Geometry Processing of Conventionally Produced Mouse Brain Slice Images

Brain mapping research in most neuroanatomical laboratories relies on conventional processing techniques, which often introduce histological artifacts such as tissue tears and tissue loss. In this paper we present techniques and algorithms for automatic registration and 3D reconstruction of conventionally produced mouse brain slices in a standardized atlas space. This is achieved first by constructing a virtual 3D mouse brain model from annotated slices of Allen Reference Atlas (ARA). Virtual re-slicing of the reconstructed model generates ARA-based slice images corresponding to the microscopic images of histological brain sections. These image pairs are aligned using a geometric approach through contour images. Histological artifacts in the microscopic images are detected and removed using Constrained Delaunay Triangulation before performing global alignment. Finally, non-linear registration is performed by solving Laplace's equation with Dirichlet boundary conditions. Our methods provide significant improvements over previously reported registration techniques for the tested slices in 3D space, especially on slices with significant histological artifacts. Further, as an application we count the number of neurons in various anatomical regions using a dataset of 51 microscopic slices from a single mouse brain. This work represents a significant contribution to this subfield of neuroscience as it provides tools to neuroanatomist for analyzing and processing histological data.Comment: 14 pages, 11 figure

Answering Spatial Multiple-Set Intersection Queries Using 2-3 Cuckoo Hash-Filters

We show how to answer spatial multiple-set intersection queries in O(n(log w)/w + kt) expected time, where n is the total size of the t sets involved in the query, w is the number of bits in a memory word, k is the output size, and c is any fixed constant. This improves the asymptotic performance over previous solutions and is based on an interesting data structure, known as 2-3 cuckoo hash-filters. Our results apply in the word-RAM model (or practical RAM model), which allows for constant-time bit-parallel operations, such as bitwise AND, OR, NOT, and MSB (most-significant 1-bit), as exist in modern CPUs and GPUs. Our solutions apply to any multiple-set intersection queries in spatial data sets that can be reduced to one-dimensional range queries, such as spatial join queries for one-dimensional points or sets of points stored along space-filling curves, which are used in GIS applications.Comment: Full version of paper from 2017 ACM SIGSPATIAL International Conference on Advances in Geographic Information System

A Comparison of Tests for Embeddings

It is possible to compare results for the classical tests for embeddings of chaotic data with the results of a recently proposed test. The classical tests, which depend on real numbers (fractal dimensions, Lyapunov exponents) averaged over an attractor, are compared with a topological test that depends on integers. The comparison can only be done for mappings into three dimensions. We find that the classical tests fail to predict when a mapping is an embedding and when it is not. We point out the reasons for this failure, which are not restricted to three dimensions

Inter-vehicle gap statistics on signal-controlled crossroads

We investigate a microscopical structure in a chain of cars waiting at a red signal on signal-controlled crossroads. Presented is an one-dimensional space-continuous thermodynamical model leading to an excellent agreement with the data measured.Moreover, we demonstrate that an inter-vehicle spacing distribution disclosed in relevant traffic data agrees with the thermal-balance distribution of particles in the thermodynamical traffic gas (discussed in [1]) with a high inverse temperature (corresponding to a strong traffic congestion). Therefore, as we affirm, such a system of stationary cars can be understood as a specific state of the traffic sample operating inside a congested traffic stream.Comment: 6 pages, 4 figures, accepted for publication in J. Phys. A: Math. Theo