TDM 40100: Project 7 — 2022

Motivation: Images are everywhere, and images are data! We will take some time to dig more into working with images as data in this series of projects.

Context: In the previous project, we learned to sharpen images using unsharp masking. In this project, we will perform edge detection using Sobel filtering.

Scope: Python, images, JAX

Learning Objectives
• Process images using numpy, skimage, and JAX.

Make sure to read about, and use the template found here, and the important information about projects submissions here.

Dataset(s)

The following questions will use the following dataset(s):

• /anvil/projects/tdm/data/apple.jpg

• /anvil/projects/tdm/data/drward.jpg

Questions

Question 1

Let’s, once again, work with our apple.jpg image. In the previous project, we sharpened the image using unsharp masking. In this project, we are going to try to detect edges using a Sobel filter. The first step in this process is to convert our image from color to greyscale.

There are a few ways to do this, we will use the luminosity method. Create a function called to_greyscale that accepts the image in numeric numpy ndarray form, and returns the modified image in the numeric numpy ndarray form.

 The luminosity method of conversion takes into consideration that our eyes don’t react to each color the same way. You can read about some of the other methods here.

$gray = \frac{(0.2989*R + 0.5870*G + 0.1140*B)}{255}$

img = io.imread("/anvil/projects/tdm/data/apple.jpg")
img = to_greyscale(img)
io.imsave("grey.jpg", img)
with open("grey.jpg", "rb") as f:

m = hashlib.sha256()
m.update(my_bytes)
m.hexdigest()
output
d3aac435526a98d5d8665c558a96b834b63e5f17531b6e197b14d3b527406970

To display the greyscale image using imshow, you must include the cmap="gray" option.

imshow(img, cmap="gray")
Items to submit
• Code used to solve this problem.

• Output from running the code.

Question 2

The big picture with edge detection is detecting sudden changes in pixel intensities. A natural way to find changes is by using gradients/derivatives! That could be time consuming, hence the genius of the Sobel filter.

Write a function called estimate_gradients that uses the Sobel filter to estimate the gradients, gx and gy. gx is the gradient in the x direction and gy is the gradient in the y direction. estimate_gradients should accept the image and return both gx and gy.

To calculate the estimated gradients, you must take a pixel and its eight neighbors, multiply them by a 3x3 "kernel", and sum the results. In a lot of ways, this is very similar to what you did manually in the previous project. However, this operation is much more popular — so popular, it has a name — convolution.

Read the Sobel operator wikipedia page, and look at the provided kernels used to calculate the gradient estimates. Use this function to calculate and return both gx and gy.

 You will want your resulting image to be the same dimesion as before the convolve function.
 You can verify your output. img = io.imread("/anvil/projects/tdm/data/apple.jpg") img = to_greyscale(img) gx, gy = estimate_gradients(img) io.imsave("gx.jpg", gx) with open("gx.jpg", "rb") as f: my_bytes = f.read() m = hashlib.sha256() m.update(my_bytes) print(m.hexdigest()) io.imsave("gy.jpg", gy) with open("gy.jpg", "rb") as f: my_bytes = f.read() m = hashlib.sha256() m.update(my_bytes) print(m.hexdigest()) output 966c8530c02913ccc44b922ce9b42e6b85679a743b5e44757dc88ec2adfd21af e06ff1ed6edb589887a52d7fe154b84a12495d0ab487045e26cb0b34fc0b5402
Items to submit
• Code used to solve this problem.

• Output from running the code.

Question 3

What we really want is a single gradient that combines both gx and gy. We can obtain it using the following formula.

$G = \sqrt{gx^2 + gy^2}$

Alternatively, the following would work as well.

$G = |gx| + |gy|$

Decide which formula to implement. Bring everything you’ve written so far together into a single function called get_edges. get_edges should accept the image (as a numeric np.ndarray, and return the final result, a greyscale image with edges clearly defined.

You can verify your solution with the following. Note that depending on which method you chose, the resulting hash will be different. We’ve included both possibilities.

Which method did you choose and why?

img = io.imread("/anvil/projects/tdm/data/apple.jpg")
img = get_edges(img)
io.imsave("edge.jpg", img)
with open("edge.jpg", "rb") as f:

m = hashlib.sha256()
m.update(my_bytes)
m.hexdigest()
output options
6386859f42d9d7664b79d75f2b375058c1d0a61defb9a055caaaa69ad95504ad
3ac023a3900013e000e40812b96f7c120edd921cc483cec2f3d0d547a6e2675b
Items to submit
• Code used to solve this problem.

• Output from running the code.

Question 4

The Sobel filter is very effective, but like most things, has flaws. One such flaw is the sensitivity to noise. There are some ways around that.

• You could threshold the output. If G is less than a certain value, you can force the value to be 0.

• You can apply another filter to blur the image prior to calculating the gradient estimates (just like we did with the median filter in the previous project!).

Create two new functions: get_edgesv1, and get_edgesv2. Version 1 should use the cutoff method and version 2 should use the blur method.

This question will be graded by looking at the outputted images, since there are many variations of possible result. Play around with the cutoff value in version 1. For version 2, please feel free to use our new convolve function to use a mean instead of median blur.

 The convolve function makes it super easy to apply a mean blur. Think about what convolve does and you should be able to figure out how to create a mean blur really quickly.
Items to submit
• Code used to solve this problem.

• Output from running the code.

Question 5

Apply your favorite edge detection function that you’ve built to a new image. How did it work? Why did you like the edge detection function you chose best? Write 1-2 sentences about your choice, and make sure to show the results of your image.

Feel free to use /anvil/projects/tdm/data/coke.jpg — the results are pretty neat!

Items to submit
• Code used to solve this problem.

• Output from running the code.

 Please make sure to double check that your submission is complete, and contains all of your code and output before submitting. If you are on a spotty internet connection, it is recommended to download your submission after submitting it to make sure what you think you submitted, was what you actually submitted. In addition, please review our submission guidelines before submitting your project.