Today we are going to kick-off a three part series on **calculating the size of objects in images** along with **measuring the distances between them**.

These tutorials have been some of the most *heavily requested *lessons on the PyImageSearch blog. I’m super excited to get them underway — *and I’m sure you are too.*

However, before we start learning how to measure the size (and not to mention, the distance between) objects in images, we first need to talk about something…

A little over a year ago, I wrote one my favorite tutorials on the PyImageSearch blog: **How to build a kick-ass mobile document scanner in just 5 minutes**. Even though this tutorial is over a year old, its *still* one of the most popular blog posts on PyImageSearch.

Building our mobile document scanner was predicated on our ability to **apply a 4 point cv2.getPerspectiveTransform with OpenCV**, enabling us to obtain a top-down, birds-eye-view of our document.

However. Our perspective transform has a * deadly flaw* that makes it unsuitable for use in production environments.

You see, there are cases where the pre-processing step of arranging our four points in top-left, top-right, bottom-right, and bottom-left order can return* incorrect results!*

**To learn more about this bug, and how to squash it, keep reading.**

#### Looking for the source code to this post?

Jump Right To The Downloads Section## Ordering coordinates clockwise with Python and OpenCV

The goal of this blog post is two-fold:

- The
**primary purpose**is to learn how to arrange the*(x, y)*-coordinates associated with a rotated bounding box in top-left, top-right, bottom-right, and bottom-left order. Organizing bounding box coordinates in such an order is a prerequisite to performing operations such as perspective transforms or matching corners of objects (such as when we compute the distance between objects). - The
**secondary purpose**is to address a subtle, hard-to-find bug in the`order_points`

method of the imutils package. By resolving this bug, our`order_points`

function will no longer be susceptible to a debilitating bug.

All that said, let’s get this blog post started by reviewing the original, flawed method at ordering our bounding box coordinates in clockwise order.

### The original (flawed) method

Before we can learn how to arrange a set of bounding box coordinates in (1) clockwise order and more specifically, (2) a top-left, top-right, bottom-right, and bottom-left order, we should first review the `order_points`

method detailed in the original 4 point getPerspectiveTransform blog post.

I have renamed the (flawed) `order_points`

method to `order_points_old`

so we can compare our original and updated methods. To get started, open up a new file and name it `order_coordinates.py`

:

# import the necessary packages from __future__ import print_function from imutils import perspective from imutils import contours import numpy as np import argparse import imutils import cv2 def order_points_old(pts): # initialize a list of coordinates that will be ordered # such that the first entry in the list is the top-left, # the second entry is the top-right, the third is the # bottom-right, and the fourth is the bottom-left rect = np.zeros((4, 2), dtype="float32") # the top-left point will have the smallest sum, whereas # the bottom-right point will have the largest sum s = pts.sum(axis=1) rect[0] = pts[np.argmin(s)] rect[2] = pts[np.argmax(s)] # now, compute the difference between the points, the # top-right point will have the smallest difference, # whereas the bottom-left will have the largest difference diff = np.diff(pts, axis=1) rect[1] = pts[np.argmin(diff)] rect[3] = pts[np.argmax(diff)] # return the ordered coordinates return rect

**Lines 2-8** handle importing our required Python packages for this example. We’ll be using the `imutils`

package later in this blog post, so if you don’t already have it installed, be sure to install it via `pip`

:

$ pip install imutils

Otherwise, if you *do* have `imutils`

installed, you should upgrade to the latest version (which has the updated `order_points`

implementation):

$ pip install --upgrade imutils

**Line 10** defines our `order_points_old`

function. This method requires only a single argument, the set of points that we are going to arrange in top-left, top-right, bottom-right, and bottom-left order; although, as we’ll see, this method has some flaws.

We start on **Line 15** by defining a NumPy array with shape `(4, 2)`

which will be used to store our set of four *(x, y)*-coordinates.

Given these `pts`

, we add the *x* and *y* values together, followed by finding the smallest and largest sums (**Lines 19-21**). These values give us our top-left and bottom-right coordinates, respectively.

We then take the difference between the *x* and *y* values, where the top-right point will have the smallest difference and the bottom-left will have the largest distance (**Lines 26-28**).

Finally, **Line 31** returns our ordered *(x, y)*-coordinates to our calling function.

So all that said, can you spot the flaw in our logic?

I’ll give you a hint:

**What happens when the sum or difference of the two points is the ****same ?**

In short, tragedy.

If either the sum array `s`

or the difference array `diff`

have the same values, we are at risk of choosing the incorrect index, which causes a cascade affect on our ordering.

Selecting the wrong index implies that we chose the incorrect point from our `pts`

list. And if we take the incorrect point from `pts`

, then our clockwise top-left, top-right, bottom-right, bottom-left ordering will be be destroyed.

So how can we address this problem and ensure that it doesn’t happen?

To handle this problem, we need to devise a better `order_points`

function using more sound mathematic principles. And that’s exactly what we’ll cover in the next section.

