Statistics of Medical Imaging

Performance Evaluation of Image Analysis Methods 395

TABLE 12.12

Classification Results (Images in Fig ures 12.5a–l)

R

1

:

(x

′

1

, x

′′

1

] R

2

: (x

′

2

, x

′′

2

] R

3

: (x

′

3

, x

′′

3

] R

4

: (x

′

4

, x

′′

4

]

overlap

a −48, −42 −18, −12 11, 18 42, 48 N o

b −52, −37 −21, −7 6, 22 38, 52 No

c −5 6, −34 −24, −4 2, 25 35, 55 No

d −60, −31 −30, −2 0, 29 30, 58 N o

e −63, −30 −30, −1 0, 30 31, 61 P artial

f −6 6, −30 −30, −1 −1, 30 31, 64 P artial

g −69, −30 −30, −1 −1, 31 31, 66 Y es

h −71, −29 −29, −2 −1, 3 1 31, 68 Y es

i −73, −29 −29, −2 −2, 32 32, 70 Y es

j −75, −2 9 −29, −3 −3, 32 32, 72 Y es

k −77, −28 −28, −4 −4, 33 33, 7 3 Y es

l −78, −28 −28, −5 −5, 34 34, 75 Y es

TABLE 12.13

Misclassification Probabilities for the Images in

Figures 12.5

P

mis

(•|1) P

mis

(•|2) P

mis

(•|3) P

mis

(•|4)

a 0.00000 0.00000 0.00000 0.00000

b 0.00000 0.000 00 0.00000 0.00000

c 0.00000 0.00000 0.00000 0.00000

d 0.00009 0.00010 0.00015 0.00004

e 0.00060 0.00127 0.00114 0.00075

f 0.00189 0.00447 0.00399 0.00211

g 0.00404 0.00720 0.00917 0.00556

h 0.00509 0.01100 0.01494 0.00771

i 0.00790 0.01447 0.02229 0.01194

j 0.01117 0.01750 0.03171 0.01277

k 0.01221 0.02236 0.03900 0.01626

l 0.01586 0.02433 0.04678 0.01971

TABLE 12.14

Classification Performance for the Images in Figures 12.5

a − d No overlap 17.2 db ≤ SN R ≤ 30.2 db P

mis

< 0.015%

e − f Small overlap 14.2 db ≤ SN R ≤ 15.5 db P

mis

< 0.447%

g − l Some overlap 10.2 db ≤ SN R ≤ 13.2 db P

mis

< 4.678%