Biomedical Engineering Reference
In-Depth Information
scattering, imperfect manufacture of CCDs, loss of higher bits during analog-to
digital conversion (called clipping or wrap-around), imperfect isolation of detec-
tors from each other (called blooming), effect of quantitation as a sample of inten-
sity from a discrete area of scene, and geometric aberration due to lenses. Compu-
ter vision is a discipline that focuses on information extraction from the output of
sensors, and on the representation of this information in a computer model. Image
registration enables a computer to register (apprehend and allocate) objects as they
appear in an internal computer model. A parametric image registration algorithm
specifies the parameters of a transformation in a way that physically corresponding
points at two consecutive time steps are brought together as close as possible. Fou-
rier transform provides the mathematical and algorithmic foundation for a number
of imaging techniques including X-ray CT, PET, SPECT, optical microscopy, and
MRI. A more recent development is the wavelet transform that appears to be ide-
ally suited for signal and image processing. Although one class of algorithms oper-
ates on previously extracted surface points, other algorithms register the images
directly based on the gray-value changes. Most commonly, a cost or error function
is defined and an optimization method is chosen that iteratively adjusts the param-
eters until an optimum is reached. Other approaches extract specific features (e.g.,
correspondence between points) that serve as a basis for directly calculating the
model parameters.
8.4.3 3DImageReconstruction
In a typical 2D image formed on a film, the information sought could be hidden
behind other structures in the object. In these cases, the desired information may
be obtained by repositioning the object in the beam several times to see the desired
image in detail. To overcome these difficulties, 3D image reconstruction (or render-
ing) or medical image volume visualization has been developed. In order to access
this information efficiently, a model is necessary for the integration of knowledge,
which is extracted from the images. In order to have enough data to mathemati-
cally reconstruct virtual slices, one needs projections from different angles. The
quality of the reconstruction and resolution in an image increases with the number
of projections.
The three basic operations performed in 3D medical imaging are data collec-
tion, data analysis, and data display. Data collection is similar to image acquisi-
tion in the digital form at different angles. For example, in X-ray CT, a series of
2D X-ray images (Figure 8.7) are obtained by rotating an X-ray emitter around
the patient, and measuring the intensity of transmitted rays from different angles.
From the 2D images at different angles, a projection function of the image is devel-
oped by mathematically (using Radon transform) transforming images with lines
into a domain of possible line parameters (refer to [2] for more information). To
reconstruct the images, the Fourier slice theorem is used to convert the projection
function to the 2D Fourier transform of the image. From the 2D Fourier transform
of the image, the inverse 2D Fourier transform projection function is developed.
Then, projections are run back along the same angles from where the images were
collected (hence the name back projection) to obtain a rough approximation to the
original. The projections interact constructively in regions that correspond to the
