Motion Estimation - Motion Correction in Thoracic Positron Emission Tomography - page 56

Validation

The results which are shown in Fig. 2.10 and the underlying motion estimates are
quantitatively evaluated. The results are given in Table 2.1 . The endpoint error e
is used to determine the Euclidean distance of the estimated and the ground-truth
deformation. For two transformations y 1 ,

3 3 and a non-empty set 3

y 2 : R → R Ω ⊂ R

the endpoint error is defined as

1
| Ω |

(

y 1 , y 2 )

=

Ω |

y 1 ( x

) −

y 2 ( x

) |

dx

,

e : (2.89)

= Ω where is the Euclidean norm. The values given in the

table are averaged values over all gates. The maximum endpoint error is considered
to analyze the worst case of the transformation mismatch and is defined as

| Ω | : dx and for vectors |·|

e max ( y 1 , y 2 ) : = max

x ∈ Ω |

y 1 ( x ) − y 2 ( x ) | . (2.90)

Fig. 2.10 The cardiac planes (from top to bottom : SA, HLA, and VLA) are shown for the single
reference gate R in ( a ) out of a 5 × 5 dual gating. The combination of all gates without any
motion correction can be seen in ( b ). Motion artifacts in terms of blurring can be clearly seen.
The motion corrected image based on the ground-truth motion is shown in ( c ). The image shows a
reduced blurring, e.g., in the blood pool. The results of the image registration based SAD V AMPIRE
approach and the optical flow based MPOF approach are shown in ( d )and( e ). The image quality
of the proposed V AMPIRE and MPOF approach is comparable to the best possible result based
on ground-truth motion and considerably better than the resulting image without any motion
correction. All images are corrected for attenuation