Three-dimensional reprojection and backprojection methods and algorithms for implementation thereof
Methods for three-dimensional projecting and backprojecting rays with respect to voxels/detector bins to attenuate/eliminate high-frequency artifacts, are disclosed. A distance-driven technique wherein the transitions of the voxels and the detector bins are respectively projected onto a predetermined plane. This projection allows a determination of the contribution of each of the voxels/bins for each of the bins/voxels with lower computation time and improved artifact free images.
1. A method of image processing comprising:
projecting edges of each voxel of a voxel grid, which are intersected by a plurality of rays projected from a source to a detector, in a predetermined sequence of voxels in the voxel grid, onto a predetermined plane;
projecting the edges of each bin of a detector onto the predetermined plane; and
determining the contribution of each voxel to a bin of the detector array or vice versa in accordance with the projections of the voxel edges and the detector bin edges on the predetermined plane.
2. A method of image processing as set forth in claim 1 , wherein the step of projecting the edges of the voxel onto the predetermined plane comprises projecting a selected line on a side of the voxel onto the predetermined plane.
3. A method of image processing as set forth in claim 1 , wherein the predetermined plane is an arbitrarily selected plane.
4. A method of image processing as set forth in claim 1 , wherein the predetermined plane is parallel to an x-z plane.
5. A method of image processing comprising:
establishing a voxel grid containing image voxels, which are arranged in image rows, columns and planes;
continuously mapping transitions between image voxels and transitions between detector-bins of a detector which has detected radiation from a source comprising:
projecting detector bin transitions onto a predetermined plane;
projecting the voxel transitions onto the predetermined plane; and
weighting at least one of the detector bins and voxels with an area on the predetermined plane, based on an area limited by adjacent projections.
6. A computer readable medium encoded with a program executable by a computer for processing an image, said program being configured to instruct the computer to:
project edges of each voxel of a voxel grid, which is intersected by a plurality of rays projected from a source to a detector, in a predetermined sequence of voxels in the voxel grid, onto a predetermined plane;
project the edges of each bin of a detector onto the predetermined plane; and
determine the contribution of each voxel to a bin of the detector array or vice versa in accordance with the projections of the voxel edges and the detector bin edges on the predetermined plane.
7. A computer readable medium as set forth in claim 6 , wherein the step of projecting the edges of the voxel onto the predetermined plane comprises projecting a selected line on a side of the voxel onto the predetermined plane.
8. A computer readable medium as set forth in claim 6 , wherein the predetermined plane is an arbitrarily selected plane.
9. A computer readable medium as set forth in claim 6 , wherein the predetermined plane is parallel to an x-z plane.
10. A computer readable medium encoded with a program executable by a computer for processing an image, said program being configured to instruct the computer to:
establish a voxel grid containing image voxels, which are arranged in image rows, columns and planes;
continuously map transitions between image voxels and transitions between detector-bins of a detector which has detected radiation from a source comprising:
project detector bin transitions onto a predetermined plane;
project the voxel transitions onto the predetermined plane; and
weight at least one of the detector bins and voxels with an area on the predetermined plane, based on an area limited by adjacent projections.