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For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually a better, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step. [1]
ART can be considered as an iterative solver of a system of linear equations =, where: A {\displaystyle A} is a sparse m × n {\displaystyle m\times n} matrix whose values represent the relative contribution of each output pixel to different points in the sinogram ( m {\displaystyle m} being the number of individual values in the sinogram, and ...
This is an iterative process requiring adjustment of objects, shapes, depth, and visualization of intermediate results in stereo. Depth micro-relief, 3D shape is added to most important surfaces to prevent the "cardboard" effect when stereo imagery looks like a combination of flat images just set at different depths.
The Kaczmarz method or Kaczmarz's algorithm is an iterative algorithm for solving linear equation systems =.It was first discovered by the Polish mathematician Stefan Kaczmarz, [1] and was rediscovered in the field of image reconstruction from projections by Richard Gordon, Robert Bender, and Gabor Herman in 1970, where it is called the Algebraic Reconstruction Technique (ART). [2]
3D reconstruction from multiple images is the creation of three-dimensional models from a set of images. It is the reverse process of obtaining 2D images from 3D scenes. The essence of an image is a projection from a 3D scene onto a 2D plane, during which process the depth is lost.
Because the notation f n may refer to both iteration (composition) of the function f or exponentiation of the function f (the latter is commonly used in trigonometry), some mathematicians [citation needed] choose to use ∘ to denote the compositional meaning, writing f ∘n (x) for the n-th iterate of the function f(x), as in, for example, f ...
In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the i-th approximation (called an "iterate") is derived from the previous ones.
This process is continued to the Nth level. For example, in constructing such a model down to level 8 we produce a 4 8 array of cells. Thirdly, the cells are filled as follows: We take the probability of a cell being occupied as the product of the cell's own p i and those of all its parents (up to level 1).