Image Processing Toolbox User's Guide

Computing Fan-Beam Projection Data

To compute fan-beam projection data, use the fanbeam function. You specify as arguments an image and the distance between the vertex of the fan-beam projections and the center of rotation (the center pixel in the image). The fanbeam function determines the number of beams, based on the size of the image and the settings of fanbeam parameters.

The FanSensorGeometry parameter specifies how sensors are aligned. If you specify the value 'arc' for FanSensorGeometry (the default), fanbeam positions the sensors along an arc, spacing the sensors at 1 degree intervals. Using the FanSensorSpacing parameter, you can control the distance between sensors by specifying the angle between each beam. If you specify the value 'line' for FanSensorGeometry parameter, fanbeam position sensors along a straight line, rather than an arc. With 'line' geometry, the FanSensorSpacing parameter specifies the distance between the sensors, in pixels, along the x' axis.

fanbeam takes projections at different angles by rotating the source around the center pixel at 1 degree intervals. Using the FanRotationIncrement parameter you can specify a different rotation angle increment.

The following figures illustrate both these geometries. The first figure illustrates geometry used by the fanbeam function when FanSensorGeometry is set to 'arc' (the default). Note how you specify the distance between sensors by specifying the angular spacing of the beams.

Fan-Beam Projection with Arc Geometry

The following figure illustrates the geometry used by the fanbeam function when FanSensorGeometry is set to 'line'. In this figure, note how you specify the position of the sensors by specifying the distance between them in pixels along the x' axis.

Fan-Beam Projection with Line Geometry

Fan-Beam Projection Data

Reconstructing an Image from Fan-Beam Projection Data

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