Answers

U11.5 Colour, and why it breaks

Vision · University · about 35 min

What this lesson is about

Segmentation by threshold, what the threshold is really measuring, and where it fails.

• What a camera pixel measures
• Brightness is not colour
• The other four ways it fails outside the lab
• What to do instead, in order of effort
• Finding the centre

Questions 6 marks in all

1. [1 mark]Why does the test r > 150 fail to find a red ball on the nearly white mat, even in a simulator with no lighting model?

   1. AIt tests brightness, and white is red-rich, so the mat passes too
   2. BThe simulator's red is below 150
   3. CThe camera's white balance shifts the ball towards grey
   4. DThe threshold should be in radians
   Answer: A. A white or pale surface has a large r. The question to ask is whether red dominates, not whether it is large.

2. [1 mark]Four pixels: white mat, a red ball, the same ball in shadow, and a pale pink wall. What does this print?

   pixels = [(230, 225, 220), (200, 40, 30), (120, 30, 25), (240, 200, 180)]
   bright = sum(1 for (r, g, b) in pixels if r > 150)
   dominant = sum(1 for (r, g, b) in pixels if r - max(g, b) > 60)
   chroma = sum(1 for (r, g, b) in pixels if r / (r + g + b + 1) > 0.5)
   print(bright, dominant, chroma)

   Answer:

   3 2 2

   The brightness test passes the mat, the ball and the wall but misses the shadowed ball. Both colour tests pass exactly the two ball pixels, lit and shadowed.

3. [1 mark]In a 64 pixel wide picture from the 320 pixel camera, the red pixels' centroid is at column 40. What is the bearing in degrees to 1 decimal place, using f = 92.4?

   Answer: 23.4 (accept within 0.1). Scale to the full frame first: column 40 x 5 = 200. Then atan((200 - 160) / 92.4) = 23.4 degrees. The intrinsics belong to the full frame.

4. [1 mark]In pixel = illumination x reflectance x sensor response, which factor is a property of the object?

   1. AReflectance
   2. BIllumination
   3. CSensor response
   4. DAll three
   Answer: A. Illumination belongs to the room and sensor response to the camera. A raw RGB threshold is a threshold on all three.

5. [1 mark]Which of these break a colour threshold that worked in the lab?

   Tick every answer that is true.

   1. AAuto exposure changing the gain when a dark object fills the view
   2. BAuto white balance shifting the channels
   3. CA shadow or a specular highlight across the object
   4. DDifferent light, such as fluorescent instead of daylight
   5. EConverting the column to a bearing with the pinhole model
   Answer: A, B, C, D. Each changes the pixel values without changing the object. The pinhole conversion is geometry and does not touch colour.

6. [1 mark]Why is a specular highlight worse for a chromaticity test than a shadow?

   1. AA highlight saturates the channels, and a clipped channel has thrown its information away for good
   2. BA shadow is darker, so it is easier to threshold
   3. CChromaticity divides by brightness, which is zero in a highlight
   4. DHighlights only affect the red channel
   Answer: A. A shadow drops all three channels and can partly survive normalisation. Once a channel clips at its maximum the ratio is gone and cannot be recovered.

The task: threshold a picture

from bugbot import *
import math
connect()

F = 92.4
W, H = 64, 48
img = camera_image(W, H)

from bugbot import *
import math
connect()

F = 92.4
W, H = 64, 48

img = camera_image(W, H)

bright = 0
cols = []
for row in img:
    for u in range(W):
        r, g, b = row[u]
        if r > 150:
            bright += 1                       # the beginner's test: bright, not red
        if r - max(g, b) > 60:
            cols.append(u)                    # red dominates the other two channels

print("naive:", round(100.0 * bright / (W * H), 1))
print("red:", len(cols))

u = sum(cols) / len(cols)
x = (u + 0.5) * 320.0 / W                     # back to the camera's own 320 wide frame
print("bearing:", round(math.degrees(math.atan((x - 160) / F)), 2))