Problem Set 3 CMSC 426
Due: Thursday, April 3
Overview:
This problem set will work a little different. There will be a standard part,
and an advanced part. Students may choose to do either part. Alternately, they may
choose to complete the standard par
t, and hand in any portions of the advanced part for
extra credit. Not that the standard part totals 100 points, while the advanced part totals
120. A student may receive no more than 140 points total. Grad students may feel that
they should focus on th
e advanced part.
Remember, everything you do should be turned in as a hardcopy. All code should be
emailed to the TA. Write the date that you hand in assignments on the hardcopy,
especially if you hand them in late. If you leave an assignment under my
door on in my
mailbox, always include the date.
Standard Assignment
1)
Programming RANSAC. 70 points total.
a.
Write a function of the form: [a, b, c] = gen_line(pt1, pt2). This function
should take two points as input, and return the parameters of a line t
hat fit
these points. The line should be ax + by + c = 0, where sqrt(a*a + b*b) =
1. Test this function using the pairs of points: i) (1,1) (2,1) ii) (1,1)
(1,2); iii) (1,1) (3,2). Turn in your code, and show calls to the routine and
responses for these inputs.
5 points
b.
Write a function of the form: d = line_dist(L, p). L represents a line
(perhaps as a vector of [a,b,c]). p represents a point. d is the distance
from the point to the line. Test your code with i) The line formed by the
points:
(0,1) (2,1) and the point (5,2). ii) The line formed by the points
(1,1) and (3,2) and the point (7,4). Turn in your code and show calls to the
routine and responses for these inputs.
5 points
c.
Compute the correct answers to the problems in (b) by hand.
Show your
work and the results.
5 points
d.
Write a function of the form: k = num_samples(n, m, p). If there are n
points in an image, and m of them come from a single line, then if we
randomly sample k pairs of points we should have a probability greater
t
han p of picking a pair of points that come from the line. k should be the
smallest integer for which this is true. Test this with n = 20, m = 8, p = .9.
Turn in your code, and show calls to the routine and responses for these
inputs.
10 points
e.
Write a
function of the form: pts_cor = verify(p1, p2, pts, eps). p1 and p2
are points that will be used to form a line. pts is a list of different pts.
pts_cor should contain a list of all points in pts whose distance to the line
formed by p1 and p2 is less t
han eps. Test this routine with p1 = (1,1), p2
= (2,2), pts = [(3,4), (5,7), (3,8)], eps = 2. Turn in your code, and show
calls to the routine and responses for these inputs.
10 points
