ECE468: HOMEWORK 6
due 02/26
1) Problems from the textbook:
•5.24 (20pts)
•5.29 (20pts)
•5.30 (10pts) – Solution is available on the official webpage of the textbook
2) (20pts) Consider a linear, space-invariant, image-degradation system with the impulse response
h(x, y) = e−[x2+y2].
Suppose that the input to the system is an image that shows a line of infinitesimal width, located
at y=y0, and modeled by
f(x, y) = δ(y−y0),
where δ(·)is the standard impulse function. Assuming no noise, compute the output image g(x, y) =
f(x, y)⋆ h(x, y).
3) (20pts) An image acquisition system captures blurred images, because the camera moves while its
shutter is open. Suppose the shutter speed, i.e., the time interval while the film is exposed to light, is
[0, T ]. It is known that the camera motion in [0, T ]is characterized by a spatially uniform acceleration
~a = [ax, ay]along both xand yimage axes. That is, the ray of light passes in the interval [0, t]
the length of x(t) = axt2/2along the x-axis in the image, and the length of y(t) = ayt2/2along
the y-axis in the image. Find the blurring degradation function H(u, v )of this image acquisition
system.
4) (10pts) Let the Radon transform of an input image f(x, y)be g(ρ, θ). Also, let G(ω, θ)be the 1D
Fourier Transform of g(ρ, θ). Prove that
G(ω, θ + 180◦) = G(−ω, θ).