ECE 470: Introduction to Robotics Homework 7

1) In Canny edge detection algorithm, a Gaussian filter is first applied on an image.

Explain the rationale for doing so and what might happen if this step is not done.

(2 Points)

2) When using Hough Transform to detect lines, one option is to use (m, c) as the Hough

space (also known as parameter space) with the equation of line y= mx+c.

a) How will a point (xi,yi) look like when transformed to the (m, c) space? (1 Points)

b) How is a point on the (m, c) space represented in (x,y) space? (1 Points)

c) Describe graphically how 4 collinear points on a line can be identified? (4 Points)

d) What is the disadvantage of using (m,c) over ( ρ, θ) as the Hough space? (2 Points)

3) Fig. 5 shows the orientation and position of a camera frame {C} with respect to the

world reference frame {W}.

Fig. 5

a) Write down the rotation matrix representing the orientation of the world

frame {W} with respect to the camera frame {C} i.e. CRW. (1 Points)

b) Write down the 3×4 extrinsic matrix of the camera i.e. C

[R|t] W. (1 Points)

c) A point referenced from the world frame (5, 10, 5)T

is observed to have image

coordinates (600, 300). Given that fx=fy and ic=jc and assuming skew coefficient

a=0, solve for the intrinsic camera matrix

𝐾 = [

𝑓𝑥 𝑎 𝑖𝑐

0 𝑓𝑦 𝑗𝑐

0 0 1

]

(8 Points)

# Introduction to Robotics Homework 7

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ECE 470: Introduction to Robotics Homework 7

1) In Canny edge detection algorithm, a Gaussian filter is first applied on an image.

Explain the rationale for doing so and what might happen if this step is not done.

(2 Points)

2) When using Hough Transform to detect lines, one option is to use (m, c) as the Hough

space (also known as parameter space) with the equation of line y= mx+c.

a) How will a point (xi,yi) look like when transformed to the (m, c) space? (1 Points)

b) How is a point on the (m, c) space represented in (x,y) space? (1 Points)

c) Describe graphically how 4 collinear points on a line can be identified? (4 Points)