Pioneer/Imaging Lab 1

This page serves as a supplement to the first Digital Image Processing Lab for the Summer 2021 Pioneer Program.

Corrections / Clarifications to the Handout

• None yet

Running Python

You need to have Anaconda installed, which includes the Spyder IDE and all the modules that we need for this assignment.

Scikit Image

See Pioneer21/Lecture03 for more details about using the scikit-image module.

Links

• 2D Convolution description: HTTP://www.songho.ca/dsp/convolution/convolution2d_example.HTML
• Kernel page on Wikipedia: https://en.wikipedia.org/wiki/Kernel_(image_processing)
• Test Card for Exercise 8: https://en.wikipedia.org/wiki/Test_card

Examples

The following sections will contain both the example programs given in the lab as well as the image or images they produce. You should still type these into your own version of Python to make sure you are getting the same answers. These are provided so you can compare what you get with what we think you should get. All examples and exercises assume you have already run the following code:

import numpy as np
import skimage as ski
import scipy.signal as sig
import matplotlib.pyplot as plt

If there are any other required modules, they will explicitly show up at the top of the example or exercise code.

Example 1: Black & White Images

a = np.array([
    [1, 0, 1, 0, 0],
    [1, 0, 1, 0, 1],
    [1, 1, 1, 0, 0],
    [1, 0, 1, 0, 1],
    [1, 0, 1, 0, 1]])
fig, ax = plt.subplots(num=1, clear=True)
ax.imshow(a, cmap=plt.cm.gray)
ax.set_axis_off()
fig.tight_layout()
fig.savefig("PS21DI1E1Plot1.png")
fig, ax = plt.subplots(num=2, clear=True)
aplot2 = ax.imshow(a, cmap=plt.cm.gray)
fig.colorbar(aplot2)
fig.tight_layout()
fig.savefig("PS21DI1E1Plot2.png")

Example 2: Simple Grayscale Images

bx, by = np.meshgrid(range(255), range(255))
fig, ax = plt.subplots(num=1, clear=True)
aplot1 = ax.imshow(bx, cmap=plt.cm.gray)
fig.colorbar(aplot1)
fig.tight_layout()
fig.savefig("PS21DI1E2Plot1.png")
fig, ax = plt.subplots(num=2, clear=True)
aplot2 = ax.imshow(by, cmap=plt.cm.gray)
fig.colorbar(aplot2)
fig.tight_layout()
fig.savefig("PS21DI1E2Plot1.png")

Example 3: Less Simple Grayscale Images

x, y = np.meshgrid(np.linspace(0, 2*np.pi, 201),
                   np.linspace(0, 2*np.pi, 201));
z = np.cos(x)*np.cos(2*y);
fig, ax = plt.subplots(num=1, clear=True)
zplot = ax.imshow(z, cmap=plt.cm.gray)
ax.axis('equal')
fig.colorbar(zplot)
fig.tight_layout()
fig.savefig("PS21DI1E3Plot1.png")

Notice how the use of ax.axis('equal') made the image look like a square since it is 201x201 but also caused the display to be filled with whitespace as a result of the figure size versus the image size.

Example 4: Building an Image

rad = 100
delta = 10
x, y =np.meshgrid(range((-3*rad-delta),(3*rad+delta)+1),
                  range((-3*rad-delta),(3*rad+delta)+1))
rows, cols = x.shape
dist = lambda x, y, xc, yc: np.sqrt((x-xc)**2+(y-yc)**2)
venn_img = np.zeros((rows, cols, 3));
venn_img[:,:,0] = (dist(x, y, rad*np.cos(0), rad*np.sin(0)) < 2*rad);
venn_img[:,:,1] = (dist(x, y, rad*np.cos(2*np.pi/3), rad*np.sin(2*np.pi/3)) < 2*rad);
venn_img[:,:,2] = (dist(x, y, rad*np.cos(4*np.pi/3), rad*np.sin(4*np.pi/3)) < 2*rad);
fig, ax = plt.subplots(num=1, clear=True)
ax.imshow(venn_img)
ax.axis('equal')
fig.tight_layout()
fig.savefig("PS21DI1E4Plot1.png")

Example 5: Exploring Colors

nr = 256
nc = 256
x, y = np.meshgrid(np.linspace(0, 1, nc),
                   np.linspace(0, 1, nr))
other = 0.5;
palette = np.zeros((nr, nc, 3))
palette[:,:,0] = x
palette[:,:,1] = y
palette[:,:,2] = other
fig, ax = plt.subplots(num=1, clear=True)
ax.imshow(palette)
ax.axis('equal')
fig.tight_layout()
fig.savefig("PS21DI1E5Plot1.png")

Example 6: 1D Convolution

x = np.array([1, 2, 4, 8, 7, 5, -1])
h = np.array([1, -1])
y = sig.convolve(x, h)
print("x: {}\nh: {}\ny: {}".format(x, h, y))

x: [ 1  2  4  8  7  5 -1]
h: [ 1 -1]
y: [ 1  1  2  4 -1 -2 -6  1]

