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Parametric model fitting techniques, including least squares methods for fitting lines and curves, ransac for estimating homographies and fundamental matrices, and the hough transform for finding lines and curves in data. Critical issues such as noisy data, outliers, and missing data are addressed, as well as techniques for dealing with them. The document also covers the limitations and assumptions of each method.
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Reading:
[HZ] Chapters: 4, 11^ [FP] Chapters: 16
Some slides of this lectures are courtesy of profs. S. Lazebnik & K. Grauman
Fitting
H
Fitting
H
Fitting
Techniques:•Least square methods•RANSAC•Hough transform•EM (Expectation Maximization)
[forthcoming lecture]
( x
,^1 y ), …, (^1
x^ , n
yn
)
y^ i
= m x
+ bi^
m ,
b ) to minimize ∑
=^
−
−
=^
n i^
i
i^
b x m y
E^
1
(^2) )
(
( x^ i
,^ y
) i
y=mx+b
b
Ax
=
||Ax-b|| = (Ax-b)
T(Ax-b)
0 ) ()
(^
=
∂
−
− ∂
T x^ i
b Ax b Ax
b A
A A
x^
T
T^
1 )
(^
−
=
t 1 t^
−
1
1
−
−^
with
equal to
for all nonzero singular
values and zero otherwise
(^1) − ∑
∑
= pseudo-inverse of A
t
t^
1
−
+^
= SVD decomposition of A
( x^ n
,^ y
)^ n and line
ax+by=d
( a
,^ b
,^ d
)^ to minimize the
sum of squared perpendiculardistances
ax+by=d
∑
=^
−
=^
n i^
i
i^
d yb
xa
E^
1
(^2) )
(
( x^ i
,^ y
) i
0
N ) U U(
T^
=
data
1 || h||
to
subject || h A||
Minimize
=
T
UDV A
=
V of
column
last h^
=
