4 research outputs found
Landmark-Matching Transformation with Large Deformation Via n-dimensional Quasi-conformal Maps
We propose a new method to obtain landmark-matching transformations between n-dimensional Euclidean spaces with large deformations. Given a set of feature correspondences, our algorithm searches for an optimal folding-free mapping that satisfies the prescribed landmark constraints. The standard conformality distortion defined for mappings between 2-dimensional spaces is first generalized to the n-dimensional conformality distortion K(f) for a mapping f between n-dimensional Euclidean spaces (n ≥ 3). We then propose a variational model involving K(f) to tackle the landmark-matching problem in higher dimensional spaces. The generalized conformality term K(f) enforces the bijectivity of the optimized mapping and minimizes its local geometric distortions even with large deformations. Another challenge is the high computational cost of the proposed model. To tackle this, we have also proposed a numerical method to solve the optimization problem more efficiently. Alternating direction method with multiplier is applied to split the optimization problem into two subproblems. Preconditioned conjugate gradient method with multi-grid preconditioner is applied to solve one of the sub-problems, while a fixed-point iteration is proposed to solve another subproblem. Experiments have been carried out on both synthetic examples and lung CT images to compute the diffeomorphic landmark-matching transformation with different landmark constraints. Results show the efficacy of our proposed model to obtain a folding-free landmark-matching transformation between n-dimensional spaces with large deformations
A novel explicit design method for complex thin-walled structures based on embedded solid moving morphable components
In this article, a novel explicit approach for designing complex thin-walled
structures based on the Moving Morphable Component (MMC) method is proposed,
which provides a unified framework to systematically address various design
issues, including topology optimization, reinforced-rib layout optimization,
and sandwich structure design problems. The complexity of thin-walled
structures mainly comes from flexible geometries and the variation of
thickness. On the one hand, the geometric complexity of thin-walled structures
leads to the difficulty in automatically describing material distribution
(e.g., reinforced ribs). On the other hand, thin-walled structures with
different thicknesses require various hypotheses (e.g., Kirchhoff-Love shell
theory and Reissner-Mindlin shell theory) to ensure the precision of structural
responses. Whereas for cases that do not fit the shell hypothesis, the
precision loss of response solutions is nonnegligible in the optimization
process since the accumulation of errors will cause entirely different designs.
Hence, the current article proposes a novel embedded solid component to tackle
these challenges. The geometric constraints that make the components fit to the
curved thin-walled structure are whereby satisfied. Compared with traditional
strategies, the proposed method is free from the limit of shell assumptions of
structural analysis and can achieve optimized designs with clear load
transmission paths at the cost of few design variables and degrees of freedom
for finite element analysis (FEA). Finally, we apply the proposed method to
several representative examples to demonstrate its effectiveness, efficiency,
versatility, and potential to handle complex industrial structures
Multiscale Geometric Methods for Isolating Exercise Induced Morphological Adaptations in the Proximal Femur
The importance of skeletal bone in the functioning of the human body is well-established and acknowledged. Less pervasive among the populace, is the understanding of bone as an adaptive tissue which modulates itself to achieve the most construction sufficient for the role it is habituated to. These mechanisms are more pronounced in the long load bearing bones such as the femur. The proximal femur especially, functions under significant loads and does so with high degree of articulation, making it critical to mobility. Thus, exercising to buttress health and reinforce tissue quality is just as applicable to bone as it is to muscles. However, the efficiency of the adaptive (modelling/remodelling) processes is subdued after maturity, which makes the understanding of its potential even more important. Classically, studies have translated the evaluation of strength in terms of its material and morphology. While the morphology of the femur is constrained within a particular phenotype, minor variations can have a significant bearing on its capability to withstand loads. Morphology has been studied at different scales and dimensions wherein parameters quantified as lengths, areas, volumes and curvatures in two and three dimensions contribute towards characterising strength. The challenge has been to isolate the regions that show response to habitual loads. This thesis seeks to build on the principles of computational anatomy and develop procedures to study the distribution of mechanically relevant parameters. Methods are presented that increase the spatial resolution of traditional cross-sectional studies and develop a conformal mapping procedure for proximal femur shape matching. In addition, prevalent methods in cross-sectional analyses and finite element simulations are employed to analyse the morphology of the unique dataset. The results present the spatial heterogeneity and a multi-scale understanding of the adaptive response in the proximal femur morphology to habitual exercise loading