How do I crop an image using a binary mask image of the same picture to remove the background in python?

If I understand correctly, you want to extract the object and remove the background. To do this, you can just do a simple cv2.bitwise_and() with the mask and the original input image.

Does anyone know how I could make the edge image better and how I could use this to crop the normal image?

To extract the background from the image, you don't need an edge image, the thresholded image can be used to remove only the desired parts of the image. You can use the mask image to directly drop the image and remove the background. Other approaches of obtaining a binary mask include using a fixed threshold value, adaptive threshold, or Canny edge detection. Here's a simple example using Otsu's threshold to obtain a binary mask followed by a bitwise-and operation.

Here's the result with the removed background

You can also turn all pixels on the mask to white if you wanted the removed background to be white

Note: Depending on how "smooth" you want the result, you can apply any blur to the image before thresholding to smooth out the edges. This can include averaging, Gaussian, median, or bilaterial filtering.

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Code

import cv2

# Load image, grayscale, Otsu's threshold
image = cv2.imread('1.jpg')
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
thresh = cv2.threshold(gray, 0, 255, cv2.THRESH_BINARY_INV + cv2.THRESH_OTSU)[1]

# Remove background using bitwise-and operation
result = cv2.bitwise_and(image, image, mask=thresh)
result[thresh==0] = [255,255,255] # Turn background white

cv2.imshow('thresh', thresh)
cv2.imshow('result', result)
cv2.waitKey()