How to crop the biggest object in image with python opencv?

You can use function findContours to do this.

For example, like this:

#!/usr/bin/env python

import cv2
import numpy as np

# load image
img = cv2.imread('Image.jpg')
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY) # convert to grayscale
# threshold to get just the signature (INVERTED)
retval, thresh_gray = cv2.threshold(gray, thresh=100, maxval=255, 
                                   type=cv2.THRESH_BINARY_INV)

image, contours, hierarchy = cv2.findContours(thresh_gray,cv2.RETR_LIST, 
                                   cv2.CHAIN_APPROX_SIMPLE)

# Find object with the biggest bounding box
mx = (0,0,0,0)      # biggest bounding box so far
mx_area = 0
for cont in contours:
    x,y,w,h = cv2.boundingRect(cont)
    area = w*h
    if area > mx_area:
        mx = x,y,w,h
        mx_area = area
x,y,w,h = mx

# Output to files
roi=img[y:y+h,x:x+w]
cv2.imwrite('Image_crop.jpg', roi)

cv2.rectangle(img,(x,y),(x+w,y+h),(200,0,0),2)
cv2.imwrite('Image_cont.jpg', img)

Note that I used THRESH_BINARY_INV instead of THRESH_BINARY.

Image_cont.jpg:

Image_crop.jpg:

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You can also use this with skewed rectangles as @Jello pointed out. Unlike simpler solution above, this will correctly filter out diagonal lines.

For example:

#!/usr/bin/env python

import cv2
import numpy as np

# load image
img = cv2.imread('Image2.png')
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY) # convert to grayscale
# threshold to get just the signature (INVERTED)
retval, thresh_gray = cv2.threshold(gray, 100, maxval=255, 
                                   type=cv2.THRESH_BINARY_INV)

image, contours, hierarchy = cv2.findContours(thresh_gray,cv2.RETR_LIST, 
                                   cv2.CHAIN_APPROX_SIMPLE)

def crop_minAreaRect(img, rect):
    # Source: https://stackoverflow.com/questions/37177811/

    # rotate img
    angle = rect[2]
    rows,cols = img.shape[0], img.shape[1]
    matrix = cv2.getRotationMatrix2D((cols/2,rows/2),angle,1)
    img_rot = cv2.warpAffine(img,matrix,(cols,rows))

    # rotate bounding box
    rect0 = (rect[0], rect[1], 0.0)
    box = cv2.boxPoints(rect)
    pts = np.int0(cv2.transform(np.array([box]), matrix))[0]
    pts[pts < 0] = 0

    # crop and return
    return img_rot[pts[1][1]:pts[0][1], pts[1][0]:pts[2][0]]

# Find object with the biggest bounding box
mx_rect = (0,0,0,0)      # biggest skewed bounding box
mx_area = 0
for cont in contours:
    arect = cv2.minAreaRect(cont)
    area = arect[1][0]*arect[1][1]
    if area > mx_area:
        mx_rect, mx_area = arect, area

# Output to files
roi = crop_minAreaRect(img, mx_rect)
cv2.imwrite('Image_crop.jpg', roi)

box = cv2.boxPoints(mx_rect)
box = np.int0(box)
cv2.drawContours(img,[box],0,(200,0,0),2)
cv2.imwrite('Image_cont.jpg', img)

Image2.png (the input image):

Image_cont.jpg:

Image_crop.jpg:

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If you use opencv-python 4.x, change image, contours, hierarchy to just contours, hierarchy.