Apparatus and method for computing the radon transform of digital images

Claim 3

In a system including display means for displaying an image in raster form, array generator means connected to the display means for producing an array of picture elements (pixels) representing the raster image, and a processing means for performing a Radon transform of a digital image represented by the pixel array, the processing means including a storage means having a storage mechanism with a plurality of projection storage locations, each projection storage location being identified and accessed by a storage location address, a method for constructing a Radon projection of said image at a projection angle Θ in the storage means, the method including the steps of: (a) providing said array of pixels to said processing means in row order; (b) in said processing means, for each pixel in said array of pixels: (b1) determining a reference location z on an axis which corresponds said Radon projection with said array of pixels, said reference location corresponding with a row of said array of pixels which contains said pixel; (b2) determining a storage location address, zu, defining a projection storage location in said storage means by combining z with Θ according to: zu=floor((x-0.5)*cos Θ+(y+0.5)*sin Θ+z where, floor (w) is the greatest integer less than or equal to w, and x,y corresponds to the location of the center of said pixel in said array of pixels, said projection storage location address zu corresponding to a ray of said projection which intersects said pixel; (b3) determining a length of the portion of said ray which is contained in said pixel; (b4) combining said length with an intensity magnitude of said pixel to obtain a ray segment value; and (b5) combining said ray segment value with a partial ray value stored at the projection storage location corresponding to said address and storing the result at said projection storage location as an updated partial ray value; and, then (c) assembling said projection by accumulating in said projection storage locations the updated partial ray values for the pixels in said array of pixels.

Claim 4

In a system including display means for displaying an image in raster form, array generator means connected to the display means for producing an array of picture elements (pixels) representing the raster image, and a processing means for performing a Radon transform of a digital image represented by the pixel array, the processing means including a storage means having a storage mechanism with a plurality of projection storage locations, each projection storage location being identified and accessed by a storage location address, a method for constructing a Radon projection of said image at a projection angle Θ in the storage means, the method including the steps of: (a) providing said array of pixels to said processing means in row order; (b) in said processing means, for each pixel in said array of pixels: (b1) determining a reference location z on an axis which corresponds said Radon projection with said array of pixels, said reference location corresponding with a row of said array of pixels which contains said pixel; (b2) determining a storage location address, zu, defining a projection storage location in said storage means by combining z with Θ according to: zu=floor((x-0.5)*cos Θ+(y+0.5)*sin Θ+z where, floor (w) is the greatest integer less than or equal to w, and x,y corresponds to the location of the center of said pixel in said array of pixels, said projection storage location address zu corresponding to a ray of said projection which intersects said pixel; (b3) determining a length of the portion of said ray which is contained in said pixel; (b4) combining said length with an intensity magnitude of said pixel to obtain a ray segment value; and (b5) combining said ray segment value with a partial ray value stored at the projection storage location corresponding to said address and storing the result at said projection storage location as an updated partial ray value; and, then (c) assembling said projection by accumulating in said projection storage locations the updated partial ray values for the pixels in said array of pixels.

Claim 5

The method of claim 2: wherein step (b2) further includes determining a projection storage location, zl, by combining z with Θ according to: zl=ceil((x+0.5)xcos Θ+(y-0.5)*sin Θ+z) where ceil(w) is the smallest integer greater than or equal to (w), said storage location zl corresponding to a ray of said projection which intersects said pixel; between step (b2) and step (b3), identifying a plurality of projection storage locations, each of said projections storage locations corresponding to one of a plurality of rays which intersect that pixel, and each of said projections storage locations identified by a respective integer of the set zl, zl+1 . . . , zu; and performing steps (b3)-(b5) for each ray of said plurality of rays.