Example 7: 1D Convolution Using "same"

x = np.array([1, 2, 4, 8, 7, 5, -1])
h = np.array([1, -1])
y = sig.convolve(x, h, "same")
print("x: {}\nh: {}\ny: {}".format(x, h, y))

x: [ 1  2  4  8  7  5 -1]
h: [ 1 -1]
y: [ 1  1  2  4 -1 -2 -6]

Example 8: 11x11 Blurring

x = ski.data.coins()
h = np.ones((11, 11))/11**2;
y = sig.convolve2d(x, h, 'same');
fig, ax = plt.subplots(num=1, clear=True)
aplot1 = ax.imshow(x, cmap=plt.cm.gray, vmin=0, vmax=255)
ax.axis('equal')
ax.set(title='Original')
fig.colorbar(aplot1)
fig.tight_layout()
fig.savefig("PS21DI1E8Plot1.png")
fig, ax = plt.subplots(num=2, clear=True)
aplot2 = ax.imshow(y, cmap=plt.cm.gray, vmin=0, vmax=255)
ax.axis('equal')
ax.set(title='Blurred')
fig.colorbar(aplot2)
fig.tight_layout()
fig.savefig("PS21DI1E8Plot2.png")

Example 9: Make No Assumptions

x = np.array([1, 2, 4, 8, 7, 5, -1])
h = np.array([1, -1])
y = sig.convolve(x, h, "valid")
print("x: {}\nh: {}\ny: {}".format(x, h, y))

x: [ 1  2  4  8  7  5 -1]
h: [ 1 -1]
y: [ 1  2  4 -1 -2 -6]

Example 10: Basic Edge Detection and Display

x, y = np.meshgrid(np.linspace(-1, 1, 200),
                   np.linspace(-1, 1, 200));
z1 = (.7<np.sqrt(x**2+y**2)) * (np.sqrt(x**2+y**2)<.9)
z2 = (.3<np.sqrt(x**2+y**2)) * (np.sqrt(x**2+y**2)<.5)
zimg = 100*z1+200*z2;
fig, ax = plt.subplots(num=1, clear=True)
aplot1 = ax.imshow(zimg, cmap=plt.cm.gray, vmin=0, vmax=255)
ax.axis('equal')
ax.set(title='Original')
fig.colorbar(aplot1)
fig.tight_layout()
fig.savefig("PS21DI1E9Plot1.png")

hx = np.array([[1, -1], [1, -1]])
edgex = sig.convolve2d(zimg, hx, 'valid')
fig, ax = plt.subplots(num=2, clear=True)
aplot2 = ax.imshow(edgex, cmap=plt.cm.gray)
ax.axis('equal')
ax.set(title='Vertical Edges')
fig.colorbar(aplot2)
fig.tight_layout()
fig.savefig("PS21DI1E9Plot2.png")

hy = np.array([[1, 1], [-1, -1]])
edgey = sig.convolve2d(zimg, hy, 'valid')
fig, ax = plt.subplots(num=3, clear=True)
aplot3 = ax.imshow(edgey, cmap=plt.cm.gray)
ax.axis('equal')
ax.set(title='Horizontal Edges')
fig.colorbar(aplot3)
fig.tight_layout()
fig.savefig("PS21DI1E9Plot3.png")

edges = np.sqrt(edgex**2 + edgey**2)
fig, ax = plt.subplots(num=4, clear=True)
aplot4 = ax.imshow(edges, cmap=plt.cm.gray)
ax.axis('equal')
ax.set(title='Edges')
fig.colorbar(aplot4)
fig.tight_layout()
fig.savefig("PS21DI1E9Plot4.png")

• 

  Original

• 

  Vertical Edges

• 

  Horizontal Edges

• 

  Edges

Example 11: Chips!

For this example, save the image at right to a file called "amandajones_chips_unsplash.jpg" in the same folder as Python is running. This image comes from, Amanda Jones' Unsplash page and is free to use for non-commercial use.

import matplotlib.image as mpimg
from matplotlib.colors import ListedColormap
img = mpimg.imread("amandajones_chips_unsplash.jpg")

fig, ax = plt.subplots(num=1, clear=True)
ax.imshow(img)
ax.axis('equal')
ax.set(title='Original')
fig.tight_layout()
fig.savefig("PS21DI1E11Plot1.png")
vals = np.linspace(0, 1, 256)
names = ['Red', 'Green', 'Blue']
for k in range(3):
    fig, ax = plt.subplots(num=k+2, clear=True)
    aplot1 = ax.imshow(img[:,:,k], cmap=plt.cm.gray, vmin=0, vmax=255)
    ax.axis('equal')
    ax.set(title=names[k]+" as Gray")
    fig.colorbar(aplot1)
    fig.tight_layout()
    fig.savefig("PS21DI1E11Plot{}.png".format(k+2))
    
    fig, ax = plt.subplots(num=k+5, clear=True)
    mycmvals = np.zeros((256,4))
    mycmvals[:,k] = vals
    mycmvals[:,3] = 1
    mycm = ListedColormap(mycmvals)
    aplot2 = ax.imshow(img[:,:,k], cmap=mycm, vmin=0, vmax=255)
    ax.axis('equal')
    ax.set(title=names[k]+" as "+names[k])
    fig.colorbar(aplot2)
    fig.tight_layout()
    fig.savefig("PS21DI1E11Plot{}.png".format(k+5))

