5 Best Ways to Find the Shortest Distance Between a Point and a Contour in OpenCV with Python

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💡 Problem Formulation: In various computer vision tasks, we are often required to calculate the shortest distance from a given point to a contour within an image. This operation is critical in applications like object tracking, collision avoidance, and area measurement. For example, given the coordinates of a point and a binary image where the contour is defined, we desire the minimum Euclidean distance between them.

Method 1: Using cv2.pointPolygonTest()

This method utilizes the cv2.pointPolygonTest() function, which determines the shortest distance between a point and a contour. This function returns a positive value if the point is inside the contour, a negative value if it’s outside, and zero if the point is on the contour. The third argument measureDist=True indicates that we want to calculate the actual distance.

Here’s an example:

import cv2
# Assume contour is obtained from some previous operations
# point is a tuple of (x, y)
distance = cv2.pointPolygonTest(contour, point, True)
print("Shortest distance:", distance)

Output:

Shortest distance: 25.4

In this snippet, we first import OpenCV. Assume we have previously obtained a contour and have a point. We then pass these to cv2.pointPolygonTest(), which returns the shortest distance. The printed result shows this distance.

Method 2: Calculating Distances to All Contour Points

Another approach is to calculate the Euclidean distance between the point and all points of the contour, and then find the minimum value. This is not the most efficient method, but it can be used when you need to find the actual closest contour point.

Here’s an example:

import cv2
import numpy as np

# Assume contour is a NumPy array of points and point is a coordinate pair
distances = np.sqrt(((contour - point)**2).sum(axis=2))
min_distance = np.min(distances)
print("Shortest distance:", min_distance)

Output:

Shortest distance: 15.3

This code calculates the Euclidean distance using NumPy operations between the given point and all points in the contour, then finds the minimum distance. The result is the shortest distance from the point to the contour.

Method 3: Using cv2.distanceTransform()

In cases where you have a binary image, you can use cv2.distanceTransform() to calculate the distance to the closest zero pixel for each pixel of the image (which corresponds to the contour if the image is a mask). Then you simply extract the value at the point’s location.

Here’s an example:

import cv2

# Assume binary_img is a binary image and point is a tuple of (x, y)
dist_transform = cv2.distanceTransform(binary_img, cv2.DIST_L2, 5)
min_distance = dist_transform[point[1], point[0]]
print("Shortest distance:", min_distance)

Output:

Shortest distance: 12.7

After performing a distance transform on binary_img, this returns a matrix of distances. The shortest distance to the nearest contour from the specified point is simply retrieved from this matrix.

Method 4: Using scipy.spatial.distance.cdist()

The cdist() function from SciPy calculates the distance between each pair in two collections of inputs. You can use this to calculate distances from the point to all points on the contour. It uses more computational resources but is a simple one-liner.

Here’s an example:

from scipy.spatial import distance
import numpy as np

# contour is a set of points and point needs to be reshaped to fit cdist expected dimensions
min_distance = np.min(distance.cdist(np.array([point]), contour, 'euclidean'))
print("Shortest distance:", min_distance)

Output:

Shortest distance: 15.3

Using SciPy’s distance.cdist(), we calculate all pairwise distances between the point and the contour, and then determine the smallest one, which gives us the shortest distance.

Bonus One-Liner Method 5: Use numpy.min() and numpy.linalg.norm()

By combining NumPy’s min() function with linalg.norm(), you can calculate the minimum distance in a memory-efficient and arguably more readable way compared to method 2.

Here’s an example:

import numpy as np

# contour is a numpy array of contour points; point is a tuple (x, y)
min_distance = np.min([np.linalg.norm(p-point) for p in contour])
print("Shortest distance:", min_distance)

Output:

Shortest distance: 15.3

This one-liner uses a list comprehension inside np.min() to find the smallest distance calculated by np.linalg.norm(), which computes the Euclidean distance between the point and each contour point, p.

Summary/Discussion

  • Method 1: cv2.pointPolygonTest(). Efficient and robust. No additional libraries needed. Does not give the actual closest contour point.
  • Method 2: Calculating distances to all points manually. Straightforward but not as optimized. Precise, since it allows finding the actual closest point on the contour.
  • Method 3: cv2.distanceTransform(). Fast and efficient, especially for binary images and repeated queries. Requires the input to be a binary image.
  • Method 4: Using scipy.spatial.distance.cdist(). Very simple syntax but less efficient for large contours. Requires SciPy, which is not always available.
  • Bonus Method 5: Combining numpy.min() and numpy.linalg.norm(). Memory-efficient and easy to read. Might not be as optimized for large data sets.