Features

# to run in google colab
import sys

if "google.colab" in sys.modules:

    def download_from_web(url):
        import requests

        response = requests.get(url)
        if response.status_code == 200:
            with open(url.split("/")[-1], "wb") as file:
                file.write(response.content)
        else:
            raise Exception(
                f"Failed to download the image. Status code: {response.status_code}"
            )

    download_from_web(
        "https://github.com/YoniChechik/AI_is_Math/raw/master/c_08_features/chess.jpg"
    )

import cv2
import matplotlib.pyplot as plt
import numpy as np

imgBGR = cv2.imread("chess.jpg")
imgRGB = cv2.cvtColor(imgBGR, cv2.COLOR_BGR2RGB)
img = cv2.cvtColor(imgBGR, cv2.COLOR_BGR2GRAY).astype(float) / 255

plt.figure(figsize=(10, 10))
plt.imshow(imgRGB)
plt.show()

# derivatives in x and y dirs
kernel_x = np.array([[-1, 0, 1], [-2, 0, 2], [-1, 0, 1]])
Ix = cv2.filter2D(img, -1, kernel_x)

kernel_y = np.array([[1, 2, 1], [0, 0, 0], [-1, -2, -1]])
Iy = cv2.filter2D(img, -1, kernel_y)

window_size = 3
offset = int(np.floor(window_size / 2))

l_max = np.zeros(img.shape)
l_min = np.zeros(img.shape)
det = np.zeros(img.shape)
trace = np.zeros(img.shape)

# for each window in image
for y in range(offset, img.shape[0] - offset):
    for x in range(offset, img.shape[1] - offset):
        # build window of intersting data
        windowIx = Ix[y - offset : y + offset + 1, x - offset : x + offset + 1]
        windowIy = Iy[y - offset : y + offset + 1, x - offset : x + offset + 1]

        # this is added to be consistent with PCA
        # windowIx = windowIx-np.mean(windowIx)
        # windowIy = windowIy-np.mean(windowIy)

        # build second moments matrix
        Sxx = np.sum(windowIx * windowIx)
        Syy = np.sum(windowIy * windowIy)
        Sxy = np.sum(windowIx * windowIy)

        # eigendecomposition data
        H = np.array([[Sxx, Sxy], [Sxy, Syy]])
        L, V = np.linalg.eig(H)

        l_max[y, x] = np.maximum(L[0], L[1])
        l_min[y, x] = np.minimum(L[0], L[1])

        det[y, x] = (Sxx * Syy) - (Sxy**2)
        trace[y, x] = Sxx + Syy

plt.figure(figsize=(10, 10))
plt.imshow(l_max)
plt.colorbar()
plt.title("l_max")
plt.show()

plt.figure(figsize=(10, 10))
plt.imshow(l_min)
plt.colorbar()
plt.title("l_min")
plt.show()

plt.figure(figsize=(10, 10))
plt.imshow(trace)
plt.colorbar()
plt.title("trace")
plt.show()

plt.figure(figsize=(10, 10))
plt.imshow(det)
plt.colorbar()
plt.title("det")
plt.show()

harris = det / trace
harris[np.isnan(harris)] = 0

plt.figure(figsize=(10, 10))
plt.imshow(harris > harris.max() / 10)
plt.show()

gray = np.float32(img)
dst = cv2.cornerHarris(gray, 2, 3, 0.04)

plt.figure(figsize=(10, 10))
plt.imshow(dst)
plt.show()

# result is dilated for marking the corners, not important
dst = cv2.dilate(dst, None)
# Threshold for an optimal value, it may vary depending on the image.
imgRGB[dst > 0.01 * dst.max()] = [0, 0, 255]

plt.figure(figsize=(10, 10))
plt.imshow(imgRGB)
plt.show()