3D Geometries

Volume geometry

Create a 3D volume geometry:

vol_geom = astra.create_vol_geom([n_rows, n_cols, n_slices])
vol_geom = astra.create_vol_geom(n_rows, n_cols, n_slices)

vol_geom = astra_create_vol_geom([n_rows, n_cols, n_slices]);
vol_geom = astra_create_vol_geom(n_rows, n_cols, n_slices);

Specify the extent of the 3D volume (note that rows are oriented along the Y axis, columns along the X axis and slices along the Z axis):

vol_geom = astra.create_vol_geom(
    n_rows, n_cols, n_slices,
    min_x, max_x,
    min_y, max_y,
    min_z, max_z
)

vol_geom = astra_create_vol_geom(n_rows, n_cols, n_slices, min_x, max_x, min_y, max_y, min_z, max_z);

This can be used to control the voxel size, including specifying anisotropic voxels (note that the FDK algorithm does not currently support anisotropic voxels and will raise an exception).

Projection geometries

parallel3d

Illustration of the 3D parallel beam projection geometry.

proj_geom = astra.create_proj_geom('parallel3d', det_col_spacing, det_row_spacing, det_row_count, det_col_count, angles)

proj_geom = astra_create_proj_geom('parallel3d', det_col_spacing, det_row_spacing, det_row_count, det_col_count, angles);

Create a 3D parallel beam geometry.

det_col_spacing : distance between the centers of two horizontally adjacent detector pixels
det_row_spacing : distance between the centers of two vertically adjacent detector pixels
det_row_count : number of detector rows in a single projection
det_col_count : number of detector columns in a single projection
angles : projection angles in radians

cone

proj_geom = astra.create_proj_geom('cone',  det_col_spacing, det_row_spacing, det_row_count, det_col_count, angles, source_origin_distance, origin_detector_distance)

proj_geom = astra_create_proj_geom('cone',  det_col_spacing, det_row_spacing, det_row_count, det_col_count, angles, source_origin_distance, origin_detector_distance);

Create a 3D cone beam geometry.

det_col_spacing : distance between the centers of two horizontally adjacent detector pixels
det_row_spacing : distance between the centers of two vertically adjacent detector pixels
det_row_count : number of detector rows in a single projection
det_col_count : number of detector columns in a single projection
angles : projection angles in radians
source_origin_distance : distance between the source and the center of rotation
origin_detector_distance : distance between the center of rotation and the detector array

parallel3d_vec

Illustration of the 3D parallel beam projection geometry specified by vectors.

proj_geom = astra.create_proj_geom('parallel3d_vec',  det_row_count, det_col_count, vectors)

proj_geom = astra_create_proj_geom('parallel3d_vec',  det_row_count, det_col_count, vectors);

Create a 3D parallel beam geometry specified by 3D vectors.

det_row_count : number of detector rows in a single projection
det_col_count : number of detector columns in a single projection
vectors : a matrix defining the geometry

Each row of vectors corresponds to a single projection, and consists of:

( dirX, dirY, dirZ, dX, dY, dZ, uX, uY, uZ, vX, vY, vZ )

dir : the illumination direction
d : the detector center coordinate
u : the vector from detector pixel (0,0) to (0,1)
v : the vector from detector pixel (0,0) to (1,0)

To illustrate this, here is a script to convert a single projection in a geometry of type “parallel3d” into such a 12-element row:

# ray direction
vectors[i,0] = numpy.sin(proj_geom['ProjectionAngles'][i])
vectors[i,1] = -numpy.cos(proj_geom['ProjectionAngles'][i])
vectors[i,2] = 0

# center of detector
vectors[i,3] = 0
vectors[i,4] = 0
vectors[i,5] = 0

# vector from detector pixel (0,0) to (0,1)
vectors[i,6] = numpy.cos(proj_geom['ProjectionAngles'][i]) * proj_geom['DetectorSpacingX']
vectors[i,7] = numpy.sin(proj_geom['ProjectionAngles'][i]) * proj_geom['DetectorSpacingX']
vectors[i,8] = 0

# vector from detector pixel (0,0) to (1,0)
vectors[i, 9] = 0
vectors[i,10] = 0
vectors[i,11] = proj_geom['DetectorSpacingY']

% ray direction
vectors(i,1) = sin(proj_geom.ProjectionAngles(i));
vectors(i,2) = -cos(proj_geom.ProjectionAngles(i));
vectors(i,3) = 0;

% center of detector
vectors(i,4) = 0;
vectors(i,5) = 0;
vectors(i,6) = 0;

