CS556: Homework 1
Forrest Briggs
January 18, 2010
1
Introduction
The goal in this assignment is to write code for:
1. Detecting Harrisafne corners in an image, by
(a) Detecting multiscale Harris points,
(b) Automatically selecting the scale of each detection,
(c) Fitting an ellipse to each image region occupied by a Harris corner,
2. Computing their rotation and scale invariant DAISY descriptors, based on the ellipses identied in the previous step,
3. Matching Harrisafne corners detected in two images showing the same scene, by nding for each point in image 1
another point in image 2 with the smallest Euclidean distance of their associated rotation and scale invariant DAISY
descriptors.
2
Literature Review
Moravec proposed a simple corner detector for robotic vision [1]. The idea is to measure the different between the image in a
small window centered around a candidate point and a window shifted in each of the 8 neighboring directions. This detector
would be very fast to compute, but it is not rotation invariant.
Tomasi et. al. [3] propose a variation on the Harris detector which uses the same matrix
M
(see the following section),
but rather than computing
f
σ
(
x, y
) =
det
(
M
σ
(
x,y
))
trace
(
M
σ
(
x,y
))
, they instead use
f
σ
(
x, y
) =
min
(
λ
1
, λ
2
), i.e. the minimum of the two
eigenvalues of
M
. They argue that this is a better corner detection function when affine transformations are present. This
method would be slower than Harris corners however, because it requires calculating eigenvalues.
3
Description of Methods
This section describes the Harris interest point detection and DAISY descriptors.
3.1
Detecting Multiscale Harris Points
We begin with an
m
x
n
image
I
(
x, y
). At each pixel (
x, y
) we must compute a matrix
H
, defined as:
M
σ
(
x, y
) =
G
(
x, y, σ
)
*
I
2
x
I
x
I
y
I
x
I
y
I
2
y
G
is the 2dGaussian kernel,
G
(
x, y, σ
) =
1
2
πσ
2
e

(
x
2
+
y
2
)
/
2
σ
2
, and
I
x
and
I
y
are the spatial derivatives of
I
. Then we compute
f
σ
(
x, y
) =
det
(
M
σ
(
x,y
))
trace
(
M
σ
(
x,y
))
. To make the interest point detection process scale invariant, we evaluate
f
with a range of values
for
σ
. The values are
σ
1
= 2
, σ
2
= 3
, σ