backprojected

Backprojected is an adjective used in imaging and related fields to denote a quantity obtained by backprojection, the reverse operation of projection. In tomography, backprojection takes line-integral measurements of an object, recorded as a set of projections p(θ, s) at various angles θ, and redistributes them back into image space along lines corresponding to those angles. The result, a backprojected image, assigns to each point in the reconstruction grid contributions from all projections, producing a smeared or blurred version of the original object. Because simple backprojection amplifies high-frequency noise and yields blur, reconstruction pipelines typically apply a filtering step before or during backprojection, yielding the filtered backprojection method popular in computed tomography.

In computer vision and geometry, the term is used to describe the reverse mapping of image measurements to a higher-dimensional space. Backprojecting a 2D image point through a calibrated camera yields a ray in 3D space; backprojection of a 2D probability density distribution likewise expands to a conical or ray-based distribution in scene space, used in tasks such as triangulation and probabilistic 3D reconstruction.

Across domains, backprojected results share the characteristic of representing evidence in the original domain that has been spread or reinterpreted along the geometric structures associated with projection angles or camera models. The term emphasizes the inverse relationship to projection, and is distinct from, though often paired with, filtered or regularized backprojection techniques.