Statistics of Medical Imaging

Performance Evaluation of Image Analysis Methods 381

TABLE 12.4

Approximated Probabilities of Over- and Under-Detection o f the

Number of Image Regions for Images in Figure s 12.1a–l.

µ σ ∆ P

ov

(+1)

µ σ ∆ P

ud

(−1)

a −205 18.4 −473 Φ(−14.5) −906 5.57 −1752 Φ (−152)

b −94 5.49 −251 Φ(−28.6) −34 4 2.49 −627 Φ(−114)

c −68 3.26 −198 Φ(−3 9.9) −216 1.75 −371 Φ(−88.6 )

d −53 1.90 −168 Φ(−6 0.5) −133 1.21 −203 Φ(−57.9)

e −48 1.35 −159 Φ(−82.2) −101 0.94 −139 Φ(−40.4)

f −50 1.02 −163 Φ (−111.) −83. 0.78 −104 Φ(−26.9)

g −50 0.82 −163 Φ(−138.) −71. 0.68 −80. Φ(−13.2)

h −48 0.69 −159 Φ(−161.) −61. 0.61 −61. Φ(+0.00)

i −46 0.60 −155 Φ(−182.) −53. 0.55 −44. Φ(+16.4)

j −43 0.54 −148 Φ(−194.) −45. 0.51 −28. Φ(+33.3)

k −37 0.48 −137 Φ(−208.) −37. 0.49 −13. Φ(+49.0)

l −32 0.45 −126 Φ(−209.) −30. 0.46 3.0 Φ(+71.7)

a b c

d e f

FIGURE 12.4

X-ray CT image of a physical phantom (a) and its five co mponents (b ∼ f).

2) Results from a real image

Figure 12.4a shows a real X-r ay CT phantom image that is shown in Section

10.5.1. For convenience of description, some c ontents of Section 10.5.1 are

used in this section. This physical phantom consists of six cylinders (made of

four types of materials: Poly, 0 13A, Teflon, and Bone) with nearly the same

diameters. These cylinders are mounted on a base in such a way that their axes

are parallel to each other and equia ngularly located on a circle. The resolution

of the X-ray CT scanner that was used to gene rate this image is 1.5×1.5×5.0

mm

3

. While imaging, the axes o f the cylinders are set paralle l to the moving

direction of the scanner bed. Thus, the image shown in Figure 12.4.a includes