Question

Let C be a camera with a focal length of f = 10[mm]. The sensor of this camera has kᵤ =100[pixels/mm] in the horizontal direction and kᵥ= 100[pixels/mm]. The translation of the optical center is given by u₀= 500[pixels] in the horizontal direction and by v₀= 500[pixels] in the vertical direction. Assume that the pixels are not skewed. Write the intrinsic camera parameters matrix K* (the part of the projection matrix that depends on the internal parameters of the camera). Add the entries of the matrix K* then divide the sum by 1000 and round. Use the number you get to mark the answer.

Answer 1

The intrinsic camera parameters matrix K* for a camera with the given specifications is created by multiplying the focal length by the pixel densities and incorporating the translations of the optical center. After adding the matrix entries and dividing by 1000, the value is rounded to give a final result of 3.

Step-by-step explanation:

To find the intrinsic camera parameters matrix K*, we need to use the provided camera specific values: focal length f = 10 mm, pixel densities kᵤ = 100 pixels/mm and kᵥ = 100 pixels/mm, and the translation of the optical center u₀ = 500 pixels (horizontal) and v₀ = 500 pixels (vertical). The matrix K* often has the following form:

• 
  
• kᵤ * f, 0, u₀
• 
  
• 0, kᵥ * f, v₀
• 
  
• 0, 0, 1

However, since focal length f needs to be in millimeters and kᵤ and kᵥ are in pixels per millimeter, we will multiply the focal length by the pixel density to keep consistent units. Thus:

• 
  
• kᵤ * f = 100 pixels/mm * 10 mm = 1000 pixels
• 
  
• kᵥ * f = 100 pixels/mm * 10 mm = 1000 pixels

Now we can write the matrix K* as:

10000500
01000500
001

Adding the entries we get: 1000 + 0 + 500 + 0 + 1000 + 500 + 0 + 0 + 1 = 3001. Dividing by 1000 gives us 3.001, which when rounded becomes 3. Therefore, the result after adding the entries of the matrix K*, dividing by 1000 and rounding is 3.