CS 6643 Computer Vision, Spring 2018, G. Gerig Assignment 3 Theoretical Part
Out: 4/03/2018
Due: 4/10/2018 (deadline: midnight)
Late submissions: Late submissions result in 10% deduction for each day. The assignment will no longer be accepted 3 days after the deadline.
Office hours:
Guido Gerig
Yida Zhou
Zebin Xu
Andrew Dempsey Monil D. Shah
Monday Wed Thu office 10.094 2 – 4pm
yz4499@nyu.edu 1-3pm
Fri
10 – noon
zebinxu@nyu.edu ad4338@nyu.edu mds747@nyu.edu
2 – 4pm 4 – 6pm
Location: Cubicle spaces in front of my office named 10.098 A,B,D,E,H.
A) Theoretical questions:
A1) Hough Transform: Parametrization
The standard parametrization of a line, y = m0 x + b0, with m0 and b0 slope and intercept, has not become the standard parametrization for the Hough transform for finding lines.
- Explain why this option did not become a popular choice.
- Would you still use it, what can you say about the discrete grid of the Hough space with axes m0
and b0 in regard to Hough space cell spacing and its representation of lines.
A2) Hough Transform: Polar representation I
Show that the polar representation of a line, xcosθ + ysinθ = ρ , represents a Cosine function in
parameter space with axes Θ and ρ. (Remember that a general Cosine function is given as y=a cos (α-δ)), with a=amplitude and δ= phase shift).
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Given a scenario with a line in (x,y)-space intersecting with the horizontal axis at 𝑥𝑥 and with the vertical h
the line l in image space.
A3): Hough Transform: Polar representation II
axis at 𝑥𝑥𝑣𝑣, calculate and plot the corresponding Cosine curves in the (𝜃𝜃, 𝜌𝜌) parameter space.
Calculate the intersection of the two parameter curves and discuss how its coordinates (𝜃𝜃, 𝜌𝜌) represent
A4) Noisy line structures
Given points forming a line but its locations corrupted by noise (see below), how would noise affect the clustering of curves in Hough space? What could you do to still find a peak with associated parameters that would represent the noisy line?
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A5) Hough Transform for Ellipses
We have learned that the Hough transform for circles requires three parameters, two for the center and one for the radius, thus spanning a 3-D parameter space. Now let us find ellipses in its standard form (no orientation) with varying size?
Would the Generalized Hough Transform (GHT), as discussed in the course using R-tables for creating a template, eventually offer a solution? Sketch it with a drawing and some short explanation. What about finding ellipses in different orientations given the GHT?
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