### A better method to order coordinates clockwise with OpenCV and Python

Now that we have looked at a *flawed* version of our `order_points`

function, let’s review an *updated, correct* implementation.

The implementation of the `order_points`

function we are about to review can be found in the imutils package; specifically, in the perspective.py file. I’ve included the exact implementation in this blog post as a matter of completeness:

# import the necessary packages from scipy.spatial import distance as dist import numpy as np import cv2 def order_points(pts): # sort the points based on their x-coordinates xSorted = pts[np.argsort(pts[:, 0]), :] # grab the left-most and right-most points from the sorted # x-roodinate points leftMost = xSorted[:2, :] rightMost = xSorted[2:, :] # now, sort the left-most coordinates according to their # y-coordinates so we can grab the top-left and bottom-left # points, respectively leftMost = leftMost[np.argsort(leftMost[:, 1]), :] (tl, bl) = leftMost # now that we have the top-left coordinate, use it as an # anchor to calculate the Euclidean distance between the # top-left and right-most points; by the Pythagorean # theorem, the point with the largest distance will be # our bottom-right point D = dist.cdist(tl[np.newaxis], rightMost, "euclidean")[0] (br, tr) = rightMost[np.argsort(D)[::-1], :] # return the coordinates in top-left, top-right, # bottom-right, and bottom-left order return np.array([tl, tr, br, bl], dtype="float32")

Again, we start off on **Lines 2-4** by importing our required Python packages. We then define our `order_points`

function on **Line 6** which requires only a single parameter — the list of `pts`

that we want to order.

**Line 8** then sorts these `pts`

based on their *x-*values. Given the sorted `xSorted`

list, we apply array slicing to grab the two left-most points along with the two right-most points (**Lines 12 and 13**).

The `leftMost`

points will thus correspond to the *top-left* and *bottom-left* points while `rightMost`

will be our *top-right* and *bottom-right* points — **the trick is to figure out which is which.**

Luckily, this isn’t too challenging.

If we sort our `leftMost`

points according to their *y-*value, we can derive the top-left and bottom-left points, respectively (**Lines 18 and 19**).

Then, to determine the bottom-right and bottom-left points, we can apply a bit of geometry.

Using the top-left point as an anchor, we can apply the Pythagorean theorem and compute the Euclidean distance between the top-left and `rightMost`

points. By the definition of a triangle, the hypotenuse will be the largest side of a right-angled triangle.

Thus, by taking the top-left point as our anchor, the bottom-right point will have the largest Euclidean distance, allowing us to extract the bottom-right and top-right points (**Lines 26 and 27**).

Finally, **Line 31** returns a NumPy array representing our ordered bounding box coordinates in top-left, top-right, bottom-right, and bottom-left order.

### Testing our coordinate ordering implementations

Now that we have both the *original* and *updated* versions of `order_points`

, let’s continue the implementation of our `order_coordinates.py`

script and give them both a try:

# import the necessary packages from __future__ import print_function from imutils import perspective from imutils import contours import numpy as np import argparse import imutils import cv2 def order_points_old(pts): # initialize a list of coordinates that will be ordered # such that the first entry in the list is the top-left, # the second entry is the top-right, the third is the # bottom-right, and the fourth is the bottom-left rect = np.zeros((4, 2), dtype="float32") # the top-left point will have the smallest sum, whereas # the bottom-right point will have the largest sum s = pts.sum(axis=1) rect[0] = pts[np.argmin(s)] rect[2] = pts[np.argmax(s)] # now, compute the difference between the points, the # top-right point will have the smallest difference, # whereas the bottom-left will have the largest difference diff = np.diff(pts, axis=1) rect[1] = pts[np.argmin(diff)] rect[3] = pts[np.argmax(diff)] # return the ordered coordinates return rect # construct the argument parse and parse the arguments ap = argparse.ArgumentParser() ap.add_argument("-n", "--new", type=int, default=-1, help="whether or not the new order points should should be used") args = vars(ap.parse_args()) # load our input image, convert it to grayscale, and blur it slightly image = cv2.imread("example.png") gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY) gray = cv2.GaussianBlur(gray, (7, 7), 0) # perform edge detection, then perform a dilation + erosion to # close gaps in between object edges edged = cv2.Canny(gray, 50, 100) edged = cv2.dilate(edged, None, iterations=1) edged = cv2.erode(edged, None, iterations=1)

**Lines 33-37** handle parsing our command line arguments. We only need a single argument, `--new`

, which is used to indicate whether or not the *new* or the *original* `order_points`

function should be used. We’ll default to using the *original* implementation.

From there, we load `example.png`

from disk and perform a bit of pre-processing by converting the image to grayscale and smoothing it with a Gaussian filter.

We continue to process our image by applying the Canny edge detector, followed by a dilation + erosion to close any gaps between outlines in the edge map.

After performing the edge detection process, our image should look like this:

As you can see, we have been able to determine the outlines/contours of the objects in the image.