% vector from detector pixel (0,0) to (0,1)
vectors(i,7) = cos(proj_geom.ProjectionAngles(i)) * proj_geom.DetectorSpacingX;
vectors(i,8) = sin(proj_geom.ProjectionAngles(i)) * proj_geom.DetectorSpacingX;
vectors(i,9) = 0;

% vector from detector pixel (0,0) to (1,0)
vectors(i,10) = 0;
vectors(i,11) = 0;
vectors(i,12) = proj_geom.DetectorSpacingY;

This conversion is also available as a function in the toolbox:

proj_geom_vec = astra.geom_2vec(proj_geom)

proj_geom_vec = astra_geom_2vec(proj_geom);

cone_vec

Illustration of the 3D cone beam projection geometry specified by vectors.

proj_geom = astra.create_proj_geom('cone_vec',  det_row_count, det_col_count, vectors)

proj_geom = astra_create_proj_geom('cone_vec',  det_row_count, det_col_count, vectors);

Create a 3D cone beam geometry specified by 3D vectors.

det_row_count : number of detector rows in a single projection
det_col_count : number of detector columns in a single projection
vectors : a matrix defining the geometry

Each row of vectors corresponds to a single projection, and consists of:

( srcX, srcY, srcZ, dX, dY, dZ, uX, uY, uZ, vX, vY, vZ )

src : the illumination source position
d : the detector center coordinate
u : the vector from detector pixel (0,0) to (0,1)
v : the vector from detector pixel (0,0) to (1,0)

To illustrate this, here is a script to convert a single projection in a geometry of type “cone” into such a 12-element row:

# source
vectors[i,0] = numpy.sin(proj_geom['ProjectionAngles'][i]) * proj_geom['DistanceOriginSource']
vectors[i,1] = -numpy.cos(proj_geom['ProjectionAngles'][i]) * proj_geom['DistanceOriginSource']
vectors[i,2] = 0

# center of detector
vectors[i,3] = -numpy.sin(proj_geom['ProjectionAngles'][i]) * proj_geom['DistanceOriginDetector']
vectors[i,4] = numpy.cos(proj_geom['ProjectionAngles'][i]) * proj_geom['DistanceOriginDetector']
vectors[i,5] = 0

# vector from detector pixel (0,0) to (0,1)
vectors[i,6] = numpy.cos(proj_geom['ProjectionAngles'][i]) * proj_geom['DetectorSpacingX']
vectors[i,7] = numpy.sin(proj_geom['ProjectionAngles'][i]) * proj_geom['DetectorSpacingX']
vectors[i,8] = 0

# vector from detector pixel (0,0) to (1,0)
vectors[i, 9] = 0
vectors[i,10] = 0
vectors[i,11] = proj_geom['DetectorSpacingY']

% source
vectors(i,1) = sin(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginSource;
vectors(i,2) = -cos(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginSource;
vectors(i,3) = 0;

% center of detector
vectors(i,4) = -sin(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginDetector;
vectors(i,5) = cos(proj_geom.ProjectionAngles(i)) * proj_geom.DistanceOriginDetector;
vectors(i,6) = 0;

% vector from detector pixel (0,0) to (0,1)
vectors(i,7) = cos(proj_geom.ProjectionAngles(i)) * proj_geom.DetectorSpacingX;
vectors(i,8) = sin(proj_geom.ProjectionAngles(i)) * proj_geom.DetectorSpacingX;
vectors(i,9) = 0;

% vector from detector pixel (0,0) to (1,0)
vectors(i,10) = 0;
vectors(i,11) = 0;
vectors(i,12) = proj_geom.DetectorSpacingY;

cyl_cone_vec

Illustration of the 3D cylindrical detector cone beam projection geometry specified by vectors.

Added in version 2.4.

Caution

This is an experimental feature, and the parameters or implementation may change in future releases.

proj_geom = astra.create_proj_geom('cyl_cone_vec',  det_row_count, det_col_count, vectors)

proj_geom = astra_create_proj_geom('cyl_cone_vec',  det_row_count, det_col_count, vectors);

Create a 3D cylindrical detector cone beam geometry specified by 3D vectors. U axis of the detector will be curved.

det_row_count : number of detector rows in a single projection
det_col_count : number of detector columns in a single projection
vectors : a matrix defining the geometry

Each row of vectors corresponds to a single projection, and consists of:

( srcX, srcY, srcZ, dX, dY, dZ, uX, uY, uZ, vX, vY, vZ, R )

src : the illumination source position
d : the detector center coordinate
uthe vector tangential to the curved detector surface at the center of the
detector; with length equal to the arc length covered by one column of the detector
v : the vector from detector pixel (0,0) to (1,0)
R : curvature radius of the cylindrical detector (U axis will be curved)