Einführung in die medizinische Bildverarbeitung SS 2013
Einführung in die medizinische Bildverarbeitung SS 2013
Einführung in die medizinische Bildverarbeitung SS 2013
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Grundlagen rotates. - Bilderzeugung<br />
Computertomographie<br />
‣ Projektionen<br />
veloped. In such a system, power supply to the X-ray tube and signal transfer from<br />
the detector system is guaranteed, even though the imag<strong>in</strong>g system cont<strong>in</strong>uously<br />
From a mathematical po<strong>in</strong>t of view, image reconstruction <strong>in</strong> computed tomography<br />
is the task of comput<strong>in</strong>g the spatial structure of an object that casts shadows<br />
us<strong>in</strong>g these very shadows. The solutionforthisproblemiscomplexand<strong>in</strong>volves<br />
techniques <strong>in</strong> physics, mathematics, and computer science. Thedescribedscenario<br />
is referred to as the <strong>in</strong>verse problem <strong>in</strong> mathematics.<br />
‣ Orig<strong>in</strong>alobjekt und dazu passende Projektionen<br />
Fig. 1.1. Schematic[Quelle: illustration<br />
Buzug, T., Computed<br />
of computed<br />
Tomography -<br />
tomography<br />
From Photon Statistics<br />
(CT).<br />
to Modern<br />
Three<br />
Cone-Beam<br />
homogeneous<br />
CT]<br />
objects<br />
with quadratic <strong>in</strong>tersection areas are exposed with X-ray under the projection angles γ 1<br />
and γ 2 .Eachprojectionangleproducesaspecificshadow,p γ (ξ), which,measuredwith<br />
the detector array represents the <strong>in</strong>tegral X-ray attenuation profile. The geometricshadow<br />
boundaries are <strong>in</strong>dicated with dashed l<strong>in</strong>es. However,analysisoftheprofileunderthefirst<br />
projection angle, γ 1 ,onitsowndoesnotallowonetodeduceanestimateofthenumberof<br />
separated objects<br />
© Stephan Gimbel <strong>E<strong>in</strong>führung</strong> <strong>in</strong> <strong>die</strong> mediz<strong>in</strong>ische <strong>Bildverarbeitung</strong><br />
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