Due 5:00 PM Wednesday, 2/17/99
EE 695A
Homework No. 2
Spring 1998
1.
Consider a finite dimensional model for a linear, bichromatic vision system.
Assume
that we sample at
N
=
3 wavelengths.
Supppose that the sensor response matrix is
given by
S
=
1
0
0
1
0
0
a.
Find the response of this sensor to the stimulus
r
n
=
1
2
3
[ ]
T
.
b.
Find the fundamental component
r
n
*
for this stimulus.
c.
Find the blackspace component
r
n
c
for the stimulus.
d.
Find a metamer
r
′
n
to
r
n
such that
r
′
n
≠
r
n
.
2.
Let
S
be a 31
×
3 matrix with rank 3; and let
S
=
span(
S
). Let
r
v
be any vector
∉
S
.
Show by differentiation with respect to the elements of
r
a
that the vector
r
u
∈
S
that is
closest to
r
v
in the Euclidean norm is given by
r
u
=
S
r
a
, where
r
a
=
S
T
S
[ ]

1
S
T
r
v
. (Note
that you should establish that the stationary point is in fact a minimum.)
3.
By definition, the fundamental component
r
n
*
of a stimulus
r
n
can be expressed as a
linear combination of the columns of the sensor matrix
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 Fall '08
 Staff
 Linear Algebra, Vector Space, CIE XYZ, sensor matrix

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