Meshless Monte Carlo radiation transfer method for curved geometries using signed distance functions

SIGNIFICANCE

Monte Carlo radiation transfer (MCRT) is the gold standard for modeling light transport in turbid media. Typical MCRT models use voxels or meshes to approximate experimental geometry. A voxel-based geometry does not allow for the precise modeling of smooth curved surfaces, such as may be found in biological systems or food and drink packaging. Mesh-based geometry allows arbitrary complex shapes with smooth curved surfaces to be modeled. However, mesh-based models also suffer from issues such as the computational cost of generating meshes and inaccuracies in how meshes handle reflections and refractions.

AIM

We present our algorithm, which we term signedMCRT (sMCRT), a geometry-based method that uses signed distance functions (SDF) to represent the geometry of the model. SDFs are capable of modeling smooth curved surfaces precisely while also modeling complex geometries.

APPROACH

We show that using SDFs to represent the problem's geometry is more precise than voxel and mesh-based methods.

RESULTS

sMCRT is validated against theoretical expressions, and voxel and mesh-based MCRT codes. We show that sMCRT can precisely model arbitrary complex geometries such as microvascular vessel network using SDFs. In comparison with the current state-of-the-art in MCRT methods specifically for curved surfaces, sMCRT is more precise for cases where the geometry can be defined using combinations of shapes.

CONCLUSIONS

We believe that SDF-based MCRT models are a complementary method to voxel and mesh models in terms of being able to model complex geometries and accurately treat curved surfaces, with a focus on precise simulation of reflections and refractions. sMCRT is publicly available at https://github.com/lewisfish/signedMCRT.

Interpretable exemplar-based shape classification using constrained sparse linear models

Many types of diseases manifest themselves as observable changes in the shape of the affected organs. Using shape classification, we can look for signs of disease and discover relationships between diseases. We formulate the problem of shape classification in a holistic framework that utilizes a lossless scalar field representation and a non-parametric classification based on sparse recovery. This framework generalizes over certain classes of unseen shapes while using the full information of the shape, bypassing feature extraction. The output of the method is the class whose combination of exemplars most closely approximates the shape, and furthermore, the algorithm returns the most similar exemplars along with their similarity to the shape, which makes the result simple to interpret. Our results show that the method offers accurate classification between three cerebellar diseases and controls in a database of cerebellar ataxia patients. For reproducible comparison, promising results are presented on publicly available 2D datasets, including the ETH-80 dataset where the method achieves 88.4% classification accuracy.