Motion detection with camera in Raspberry Pi - Time & Space Complexity

Time Complexity: Motion detection with camera

O(n)

Understanding Time Complexity

When using a camera on a Raspberry Pi to detect motion, the program checks many pixels repeatedly.

We want to know how the time it takes grows as the image size or number of frames increases.

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

import cv2

cap = cv2.VideoCapture(0)

while True:
    ret, frame1 = cap.read()
    ret, frame2 = cap.read()
    diff = cv2.absdiff(frame1, frame2)
    gray = cv2.cvtColor(diff, cv2.COLOR_BGR2GRAY)
    blur = cv2.GaussianBlur(gray, (5,5), 0)
    _, thresh = cv2.threshold(blur, 20, 255, cv2.THRESH_BINARY)
    contours, _ = cv2.findContours(thresh, cv2.RETR_TREE, cv2.CHAIN_APPROX_SIMPLE)
    for contour in contours:
        if cv2.contourArea(contour) > 500:
            print("Motion detected")

This code captures two frames repeatedly, compares them pixel by pixel to find differences, and checks for motion by looking at contours.

Identify Repeating Operations

• Primary operation: Looping over each pixel to compute the difference and then looping over contours to check their area.
• How many times: The pixel comparison happens for every pixel in each frame pair, and the contour loop runs once per detected contour each frame.

How Execution Grows With Input

As the image size grows, the number of pixels to compare grows too, so the work grows with the number of pixels.

Input Size (pixels)	Approx. Operations
10 x 10 (100)	About 100 pixel comparisons
100 x 100 (10,000)	About 10,000 pixel comparisons
1000 x 1000 (1,000,000)	About 1,000,000 pixel comparisons

Pattern observation: The operations grow roughly in proportion to the number of pixels, so doubling width and height quadruples the work.

Final Time Complexity

Time Complexity: O(n)

This means the time to detect motion grows roughly in direct proportion to the number of pixels in each frame.

Common Mistake

[X] Wrong: "The time to detect motion depends only on the number of frames, not the image size."

[OK] Correct: Each frame has many pixels, and the program compares all pixels between frames, so bigger images take more time even if the frame count is the same.

Interview Connect

Understanding how image size affects processing time helps you explain performance in real projects using cameras or sensors.

Self-Check

"What if we only compared a smaller region of the frame instead of the whole image? How would the time complexity change?"

Practice

1. What is the main purpose of motion detection when using a camera on a Raspberry Pi?

easy

A. To increase the camera resolution automatically

B. To find changes between consecutive images

C. To save battery life of the Raspberry Pi

D. To connect the camera to the internet

Solution

1. Step 1: Understand motion detection basics

   Motion detection works by comparing images to find differences or changes.

2. Step 2: Identify the main goal of motion detection

   The goal is to detect movement by noticing changes between frames, not to change resolution or save power.

3. Final Answer:

   To find changes between consecutive images -> Option B

4. Quick Check:

   Motion detection = find changes [OK]

Hint: Motion detection means spotting changes between pictures [OK]

Common Mistakes:

• Confusing motion detection with camera settings
• Thinking motion detection saves power
• Assuming it connects camera to internet

2. Which of the following Python code snippets correctly imports OpenCV for motion detection on Raspberry Pi?

easy

A. import camera

B. import opencv

C. import cv

D. import cv2

Solution

1. Step 1: Recall the correct OpenCV import statement

   OpenCV in Python is imported using 'import cv2'.

2. Step 2: Check other options for correctness

   Options 'opencv', 'cv', and 'camera' are incorrect or outdated module names.

3. Final Answer:

   import cv2 -> Option D

4. Quick Check:

   OpenCV import = cv2 [OK]

Hint: OpenCV Python module is always imported as cv2 [OK]

Common Mistakes:

• Using 'import opencv' instead of 'import cv2'
• Confusing 'cv' with 'cv2'
• Trying to import 'camera' module for OpenCV

3. What will be the output of this code snippet when motion is detected?

import cv2
cap = cv2.VideoCapture(0)
ret, frame1 = cap.read()
ret, frame2 = cap.read()
diff = cv2.absdiff(frame1, frame2)
gray = cv2.cvtColor(diff, cv2.COLOR_BGR2GRAY)
_, thresh = cv2.threshold(gray, 30, 255, cv2.THRESH_BINARY)
print(thresh.sum() > 10000)

medium

A. True if motion detected, False otherwise

B. Always prints True

C. Always prints False

D. Raises a syntax error

Solution

1. Step 1: Understand the code logic for motion detection

   The code compares two frames, converts difference to grayscale, thresholds it, then sums pixels to detect motion.

2. Step 2: Interpret the print statement

   If the sum of thresholded pixels is greater than 10000, it prints True (motion detected), else False.

3. Final Answer:

   True if motion detected, False otherwise -> Option A

4. Quick Check:

   Threshold sum > 10000 means motion True [OK]

Hint: Sum of thresholded diff > limit means motion detected [OK]

Common Mistakes:

• Assuming it always prints True or False
• Confusing thresholding with color conversion
• Expecting syntax errors from correct code

4. Identify the error in this motion detection code snippet:

import cv2
cap = cv2.VideoCapture(0)
ret, frame1 = cap.read()
ret, frame2 = cap.read()
diff = cv2.absdiff(frame1, frame2)
gray = cv2.cvtColor(diff, cv2.COLOR_BGR2GRAY)
_, thresh = cv2.threshold(gray, 30, 255, cv2.THRESH_BINARY)
if thresh.sum() > 10000:
    print("Motion detected")
cap.release()

medium

A. Missing loop to continuously read frames

B. Incorrect threshold value used

C. cv2.absdiff should be cv2.subtract

D. cap.release() should be called before reading frames

Solution

1. Step 1: Check code flow for continuous motion detection

   The code reads frames only once, so it cannot detect motion continuously.

2. Step 2: Identify missing loop for repeated frame capture

   Motion detection requires a loop to keep reading frames and comparing them over time.

3. Final Answer:

   Missing loop to continuously read frames -> Option A

4. Quick Check:

   Continuous detection needs a loop [OK]

Hint: Motion detection needs a loop to compare frames repeatedly [OK]

Common Mistakes:

• Thinking threshold value is wrong
• Confusing absdiff with subtract
• Releasing capture too early

5. You want to trigger an alert only when motion is detected for at least 3 seconds continuously using a Raspberry Pi camera. Which approach is best?

hard

A. Use a timer to trigger alert every 3 seconds regardless of motion

B. Trigger alert immediately on first motion detection

C. Count consecutive frames with motion and trigger alert after threshold

D. Ignore motion and trigger alert manually

Solution

1. Step 1: Understand the requirement for continuous motion detection

   We need to detect motion lasting at least 3 seconds, not just a single frame.

2. Step 2: Choose method to track motion duration

   Counting consecutive frames with motion and triggering alert after reaching a threshold time is the best approach.

3. Final Answer:

   Count consecutive frames with motion and trigger alert after threshold -> Option C

4. Quick Check:

   Continuous motion needs counting frames [OK]

Hint: Count frames with motion to confirm duration before alert [OK]

Common Mistakes:

• Triggering alert immediately on any motion
• Using timer without checking motion
• Ignoring motion detection logic