A,
	0x74, 0x48, 0x7D, 0x80, 0x7B, 0x93, 0x61, 0x46, 0x4F, 0x68, 0x83, 0xA2,
	0xA8, 0xA3, 0xA0, 0x7B, 0x2C, 0x1E, 0x15, 0x0A, 0x18, 0x20, 0x23, 0x21,
	0x1D, 0x1A, 0x1B, 0x20, 0x2B, 0x1D, 0x2C, 0x22, 0x0E, 0x53, 0x14, 0x0A,
	0x0A, 0x08, 0x09, 0x0B, 0x0E, 0x0F, 0x0F, 0x14, 0x13, 0x19, 0x19, 0x1A,
	0x16, 0x20, 0x18, 0x3D, 0x60, 0x79, 0x8B, 0x8A, 0x95, 0x8B, 0x8D, 0x90,
	0x8E, 0x8D, 0x89, 0x8A, 0x7A, 0x91, 0x8D, 0x7F, 0x76, 0x8E, 0xCB, 0xC2,
	0xA1, 0xAA, 0xBA, 0xC7, 0xB9, 0x88, 0x85, 0xA7, 0xB6, 0xBD, 0xC2, 0xC2,
	0xC5, 0xA1, 0x58, 0x79, 0x96, 0x8B, 0x57, 0x22, 0x2B, 0x44, 0x51, 0x29,
	0x16, 0x19, 0x1B, 0x1B, 0x47, 0x5C, 0x68, 0x80, 0x71, 0x57, 0x78, 0x82,
	0x80, 0x88, 0x95, 0x98, 0x93, 0x8A, 0x60, 0x56, 0x5F, 0x73, 0x69, 0x69,
	0x80, 0x7C, 0x7E, 0x59, 0x6D, 0x84, 0x7B, 0x79, 0x7C, 0x36, 0x63, 0x87,
	0x89, 0x87, 0x91, 0x63, 0x4D, 0x52, 0x6B, 0x87, 0xA5, 0xAE, 0xA3, 0xA4,
	0x8D, 0x3C, 0x1B, 0x17, 0x1C, 0x1B, 0x1D, 0x18, 0x0B, 0x14, 0x13, 0x20,
	0x2A, 0x20, 0x18, 0x0F, 0x2B, 0x45, 0x0B, 0x09, 0x08, 0x07, 0x06, 0x07,
	0x0B, 0x0D, 0x0E, 0x0F, 0x0F, 0x12, 0x14, 0x16, 0x16, 0x1F, 0x1C, 0x1E,
	0x24, 0x26, 0x29, 0x50, 0x6A, 0x7F, 0x8C, 0x87, 0x87, 0x88, 0x8C, 0x8F
])

@Pyodide.eval


{{2}}


A plot

gray.shape = (96, 128 )

fig, ax = plt.subplots()
plt.imshow(gray, cmap=plt.cm.gray)
plt.show()

plot(fig)

@Pyodide.eval


Theory of linear filters

Literature for this chapter: Gonzalez, Woods: Digital Image Processing. Third Edition. PHI Learning Private Limited. New Delhi, 2008. Chapter 3.4

Image as array

--{{0}}-- The table represents our grayscale image. Each field is one pixel marked with "p".

| p | p | p | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p |

Filter mask

--{{0}}-- You see the rectangle marked by an "k" in every field. That is our filter mask or kernel. That is normally a square with an odd side length. Why odd? Because we want to work easily with integers.

| p | p | p | p | p | p | | k | k | k | p | p | p | | k | k | k | p | p | p | | k | k | k | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p |

Current pixel

--{{0}}-- With the picture and the kernel we want to calculate the new color value for the pixel in the middle of the kernel marked with an "x". If this operation is linear, we call the whole thing "linear filter".

| p | p | p | p | p | p | | k | k | k | p | p | p | | k | x | k | p | p | p | | k | k | k | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p | | p | p | p | p | p | p |

New value of the current pixel "x" computed by using the following formula:

$new value = \dfrac{1}{m\cdot n}\cdot\sum_{i=1,j=1}^{m,n} value picture[i][j]\cdot value kernel[i][j] $

Translated into Python:

def convolve(kernel,pictpart):

    '''Performs a convolution in 2D

      does a pointwise multiplication of "kernel" and "pictpart" and computes the sum over the result

    Parameters
    ----------
    kernel : 2D array
        the filter mask
    pictpart : 2D
        the actual part of the picture to be convolved

    Returns
    -------
    float
        the sum over the multiplication's result
    '''

    s = 0.0
    temporal_array = np.multiply(kernel,pictpart)
    s = sum(temporal_array)
    s = sum(s)
    return s

@Pyodide.eval

One example of linear image filters

Remark: All following examples are ready implemented in "OpenCV". (see https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_filtering/py_filtering.html). Here working on rgb pictures is as easy as working on grayscale images.

