Grid spherical surface conformal parameterization method based on inverse spherical pole projection and application thereof

Abstract

The invention discloses a grid spherical surface conformal parameterization method based on inverse spherical pole projection and application thereof, and belongs to the field of computer image analysis. The method mainly aims at the current situation that the zero-deficit grid spherical surface conformal parameterization calculation amount is large, a grid is cut into a grid with two deficits as one; secondly, plane parameterization is carried out on the two grids, parameterization is harmonic mapping with the fixed boundary as a unit circle, kerfs are evenly mapped to the unit circle, and therefore the two grid curved surfaces with one deficit are parameterized to two unit discs in a conformal mode; complex inversion is performed on one disc to enable the two discs to cover the whole expansion complex plane; then inverse transformation of spherical pole projection is carried out, so that points on the expansion complex plane are mapped to a Riemannian spherical surface; and finally, Mobius transformation which enables harmonic energy to be minimum and meets 0 centroid constraint is found from a Mobius group, so that original grid characteristics of the parameterized grid are kept as far as possible. The method is applied to brain geometric vector analysis, the state of disease progress is known on the premise that no surgical operation is adopted, and the pain of a patient is relieved.

Description

technical field [0001] The invention belongs to the field of computer image analysis, and in particular relates to a grid spherical conformal angle parameterization method based on inverse spherical projection, which can be widely used in the field of brain pathological analysis of medical images. Background technique [0002] In the 1960s, humans dissected primate monkeys and found that the mapping from the retina to the surface of the cerebral cortex of the first-level visual center is a conformal mapping. The biggest feature of the conformal transformation is that it maintains the shape locally, but ignores the area. size. A conformal map is essentially a conformal map. In the past 20 years, with the in-depth study of the brain, it has been found that many neurological diseases are directly related to the abnormal shape of a certain area of ​​the brain. For example, Alzheimer's disease is generally accompanied by atrophy of the hippocampus and medial lobes. The traditio...

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Problems solved by technology

With the development of computer graphics and differential geometry, people have also carried out in-depth research on spherical parameterization. In summary, all methods are optimized in diffeomorphism groups. The problem is inherently difficult. First, the amount of calculation is large. The second computational complexity is large

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