Problem 2.4

to reduce noise on the image One can apply Gaussian blur to smooth it. To do so, image convolution technique is applied with Gaussian kernel
which is given by the following formula for dimensions.

application of Gaussian blur

after image is smoothed, the derivatives and can we calculated by convolution with Sobel Kernels and

then magnitude

application of Sobel filter

to make image more clear we will use thresholding with some threshold value of 30 pixels as default which can we adjusted based on the input image.

with this implementation

import numpy as np
import skimage.io as io
import skimage.color as color
import matplotlib.pyplot as plt
from scipy.signal import convolve


def convert_to_rgb_format(img):
    if img.shape[2] == 4:
        img = color.rgba2rgb(img)
    return img


def convert_to_gray_scale(img):
    return color.rgb2gray(img)


def gaussian_kernel(size, sigma=1):
    size = int(size) // 2
    x, y = np.mgrid[-size : size + 1, -size : size + 1]
    normal = 1 / (2.0 * np.pi * sigma**2)
    g = np.exp(-((x**2 + y**2) / (2.0 * sigma**2))) * normal
    return g


def gaussian_blur(img):
    ker = gaussian_kernel(5, sigma=10)
    return convolve(img, ker, mode="valid")


def sobel_filters(img):
    Kx = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]], np.float32)
    Ky = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]], np.float32)

    Ix = convolve(img, Kx)
    Iy = convolve(img, Ky)

    G = np.hypot(Ix, Iy)
    G = G / G.max() * 255
    theta = np.arctan2(Iy, Ix)

    return G, theta


def threshold(img, T=30):
    cp = np.zeros((img.shape))

    N = img.shape[0]
    M = img.shape[1]

    for i in range(N):
        for j in range(M):
            if img[i, j] >= T:
                cp[i, j] = 255
            else:
                cp[i, j] = 0
    return cp


img = io.imread("./sky.png")
img = convert_to_rgb_format(img)

gray = convert_to_gray_scale(img)

g_blur = gaussian_blur(gray)

sobel, theta = sobel_filters(g_blur)

thres = threshold(sobel)


plt.figure(figsize=(10, 5))

plt.subplot(1, 2, 1)
plt.imshow(thres, cmap="gray")
plt.title("Pic 1")
plt.axis("off")

plt.subplot(1, 2, 2)
plt.imshow(sobel, cmap="gray")
plt.title("Pic 2")
plt.axis("off")

plt.show()
Copy

Problem 2.3

Github-article
Springer-Image-Denoising
GDM-application