💡 Problem Formulation: In computer vision tasks, finding the extreme points (topmost, bottommost, rightmost, and leftmost) of an object in an image is crucial for object tracking, shape analysis, and image cropping. Suppose we have an input image with a clear object contrasted against the background. We would like to locate the extreme points of this object and visualize these points on the image.
Method 1: Using Contours and MinAreaRect
This technique involves finding contours, then creating a minimum area rectangle around the detected object to easily extract the corner points. The cv2.minAreaRect() function is specified for calculating the minimum area rectangle, and cv2.boxPoints() is used to retrieve the rectangle’s corners.
Here’s an example:
import cv2
import numpy as np
# Load image, grayscale, and find edges
image = cv2.imread('object.png')
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
edged = cv2.Canny(gray, 30, 200)
# Find contours and draw the minimum area rectangle
cnts, _ = cv2.findContours(edged.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
rect = cv2.minAreaRect(cnts[0])
box = cv2.boxPoints(rect)
box = np.int0(box)
# Draw the rectangle on the original image
cv2.drawContours(image,[box],0,(0,0,255),2)
cv2.imshow('Image', image)
cv2.waitKey(0)The output is an image with a red rectangle drawn around the object, indicating the extreme points.
This method first detects the object’s contour and calculates the smallest rectangle that can contain this contour. It then uses cv2.boxPoints() to obtain a 4-point representation of this rectangle, which practically gives the extreme points of the object. Highlighted on the image, these points provide visual cues about the object’s orientation and dimensions.
Method 2: Directly Finding Extreme Points
By directly calculating the extreme points based on contour coordinates, we can determine the object’s boundaries without needing to draw a rectangle. The np.argmax() and np.argmin() functions help identify these extreme coordinate points.
Here’s an example:
import cv2
import numpy as np
# Load image, grayscale, and threshold
image = cv2.imread('object.png')
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
thresh = cv2.threshold(gray, 45, 255, cv2.THRESH_BINARY)[1]
# Find contours
cnts, _ = cv2.findContours(thresh.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
c = cnts[0]
# Determine the most extreme points along the contour
extLeft = tuple(c[c[:, :, 0].argmin()][0])
extRight = tuple(c[c[:, :, 0].argmax()][0])
extTop = tuple(c[c[:, :, 1].argmin()][0])
extBot = tuple(c[c[:, :, 1].argmax()][0])
# Draw the outline of the object and the extreme points
cv2.drawContours(image, [c], -1, (0, 255, 255), 2)
cv2.circle(image, extLeft, 8, (0, 0, 255), -1)
cv2.circle(image, extRight, 8, (0, 255, 0), -1)
cv2.circle(image, extTop, 8, (255, 0, 0), -1)
cv2.circle(image, extBot, 8, (255, 255, 0), -1)
cv2.imshow('Image', image)
cv2.waitKey(0)The result is an image with the object’s contour and its extreme points marked in different colors.
This code snippet computes the extreme points of an object after finding its contours. It visualizes these points as colored circles on the image. The use of argmin() and argmax() on the contour array allows quick determination of the most extreme X and Y coordinates, corresponding to the desired extreme points.
Method 3: Combining with Convex Hull
Using a convex hull in conjunction with contour analysis can refine the search for extreme points by eliminating interior angles. The functions cv2.convexHull() and cv2.approxPolyDP() help in simplifying and wrapping the contour more effectively.
Here’s an example:
import cv2
import numpy as np
# Load image, grayscale, and threshold
image = cv2.imread('object.png')
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
thresh = cv2.threshold(gray, 45, 255, cv2.THRESH_BINARY)[1]
# Find contours
cnts, _ = cv2.findContours(thresh.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
c = cnts[0]
# Find the convex hull and approximate it
hull = cv2.convexHull(c)
hull_approx = cv2.approxPolyDP(hull, 0.01 * cv2.arcLength(hull, True), True)
# Draw the convex hull
cv2.drawContours(image, [hull_approx], -1, (0, 255, 255), 2)
# Draw the extreme points
for point in hull_approx:
cv2.circle(image, tuple(point[0]), 8, (0, 0, 255), -1)
cv2.imshow('Image', image)
cv2.waitKey(0)The output displays an image with the object’s convex hull and its approximate extreme points highlighted.
After finding the object’s contour, this snippet creates a convex hull to capture the outer boundary. It then approximates the hull to fewer points representing the object’s extreme points. This helps in finding a simple yet effective representation of the object’s shape, and the extreme points derived from the convex hull are often more accurate for certain objects.
Method 4: Feature-Based Approach
A feature-based approach involves keypoint detectors such as SIFT, SURF, or ORB to find points of interest in the object which may correspond to extreme points, especially when these features appear on the object’s periphery.
Here’s an example:
import cv2
import numpy as np
# Load image and initialize ORB detector
image = cv2.imread('object.png')
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
orb = cv2.ORB_create()
# Detect and draw keypoints
keypoints = orb.detect(gray, None)
keypoints, descriptors = orb.compute(gray, keypoints)
image_with_keypoints = cv2.drawKeypoints(image, keypoints, None, color=(0,255,0), flags=0)
cv2.imshow('Keypoints', image_with_keypoints)
cv2.waitKey(0)The resulting image highlights various keypoints detected on the object with green circles, some of which may be on the object’s extremities.
This method does not directly target extreme points but rather identifies key features of the object. It is conceivable that some of these keypoints could be located at or near the extreme edges of the object. This approach is dependent on the effectiveness of the feature detector used and the nature of the object in the image.
Bonus One-Liner Method 5: Using Image Moments
Image moments can provide information about the shape of an object, from which we can infer the centroid and relate it to the extreme points by understanding the object’s geometry.
Here’s an example:
import cv2
import numpy as np
# Load image, grayscale, and threshold
image = cv2.imread('object.png')
gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
thresh = cv2.threshold(gray, 45, 255, cv2.THRESH_BINARY)[1]
# Calculate Moments
cnts, _ = cv2.findContours(thresh.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
M = cv2.moments(cnts[0])
cX = int(M["m10"] / M["m00"])
cY = int(M["m01"] / M["m00"])
# Draw the center of the object
cv2.circle(image, (cX, cY), 7, (255, 255, 255), -1)
cv2.imshow('Center', image)
cv2.waitKey(0)The output displays the center point based on the image moments marked on the object.
While this one-liner does not draw the object’s extreme points directly, it does calculate and show the object’s centroid. By examining the object’s geometry in relation to its centroid, one could deduce the location of extreme points or use this information as a step towards more advanced shape analysis techniques.
Summary/Discussion
- Method 1: Using Contours and MinAreaRect. This method is reliable and straightforward, providing a visual box that encompasses the extreme points. Its main weakness is the extra step of calculating a bounding box which may not always correspond exactly to the desired extreme points.
- Method 2: Directly Finding Extreme Points. It’s highly precise for detecting extreme points and does not rely on additional constructs like rectangles. Its weakness is that it can be sensitive to noise and the contour’s resolution.
- Method 3: Combining with Convex Hull. This method can create a tight fit around the object that excludes interior angles. However, the approximations made may sometimes exclude true extreme points.
- Method 4: Feature-Based Approach. This is less direct but useful in complex scenes where the object’s features themselves may imply the extreme points. It relies heavily on the feature detector algorithm, which may not always focus on the object’s edges.
- Bonus One-Liner Method 5: Using Image Moments. Simple for finding the centroid which can be a useful reference point in object analysis, but it requires additional steps to find the actual extreme points.