• 

  Original

• 

  Red as Gray

• 

  Green as Gray

• 

  Blue as Gray

• 

  Red as Red

• 

  Green as Green

• 

  Blue as Blue

Example 12: Chip Edges!

import matplotlib.image as mpimg
imgo = mpimg.imread("amandajones_chips_unsplash.jpg")
img = imgo[::10, ::10, :]

fig, ax = plt.subplots(num=1, clear=True)
ax.imshow(img)
ax.axis('equal')
ax.set(title='Scaled Down Original')
fig.tight_layout()
fig.savefig("PS21DI1E12Plot1.png")
vals = np.linspace(0, 1, 256)
names = ['Red', 'Green', 'Blue']
h = np.array([[1, 0, -1],[ 2, 0, -2], [ 1, 0, -1]])
edgevals = np.zeros((img.shape[0]-h.shape[0]+1,
                     img.shape[1]-h.shape[1]+1,
                     3))
for k in range(3):
    fig, ax = plt.subplots(num=k+2, clear=True)
    edgevals[:,:,k] = sig.convolve2d(img[:,:,k], h, "valid")
    aplot1 = ax.imshow(edgevals[:,:,k], cmap=plt.cm.gray, vmin=-1020, vmax=1020)
    ax.axis('equal')
    ax.set(title=names[k]+" Edges as Gray")
    fig.colorbar(aplot1)
    fig.tight_layout()
    fig.savefig("PS21DI1E12Plot{}.png".format(k+2))
    
    fig, ax = plt.subplots(num=k+5, clear=True)
    aplot2 = ax.imshow(edgevals[:,:,k], cmap=plt.cm.gray, vmin=0, vmax=1020)
    ax.axis('equal')
    ax.set(title="Absolute " + names[k]+" Edges as Gray")
    fig.colorbar(aplot2)
    fig.tight_layout()
    fig.savefig("PS21DI1E12Plot{}.png".format(k+5))

fig, ax = plt.subplots(num=8, clear=True)
edgevals2 = (edgevals + abs(edgevals).max()) / 2 / abs(edgevals).max()
ax.imshow(edgevals2)
ax.axis('equal')
ax.set(title="Colorful Edges")
fig.tight_layout()
fig.savefig("PS21DI1E12Plot8.png")

fig, ax = plt.subplots(num=9, clear=True)
edgevals3 = np.linalg.norm(edgevals, ord=2, axis=2)
ax.imshow(edgevals3, cmap=plt.cm.gray)
ax.axis('equal')
ax.set(title="Absolute Edges")
fig.tight_layout()
fig.savefig("PS21DI1E12Plot9.png")

• 

  Original

• 

  Red Edges as Gray

• 

  Green Edges as Gray

• 

  Blue Edges as Gray

• 

  Absolute Red Edges as Gray

• 

  Absolute Green Edges as Gray

• 

  Absolute Blue Edges as Gray

• 

  Colorful Edges

• 

  Absolute Edges

Exercise Starter Codes

Exercise 3

tc = np.linspace(0, 1, 101)
td = np.linspace(0, 1, 11)
myfun = lambda x: np.sin(20*x)*np.exp(-2*x)
xc = myfun(tc)
xd = myfun(td)
fig, ax = plt.subplots(num=1, clear=True)
ax.plot(tc, xc, 'b-')
ax.plot(td, xd, 'bo')

Exercise 4

tc = np.linspace(0, 1, 101)
td = np.linspace(0, 1, 11)
deltatc = tc[1]-tc[0]
deltatd = td[1]-td[0]

myfun = lambda x: np.sin(20*x)*np.exp(-2*x)
xc = myfun(tc)
xd = myfun(td)

fig, ax = plt.subplots(num=1, clear=True)
ax.plot(tc, xc, 'b-')
ax.plot(td, xd, 'bo')
ax.set(title='Values')
fig.tight_layout()

fig, ax = plt.subplots(num=2, clear=True)
twopointdiff = np.diff(xc)/deltatc
twopointdiff = np.append(twopointdiff, twopointdiff[-1])
ax.plot(tc, twopointdiff, 'b-')
ax.plot(tc[::10], twopointdiff[::10], 'bo')
ax.set(title='Change Me')
fig.tight_layout()