Image histograms are useful in deciding how to represent the data value associated with a voxel as a pixel intensity on the display device. You will see the importance of a histogram in the following section.A histogram of an image is a plot of the number of pixels with a given data value. This histogram represents an image in which most of its pixels have data values between 0-80, and 600-1000.
Image histograms are useful in deciding how to represent the data value associated with a voxel as a pixel intensity on the display device. You will see the importance of a histogram in the following section.
Thus far in the teaching package we have concentrated on spin physics, pulse sequences, and hardware. A great deal of math occurs between the point that the raw data has been collected and the image is displayed. This section will take you through some of these details.
The raw data, or k-space data as it is sometimes called, is most often 256x256 data points of complex data. Here it is presented as the Mx and My or real (RE) and imaginary (IM) signals from the signal digitizer.
The presentation is in the form of an image of the raw data. The data typically has 16 bits of amplitude resolution. It will be beneficial to follow the processing of this 256x256 set of data before proceeding to smaller size matrices.
As was seen in Chapter 5
it is often times useful to smooth a frequency domain spectrum by convoluting it with a Lorentzian line shape. Recall that multiplying the time domain spectrum by an exponentially decaying function, which is the Fourier pair of the Lorentzian lineshape, is equivalent to convoluting in the frequency domain. For this reason the raw data is sometimes multiplied by an exponential cone before it is Fourier Transformed.
The Fourier transform is performed first in the vertical direction,
and then in the horizontal direction.
Once the Fourier transforms are performed, the magnitude is calculated.
The magnitude calculation cuts the amplitude information down to 15 bits of resolution. Because the magnitude image is used there will never be negative pixel intensities. The magnitude data is expanded to a 512x512 data matrix by either pixel interpolation or pixel replication.
Pixel replication duplicates even numbered pixels with the lower odd numbered pixel. Pixel interpolation inserts even numbered pixels as the average of the adjacent odd numbered pixels.
The image is typically displayed with an eight bit video display. This means there are 256 possible gray levels with which to display the 32768 possible data values from the 15 bits of magnitude information. A linear look-up table (LUT) is typically used. Here the video intensity between 0 and 255 is set by a linear relationship to the data value.
The width of the data values set to the 256 possible gray levels is called the width or contrast.
The data value assigned the center of the gray scale is referred to as the level or brightness.
Adjusting the width and level allow the viewer to set the image attributes which best display the anatomy and pathology.
Experiment with the concept of width and level by selecting a width and level from the table below. When a given width and level are selected, the spin-echo image of the human head is displayed with the following contrast and brightness.
| Width | Level | Image & LUT |
|---|---|---|
| 1153 | 576 | 
|
| 280 | 860 |
|
| 780 | 735 |
|
| 320 | 730 |
|
| 1 | 470 |
|
| 1 | 865 |
|
Often times less than 256x256 data points are collected to decrease the imaging time. For example, a 256x192 or 256x128 data matrix can be collected when there are 192 or 128 phase encoding steps. It is preferable to always have the same size matrix for input into the two dimensional Fourier transform.
In the case of a 256x192 or 256x128 acquisition the ends of the matrix are filled with zeroes.
This process is called zero filling. The process is equivalent to pixel replication to produce a 256x256 image from 256x128 data. Once filled with zeroes the data is processed as described above.
Clinical imagers do not use the XYZ magnetic resonance coordinate system for collection and presentation of images. Instead the anatomic coordinate system is used. In this system the axes are referenced to the body.
The three axes are left-right (L/R),
superior-inferior (S/I),
and anterior-posterior (A/P).
Similarly, on clinical imagers the terminology XY, XZ, and YZ are not used to indicate the imaged planes. An imaged plane perpendicular to the long axis of the body is called an axial plane.
The sides of this plane are L/R and A/P.
A plane bisecting the front of the body from the back is referred to as a coronal plane.
The sides of this plane are L/R and S/I.
A plane bisecting the left and right sides of the body is called a sagittal plane.
The sides of this plane are S/I and A/P.
What features in the image correspond to the peaks at 0-60, 720-865, and 865-1000 most likely represent?
What would be a good width and level to use to display an image of the data represented by the histogram?
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