65-XX NUMERICAL ANALYSIS
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In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and employ the approach for longitudinal analysis of 2D rat skulls shapes as well as 3D shapes derived from an imaging study on osteoarthritis. Particularly, we perform hypothesis test and estimate the mean trends.
Quantitative PA tomography of high resolution 3-D images: experimental validation in tissue phantoms
(2019)
Quantitative photoacoustic tomography aims recover the spatial distribution of absolute chromophore concentrations and their ratios from deep tissue, high-resolution images. In this study, a model-based inversion scheme based on a Monte-Carlo light transport model is experimentally validated on 3-D multispectral images of a tissue phantom acquired using an all-optical scanner with a planar detection geometry. A calibrated absorber allowed scaling of the measured data during the inversion, while an acoustic correction method was employed to compensate the effects of limited view detection. Chromophore- and fluence-dependent step sizes and Adam optimization were implemented to achieve rapid convergence. High resolution 3-D maps of absolute concentrations and their ratios were recovered with high accuracy. Potential applications of this method include quantitative functional and molecular photoacoustic tomography of deep tissue in preclinical and clinical studies.
In many applications, geodesic hierarchical models are adequate for the study of temporal observations. We employ such a model derived for manifold-valued data to Kendall's shape space. In particular, instead of the Sasaki metric, we adapt a functional-based metric, which increases the computational efficiency and does not require the implementation of the curvature tensor. We propose the corresponding variational time discretization of geodesics and apply the approach for the estimation of group trends and statistical testing of 3D shapes derived from an open access longitudinal imaging study on osteoarthritis.
Quantitative photoacoustic tomography aims to recover maps of the local concentrations of tissue chromophores from multispectral images. While model-based inversion schemes are promising approaches, major challenges to their practical implementation include the unknown fluence distribution and the scale of the inverse problem. This paper describes an inversion scheme based on a radiance Monte Carlo model and an adjoint-assisted gradient optimization that incorporates fluence-dependent step sizes and adaptive moment estimation. The inversion is shown to recover absolute chromophore concentrations, blood oxygen saturation and the Grüneisen parameter from in silico 3D phantom images for different radiance approximations. The scattering coefficient was assumed to be homogeneous and known a priori.
Traditionally, Lagrangian fields such as finite-time Lyapunov exponents (FTLE)
are precomputed on a discrete grid and are ray casted afterwards. This, however,
introduces both grid discretization errors and sampling errors during ray marching.
In this work, we apply a progressive, view-dependent Monte Carlo-based approach
for the visualization of such Lagrangian fields in time-dependent flows. Our ap-
proach avoids grid discretization and ray marching errors completely, is consistent,
and has a low memory consumption. The system provides noisy previews that con-
verge over time to an accurate high-quality visualization. Compared to traditional
approaches, the proposed system avoids explicitly predefined fieldline seeding
structures, and uses a Monte Carlo sampling strategy named Woodcock tracking
to distribute samples along the view ray. An acceleration of this sampling strategy
requires local upper bounds for the FTLE values, which we progressively acquire
during the rendering. Our approach is tailored for high-quality visualizations of
complex FTLE fields and is guaranteed to faithfully represent detailed ridge surface
structures as indicators for Lagrangian coherent structures (LCS). We demonstrate
the effectiveness of our approach by using a set of analytic test cases and real-world numerical simulations.
We present a level of detail method for trees based on ellipsoids and lines. We leverage the Expectation Maximization algorithm with a Gaussian Mixture Model to create a hierarchy of high-quality leaf clusterings, while the branches are simplified using agglomerative bottom-up clustering to preserve the connectivity. The simplification runs in a preprocessing step and requires no human interaction. For a fly by over and through a scene of 10k trees, our method renders on average at 40 ms/frame, up to 6 times faster than billboard clouds with comparable artifacts.