Average filter

The kernel is a square nxn and all entries are of the same weight.

n = 5
kernel=np.ones((n,n), dtype=np.float32)
kernel.fill(1/(n*n))
print(kernel)

@Pyodide.eval

New picture

Create empty picture to write our blurred picture values. It must have the same size as the original (grayscale) one, so you may copy it and erase it's values.

newpict = gray[0:][0:].copy() #copy rows and columns of "gray"
newpict.fill(0)

@Pyodide.eval

Have a look if you want.

fig, ax = plt.subplots()
plt.imshow(newpict, cmap = plt.get_cmap('gray'))
plt.show()
plot(fig)

@Pyodide.eval

"Pictpart"

Look into the formulas above. We need

  • an original (grayscale) image -> done
  • a kernel -> done
  • a new, empty picture -> done
  • a picture part (same size as kernel) -> left to do!
pictpart = kernel.copy()
pictpart.fill(0)

@Pyodide.eval

The "real" filter process

--{{0}}-- Imagine you have your picture and the filter mask. Now you move the filter mask step by step over the original picture, calculate the new color values for every pixel that is located in the middle of the filter mask. And you write those new color values into the new, empty image.

--{{0}}-- This process is the same for all linear filters and in fact for most filters at all.

for i in range(0+(kernel.shape[0]//2),  len(gray)-(kernel.shape[0])):
    for j in range(0+(kernel.shape[1]//2),  len(gray[1])-(kernel.shape[1])):

        for k in range(0,  (kernel.shape[0])):
            for l in range(0,  (kernel.shape[1])):
                pictpart[k][l]=gray[i+k][j+l]
        newpict[i+(kernel.shape[0]//2)][j+(kernel.shape[1]//2)]=convolve(kernel, pictpart)

@Pyodide.eval

See the blurred image

fig, ax = plt.subplots()
plt.imshow(newpict, cmap = plt.get_cmap('gray'))
plt.show()
plot(fig)

@Pyodide.eval

Further computations

Some ideas about what to do with blurred images.

Differrence picture

--{{0}}-- Now we have the original grayscale image and the blurred one. What can we do with them? Subtract one from the other!

diffPict = gray - newpict
fig, ax = plt.subplots()
plt.imshow(diffPict, cmap = plt.get_cmap('gray'))
plt.show()
plot(fig)

@Pyodide.eval

Now we see where was blurred most because that is visible best now. Especially we see edges.

Unsharp masking

Sometimes we want to sharpen edges. So let's add the "diffPict" to the grayscale one. This process is called "unsharp masking".

masked = gray + diffPict
fig, ax = plt.subplots()
plt.imshow(masked, cmap = plt.get_cmap('gray'))
plt.show()
plot(fig)

@Pyodide.eval

Comparison of all three stages of Processing

cmap = plt.get_cmap('gray')
fig = plt.figure(figsize=(12,12))
sub1 = plt.subplot(3, 3, 1)
sub1.imshow(gray, cmap = cmap)
sub1.set_title('Original grayscale')
sub2 = plt.subplot(3, 3, 2)
sub2.imshow(newpict, cmap = cmap)
sub2.set_title('Average blurred')
sub3 = plt.subplot(3, 3, 3)
sub3.imshow(masked, cmap = cmap)
sub3.set_title('Unsharp masked')

plt.show()
plot(fig)

@Pyodide.eval

Other filters

Just a short overview. The mentioned book "Digital image processing" is a good resource to go on reading.

Linear filter: Gaussian filter

This one works like the average filter. It's only difference is the kernel. Here you don't have always the same value, but something like a Gaussian bell curve in 2D. You may use any ready implemented function or you take the computation steps from above after creating your kernel by the following lines:

def create_gaussiankernel(side=5, sigma=1):

    '''creates a Gaussian kernel in 2D for image filtering

    Parameters
    ----------
    side : integer
        length of one side of the square that will be the kernel
    sigma : number
        some expression of the filter's strength

    Returns
    -------
    2D array
        the ready and normed kernel
    '''
    ax = np.arange(-side // 2 + 1., side // 2 + 1.)
    xx, yy = np.meshgrid(ax, ax)
    kernel = np.exp(-0.5 * (np.square(xx) + np.square(yy)) / np.square(sigma))
    return kernel / np.sum(kernel)

kernel = create_gaussiankernel(5,5)

Nonlinear filters

Median filter: You do also have a kind of kernel, but it is not meant to calculate values with linear algebra. The process works the following: You collect all color values in the kernel's range of the original image and sort them by size. Then you choose the one right in the middle of your list as the new color value of the current pixel.

Minimum and maximum filter: Minimum and maximum filter work in a very similar way: You do also sort your values, but choose the lowest or highest number as new color value.

Further ideas

By unsharp masking we have sharpened the edges but lost contrast. We could go on with some histogram modification to improve our "masked" image.

Remark: Als implemented in OpenCV. See https://opencv-python-tutroals.readthedocs.io/en/latest/py_tutorials/py_imgproc/py_histograms/py_histogram_equalization/py_histogram_equalization.html#histogram-equalization