MADNESS: A Multiresolution, Adaptive Numerical Environment for Scientific Simulation

MADNESS (multiresolution adaptive numerical environment for scientific simulation) is a high-level software environment for solving integral and differential equations in many dimensions that uses adaptive and fast harmonic analysis methods with guaranteed precision based on multiresolution analysis and separated representations. Underpinning the numerical capabilities is a powerful petascale parallel programming environment that aims to increase both programmer productivity and code scalability. This paper describes the features and capabilities of MADNESS and briefly discusses some current applications in chemistry and several areas of physics

Downsampling methods for medical datasets

Volume visualization software usually has to deal with datasets that are larger than the GPUs may hold. This is especially true in one of the most popular application scenarios: medical visualization. Typically, medical datasets are available for different personnel, but only radiologists have high-end systems that are able to cope with large data. For the rest of physicians, usually low-end systems are only available. As a result, most volume rendering packages downsample the data prior to uploading to the GPU. The most common approach consists in performing iterative subsampling along the longest axis, until the model fits inside the GPU memory. This causes important information loss that affects the final rendering. Some cleverer techniques may be developed to preserve the volumetric information. In this paper we explore the quality of different downsampling methods and present a new approach that produces smooth lower-resolution representations, yet still preserves small features that are prone to disappear with other approaches.Peer ReviewedPostprint (published version

The Incremental Multiresolution Matrix Factorization Algorithm

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric matrices -- an important aspect in the success of many vision problems. Our new algorithm, the incremental multiresolution matrix factorization, uncovers such structure one feature at a time, and hence scales well to large matrices. We describe how this multiscale analysis goes much farther than what a direct global factorization of the data can identify. We evaluate the efficacy of the resulting factorizations for relative leveraging within regression tasks using medical imaging data. We also use the factorization on representations learned by popular deep networks, providing evidence of their ability to infer semantic relationships even when they are not explicitly trained to do so. We show that this algorithm can be used as an exploratory tool to improve the network architecture, and within numerous other settings in vision.Comment: Computer Vision and Pattern Recognition (CVPR) 2017, 10 page