Biomedical Engineering Reference
In-Depth Information
more slices from tracked B-mode ultrasound, interventional CT, or interven-
tional MRI are to be established relative to a 3D volume. The main applica-
tion of these methods is in image-guided interventions, as described in more
detail in Chapter 12.
2.3.1.4
Time
Another class of registration problem concerns registration of image sequences
that follow some process that changes with time. An obvious example is imag-
ing of the heart, where images are acquired in synchrony with the heartbeat,
monitored by the ECG or blood pressure waveform. Synchronized or “gated”
acquisitions allow averaging of images over multiple cardiac cycles to reduce
image noise in nuclear medicine and MR imaging. In a similar way, temporal
registration of x-ray images of the heart before and after injection of contrast
material allows synchronous subtraction of mask images. All these methods
assume that the heart cycle does not change from beat to beat. The same prin-
ciple can be applied to images acquired at different stages of the breathing
cycle, although the breathing cycle is less reproducible and therefore registra-
tion errors will be greater. Acquisition of images over time and subsequent reg-
istration can be used to study dynamic processes such as tissue perfusion,
blood flow, and metabolic or physiological processes.
2.3.2
Degrees of Freedom of the Transformation
The number of parameters needed to describe a registration transformation
is referred to as the number of “degrees of freedom.” This depends on the
dimensionality of the images and the constraints of the imaged structures.
The simplest transformation corresponds to the motion of a rigid body.
For 2D-to-2D registration, there will be three degrees of freedom: two trans-
lations and one rotation. Figure 2.3 provides an example of two images
related by a rigid transformation. The middle image also shows that a trans-
formation will lead to the loss of some data from the original image and to
FIGURE 2.3
Three 2D images related by a rigid rotation (left and middle) and horizontal scaling (left and
right).
