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Publication# Anatomical Priors to improve Global Tractography

Abstract

The main assumption of fiber-tracking algorithms is that fiber trajectories are represented by paths of highest diffusion, which is usually accomplished by following the principal diffusion directions in every voxel. The state-of-the-art approaches known as “global tractography” reconstruct all the fiber tracts of the whole brain simultaneously by solving global energy minimization inverse problems. In this work we have reformulated global tractography to explicitly enforce anatomical priors in the optimization with the aim of (i) improving the quality of reconstructions and (ii) reducing the computation time.

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A computation is any type of arithmetic or non-arithmetic calculation that is well-defined. Common examples of computations are mathematical equations and computer algorithms. Mechanical or electronic devices (or, historically, people) that perform computations are known as computers. The study of computation is the field of computability, itself a sub-field of computer science. The notion that mathematical statements should be ‘well-defined’ had been argued by mathematicians since at least the 1600s, but agreement on a suitable definition proved elusive.

Computational complexity

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation time (generally measured by the number of needed elementary operations) and memory storage requirements. The complexity of a problem is the complexity of the best algorithms that allow solving the problem. The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory.

Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor.

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2023