Biomedical Engineering Reference
In-Depth Information
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FIgurE 16.7
Example of a 1D digital signal. The
x
-axis describes the sampling of the process and the
y
-axis is
the value of each sample.
variable represents distance or frequency is known as a spatial-domain or frequency-domain signal,
respectively. A fundamental area of digital signal processing deals with mathematical techniques for
converting signals from one domain to another. The Fourier transform is a well-known example of these
techniques and is used to convert time-domain signals into frequency-domain signals.
An image, such as might be acquired using the advanced imaging techniques described previously,
can be thought of as a matrix of values, with the rows and columns represented by the independent
variables
x
and
y
(denoting the distance from the origin) and the dependent variable,
f
(
x
,
y
), representing
the value of the matrix at a given location. Each one of these matrix locations is known as a pixel and,
in a grayscale image with 8 bits per pixel, the value of each pixel can range from 0 (black) to 255 (white)
(Figure 16.8). This number is related to the amount of energy reflected back from or passing through the
corresponding location on the surface of the object being imaged at acquisition [47]. The value of a pixel
is commonly referred to as the pixel's intensity. The spatial-domain information of an image is in the
form of edges—transitions between areas of high intensity and areas of low intensity.
An image may also be thought of as being composed of a complex combination of 2D signal com-
ponents. For example, Figure 16.9 shows how several 2D sinusoids may be combined to form a new
image.
Digital image processing is generally divided into four categories: image coding, image enhance-
ment, image restoration, and image feature extraction [57]. Image coding refers to processes related to
image storage and transportation. Image enhancement improves human visual perception of an image
by altering image features. Correction of noise, blurring, or distortion is known as image restoration.
Finally, image feature extraction is the transformation of one image into another image from which
quantitative measurements may be taken [57]. Feature extraction and subsequent analysis of those fea-
tures are the goals of the projects described here.
Decomposing an image into its component waveforms is a method for simplifying a complex problem
and making the task of feature extraction more manageable. Image decomposition can aid in applica-
tions such as geometric feature extraction, image filtering, image reconstruction, and image compres-
sion. One of the best known and most used image decomposition methods is the Fourier transform,
which decomposes a signal (1D or 2D) into its component sinusoids. As mentioned earlier, the Fourier
transform is a time- or space-to-frequency transform (i.e., the input is a spatial- or time-domain signal,
