System and method for characterizing 2-dimensional shapes by compactness measurements

1 . A method of classifying a shape in a digitized image comprising the steps of:

providing a digitized image comprising a plurality of intensities defined for a set of points on a 2-dimensional lattice;

selecting an object from said image;

defining a discrete compactness C D for said object;

defining a maximal compactness C D max for said object;

determining a normalized compactness C DN for said object from said discrete compactness and said maximal compactness; and

classifying said object based on its normalized compactness value.

2 . The method of claim 1 , wherein said normalized compactness is defined by

C

DN

=

C

D

C

D

⁢

⁢

max

.

3 . The method of claim 1 , wherein said discrete compactness is defined by

C

D

=

1

2

⁢

(

Tn

-

P

)

,

wherein T is the connectivity of the lattice, n is the number of pixels in the object, and P is the length of the perimeter of the object.

4 . The method of claim 3 , wherein said maximal compactness is defined by

C

D

⁢

⁢

max

=

1

2

⁢

(

Tn

-

4

⁢

n

)

.

5 . The method of claim 4 , wherein said normalized compactness is defined by

C

DN

=

Tn

-

P

Tn

-

4

⁢

n

.

6 . The method of claim 1 , wherein said lattice is a 4-connected grid.

7 . The method of claim 6 , wherein said discrete compactness is defined by

C

D

=

2

⁢

n

-

1

2

⁢

P

,

wherein n is the number of pixels in the object, and P is the length of the perimeter of the object.

8 . The method of claim 7 , wherein said maximal compactness is defined by

C D max =2( n−√{square root over (n)}).

9 . The method of claim 8 , wherein said normalized compactness is defined by

C

DN

=

n

-

1

4

⁢

p

n

-

n

.

10 . A method of classifying a shape in a digitized image comprising the steps of:

determining a normalized compactness C DN for an object in said image from the formula

C

DN

=

Tn

-

P

Tn

-

4

⁢

n

,

wherein T is the connectivity of the object, n is the number of pixels in the object, and P is the length of the perimeter of the object; and

classifying said object based on its normalized compactness value.

11 . The method of claim 10 , wherein said object is selected from a digitized image comprising a plurality of intensities defined for a set of pixels in a 2-dimensional lattice.

12 . The method of claim 11 , wherein the lattice is a rectangular lattice, wherein the connectivity T=4.

13 . The method of claim 11 , wherein the lattice is a triangular lattice, wherein the connectivity T=3.

14 . The method of claim 11 , wherein the lattice is a hexagonal lattice, wherein the connectivity T=6.

15 . A program storage device readable by a computer, tangibly embodying a program of instructions executable by the computer to perform the method steps for classifying a shape in a digitized image, said method comprising the steps of:

providing a digitized image comprising a plurality of intensities defined for a set of points on a 2-dimensional lattice;

selecting an object from said image;

defining a discrete compactness C D for said object;

defining a maximal compactness C D max for said object;

determining a normalized compactness C DN for said object from said discrete compactness and said maximal compactness; and

classifying said object based on its normalized compactness value.

16 . The computer readable program storage device of claim 15 , wherein said normalized compactness is defined by

C

DN

=

C

D

C

D

⁢

⁢

max

.

17 . The computer readable program storage device of claim 15 , wherein said discrete compactness is defined by

C

D

=

1

2

⁢

(

Tn

-

P

)

,

wherein T is the connectivity of the lattice, n is the number of pixels in the object, and P is the length of the perimeter of the object.

18 . The computer readable program storage device of claim 17 , wherein said maximal compactness is defined by

C

D

⁢

⁢

max

=

1

2

⁢

(

Tn

-

4

⁢

n

)

.

19 . The computer readable program storage device of claim 18 , wherein said normalized compactness is defined by

C

DN

=

Tn

-

P

Tn

-

4

⁢

n

.

20 . The computer readable program storage device of claim 15 , wherein said lattice is a 4-connected grid.

21 . The computer readable program storage device of claim 20 , wherein said discrete compactness is defined by

C

D

=

2

⁢

n

-

1

2

⁢

P

,

wherein n is the number of pixels in the object, and P is the length of the perimeter of the object.

22 . The computer readable program storage device of claim 21 , wherein said maximal compactness is defined by

C D max =2( n−√{square root over (n)} ).

23 . The computer readable program storage device of claim 22 , wherein said normalized compactness is defined by

C

DN

=

n

-

1

4

⁢

p

n

-

n

.