Digital Geometry in Image Processing

124 Digital Geometry in Image Processing

which asymptotically approximates to

A

2

= n

1

+

√

2n

2

+

√

3n

3

for large n.

Though A

2

is expectedly be tter than A

0

or A

1

, this is aga in a biased

estimator usually overestimating the original. Actually all these estimators

A

0

, A

1

, A

2

are expressed as linear combinations of n

1

, n

2

, and n

3

. Depending

on the choice of the coefficients we can think of a class of simple estimators,

which are of the form µ

1

n

1

+ µ

2

n

2

+ µ

3

n

3

, where µ

1

, µ

2

, µ

3

are constants.

Important among them is the one for w hich the RDEV is the least. There is

an effort [42] to obtain better estimates by minimizing RDEV with re spect to

the coefficients.

3.4.4.3 Non-linear ...