2024 Multimedia HW3

Prerequisites

Make sure that you have python and pip installed on your computer.

Run

$ python3 -m pip install -r requirements.txt

to get all you need to run the code.

Usage

Simply run

$ python3 main.py <image file path>

to get the results.

A sample image file Histogram+Edge.bmp in this directory is used as the example for the following description.

Histogram Equalization

The main package used here to compute image data is opencv.

from cv2 import imread, cvtColor, COLOR_BGR2RGB, COLOR_BGR2GRAY, COLOR_GRAY2RGB, GaussianBlur, imshow, normalize, NORM_MINMAX, threshold, THRESH_BINARY, namedWindow, createTrackbar, imwrite
from sys import argv
from matplotlib.pyplot import subplots, tight_layout, savefig, show
from numpy import histogram, array, zeros, zeros_like, where, sum, round

Methods are detailed below.

First, I simply read in the input image, show it, convert it to grayscale, and make the histogram of it.

    cimg = imread(argv[1])
    assert cimg is not None, "file could not be read, check with os.path.exists()"

    _, axes = subplots(2, 2, figsize=(10, 5))
    axes[0][0].imshow(cvtColor(cimg, COLOR_BGR2RGB))
    axes[0][0].set_title('Original Colored Image')
    axes[0][0].axis('off')

    cimg = cvtColor(cimg, COLOR_BGR2GRAY)

    # bins = 0 ~ 256
    # so x = 0 ~ 256
    y, x = histogram(cimg.flatten(), bins=range(257))
    # x will have one element more than y, and that element is the upper bound. In this case, x[-1] = 256.
    # This is because the last bin is [255, 256) to include 255.
    axes[1][0].bar(x[:-1], y)
    axes[1][0].set_xlabel('Gray Scale')
    axes[1][0].set_ylabel('Frequency')
    axes[1][0].set_title('Histogram of Original Grayscale')

Then, I apply the Histogram Equalization by pdf and cdf.

    # Histogram Equalization
    pdf = y / sum(y)
    y_normalized = pdf * 255
    cdf = round(y_normalized.cumsum()).astype('uint8')

    # Now, cdf can act like a map, so the Histogram Equalization of cimg is cdf[cimg].
    img = cdf[cimg]
    axes[0][1].imshow(cvtColor(img, COLOR_GRAY2RGB))
    axes[0][1].set_title('Equalized')
    axes[0][1].axis('off')

    y, x = histogram(img.flatten(), bins=range(257))
    axes[1][1].bar(x[:-1], y)
    axes[1][1].set_xlabel('Gray Scale')
    axes[1][1].set_ylabel('Frequency')
    axes[1][1].set_title('Histogram of Equalized')

    ...

    tight_layout()
    show()

The result looks like this

Edge Detection

After the image was histogram equalized, I apply Edge Detection by smoothing it, convolute it with sobel x and sobel y matrices, prevent it from overflowing, and normalize it.

    # Edge Detection
    sobel_x = array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]])
    sobel_y = sobel_x.T

    img = GaussianBlur(cimg, (3, 3), 0)
    zero_padding = zeros((img.shape[0] + 2, img.shape[1] + 2)).astype('int32')
    zero_padding[1:-1, 1:-1] = img
    res = zeros_like(img).astype('int32')

    for x in range(img.shape[0]):
        for y in range(img.shape[1]):
            res_x = sum(zero_padding[x : x + 3, y : y + 3] * sobel_x) ** 2
            res_y = sum(zero_padding[x : x + 3, y : y + 3] * sobel_y) ** 2
            res[x, y] = (res_x + res_y) ** 0.5

    img = normalize(where(res > 255, 255, res).astype('uint8'), None, 0, 255, NORM_MINMAX)
    ...

That looks cool, right? But it looks blurry, and edges shouldn't be blurry, so I turn it binary.

def apply_threshold(lb):
    global img
    _, timg = threshold(img, lb, 255, THRESH_BINARY)
    imshow('Edge Detection', timg)
    # imwrite('result2.png', timg)

At this point, the only thing that is left to do is give it a threshold. Otherwise, it could look messy since all positive values are white.

Don't worry. A track bar is provided below the picture on the window so you can slide it however you like to get the best result for you.

    ...
    namedWindow('Edge Detection')
    createTrackbar('Lower Bound:', 'Edge Detection', 0, 255, apply_threshold)
    apply_threshold(0)