Now that we have the outlines of the edge map, we can apply the `cv2.findContours`

function to actually *extract* the outlines of the objects:

# find contours in the edge map cnts = cv2.findContours(edged.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE) cnts = imutils.grab_contours(cnts) # sort the contours from left-to-right and initialize the bounding box # point colors (cnts, _) = contours.sort_contours(cnts) colors = ((0, 0, 255), (240, 0, 159), (255, 0, 0), (255, 255, 0))

We then sort the object contours from left-to-right, which isn’t a requirement, but makes it easier to view the output of our script.

The next step is to loop over each of the contours individually:

# loop over the contours individually for (i, c) in enumerate(cnts): # if the contour is not sufficiently large, ignore it if cv2.contourArea(c) < 100: continue # compute the rotated bounding box of the contour, then # draw the contours box = cv2.minAreaRect(c) box = cv2.cv.BoxPoints(box) if imutils.is_cv2() else cv2.boxPoints(box) box = np.array(box, dtype="int") cv2.drawContours(image, [box], -1, (0, 255, 0), 2) # show the original coordinates print("Object #{}:".format(i + 1)) print(box)

**Line 61** starts looping over our contours. If a contour is not sufficiently large (due to “noise” in the edge detection process), we discard the contour region (**Lines 63 and 64**).

Otherwise, **Lines 68-71** handle computing the rotated bounding box of the contour (taking care to use `cv2.cv.BoxPoints`

[if we are using OpenCV 2.4] or `cv2.boxPoints`

[if we are using OpenCV 3]) and drawing the contour on the `image`

.

We’ll also print the original rotated bounding `box`

so we can compare the results after we order the coordinates.

We are now ready to order our bounding box coordinates in a clockwise arrangement:

# order the points in the contour such that they appear # in top-left, top-right, bottom-right, and bottom-left # order, then draw the outline of the rotated bounding # box rect = order_points_old(box) # check to see if the new method should be used for # ordering the coordinates if args["new"] > 0: rect = perspective.order_points(box) # show the re-ordered coordinates print(rect.astype("int")) print("")

**Line 81** applies the *original* (i.e., flawed) `order_points_old`

function to arrange our bounding box coordinates in top-left, top-right, bottom-right, and bottom-left order.

If the `--new 1`

flag has been passed to our script, then we’ll apply our *updated* `order_points`

function (**Lines 85 and 86**).

Just like we printed the *original bounding box* to our console, we’ll also print the *ordered points* so we can ensure our function is working properly.

Finally, we can visualize our results:

# loop over the original points and draw them for ((x, y), color) in zip(rect, colors): cv2.circle(image, (int(x), int(y)), 5, color, -1) # draw the object num at the top-left corner cv2.putText(image, "Object #{}".format(i + 1), (int(rect[0][0] - 15), int(rect[0][1] - 15)), cv2.FONT_HERSHEY_SIMPLEX, 0.55, (255, 255, 255), 2) # show the image cv2.imshow("Image", image) cv2.waitKey(0)

We start looping over our (hopefully) ordered coordinates on **Line 93** and draw them on our `image`

.

According to the `colors`

list, the top-left point should be *red*, the top-right point *purple*, the bottom-right point *blue*, and finally, the bottom-left point *teal*.

Lastly, **Lines 97-103** draw the object number on our `image`

and display the output result.

To execute our script using the *original, flawed* implementation, just issue the following command:

$ python order_coordinates.py

As we can see, our output is anticipated with the points ordered clockwise in a top-left, top-right, bottom-right, and bottom-left arrangement — **except for Object #6!**

**Note:*** Take a look at the output circles — notice how there isn’t a blue one?*

Looking at our terminal output for Object #6, we can see why:

Taking the sum of these coordinates we end up with:

- 520 + 255 = 775
- 491 + 226 = 717
- 520 + 197 = 717
- 549 + 226 = 775

While the difference gives us:

- 520 – 255 = 265
- 491 – 226 = 265
- 520 – 197 = 323
- 549 – 226 = 323

As you can see, **we end up with duplicate values!**

And since there are duplicate values, the `argmin()`

and `argmax()`

functions don’t work as we expect them to, giving us an incorrect set of “ordered” coordinates.

To resolve this issue, we can use our updated `order_points`

function in the imutils package. We can verify that our updated function is working properly by issuing the following command:

$ python order_coordinates.py --new 1

This time, all of our points are ordered correctly, including Object #6:

When utilizing perspective transforms (or any other project that requires ordered coordinates), *make sure you use our updated implementation!*

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## Summary

In this blog post, we started a three part series on *calculating the size of objects in images* and *measuring the distance between objects*. To accomplish these goals, we’ll need to order the 4 points associated with the rotated bounding box of each object.

We’ve already implemented such a function in a previous blog post; however, as we discovered, this implementation has a fatal flaw — it can return the *wrong coordinates* under *very specific* situations.

To resolve this problem, we defined a new, updated `order_points`

function and placed it in the imutils package. This implementation ensures that our points are always ordered correctly.

Now that we can order our *(x, y)*-coordinates in a reliable manner, we can move on to *measuring the size of objects in an image*, which is exactly what I’ll be discussing in our next blog post.

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