## Registration Based FMD Estimation 531 Algorithm Overview

Our technique assumes that the vasodilation that takes place between two frames can be modeled by a constant scaling in the direction normal to the artery. This scale factor is obtained by means of image registration.

Figure 5.3: Overview of the proposed two-stage method: after motion compensation is carried out by recovering a rigid motion model, the vasodilation is measured by computing the scaling factor along the normal to the artery that best matches the two analyzed frames.

Figure 5.3: Overview of the proposed two-stage method: after motion compensation is carried out by recovering a rigid motion model, the vasodilation is measured by computing the scaling factor along the normal to the artery that best matches the two analyzed frames.

A reference frame is selected from the beginning of the sequence. All the other frames are registered to this reference frame. Changes in the relative position between the patient and the transducer are quite common during a whole examination, which may take up to 20 min. To elude wrong anatomical correspondences, motion compensation becomes necessary, and a rigid image registration technique is used to this end.

Structures surrounding the artery in the image may be important to resolve potential ambiguities in the longitudinal alignment between two frames, which occur because of the lineal nature of the arterial walls. On the other hand, ex-traluminal structures introduce artifacts when measuring the vasodilation since they do not necessarily deform in the same way as the artery does. Therefore, they should be taken into account when retrieving the global rigid motion information of the model, while arterial vasodilation estimation should only consider the artery deformation.

Our technique proceeds in two phases as summarized in Fig. 5.3: motion compensation and dilation assessment. The first phase uses the original frames and rigid image registration to recover a rigid motion model. Translation and rotation parameters are used to initialize the subsequent phase of vasodilation estimation. This second stage employs an affine registration model. To avoid artifacts when measuring arterial vasodilation it is convenient to remove background extra luminal structures by padding them out from the reference frame. Preprocessing of this frame also requires repositioning it so that the artery is normal to the scaling direction, that is to say, aligned with the horizontal axis, since our model searches for a vertical scaling factor (see Fig. 5.4). Both operations are performed manually on the reference frame. Manual masking only requires to roughly draw two lines in the reference frame and repositioning, to align a line with the direction of the artery, a process that is simple and takes only a few seconds per image sequence.

Figure 5.4: Preprocessing applied to the reference frame before the phase of vasodilation assessment. (a) Original reference frame and (b) the reference frame after alignment to the horizontal axis and padding out of background structures.

Figure 5.4: Preprocessing applied to the reference frame before the phase of vasodilation assessment. (a) Original reference frame and (b) the reference frame after alignment to the horizontal axis and padding out of background structures.

Temporal continuity is enforced in both phases by means of recursive filters in the registration parameter space prior to registering each new frame.

In the next two subsections the registration algorithm and its initialization, enforcing temporal continuity, are discussed.

5.3.2 Registration Algorithm 5.3.2.1 Motion and Vasodilation Models

Registering image B onto image A requires finding a transformation T( ) that maps B into A by maximizing a registration measure M( ) as indicated in Eq. (5.1). The similarity measure is computed over all points, P, of the overlap region of both images

Our motion model between the original (x, y) and transformed (xy') coordinates is a rigid transformation of the form

As we are imaging only a small and roughly straight vessel segment, the vasodilation can be assumed to be normal to the artery and, therefore, it can be modeled by only a scaling factor in that direction. Then, the vasodilation model

Table 5.1: Different similarity measures

SSD Sum of squared differences

CC Cross correlation

GCC Gradient image cross correlation

JE Joint entropy

MI Mutual information

NMI Normalized mutual information is a similarity transformation with four degrees of freedom: jx /cos 0 -sy ■ sin 0\ ( x\ It

5.3.2.2 Registration Measure

Several registration measures have been traditionally used in medical image matching and they main ones are listed in Table 5.1.

Among the different similarity measures, normalized mutual information (NMI) is selected in this work because of its low sensitivity to the size of the overlap region [21] and higher accuracy (see section 5.4.2.2). This measure, is defined as

where H(A) is the entropy of image A defined as

i and H(A, B) is the joint entropy between images A and B defined as

The entropies are computed from the image histograms where pi is an approximation of the probability of occurrence of intensity value i. Similarly, the joint entropy is computed from the joint histogram where p^ j is the approximation of the probability of the occurrence of corresponding intensity pairs (i, j). Linear interpolation is used to obtain intensities in noninteger pixel values to build the joint histograms.

Parameter |
Symbol |
Value |

Registration measure |
M |
See Table 5.1 |

No. of bins in joint histogram discretization |
b |
64 |

Gaussian kernel width for preblurring |
O b |
1 |

Resampling ratio |
P |
1.5 |

No. of resolution levels |
r |
3 |

Interpolation scheme |
— |
Bilinear |

5.3.2.3 Optimization Algorithm

A multiresolution framework proposed by Studholme et al. [22] is employed to recover the optimal transformation. The image is iteratively subsampled by a factor of two to build a multiresolution image pyramid. The registration problem is solved at each pyramid level in a coarse to fine fashion. The registration parameters found at each level are used as starting estimates for the parameters at the next level.

### 5.3.2.4 Summary of Registration Parameters

In Table 5.2, a summary of the parameters of the registration algorithm is provided. To compute the several registration metrics of Table 5.1, the joint histogram is discretized using 64 x 64 bins. Prior to image registration, the images are prefiltered with a Gaussian kernel of ab = 1 pixel and the images are resam-pled to a new pixel size of 1.5 with respect to the original size. These two steps can help to reduce small-scale noise and to reduce the computational load, and yield seemly registration results. Finally, the optimization strategy proceeds in three resolution levels. Image interpolation is carried out using a bilinear interpolation scheme.

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