nAdder: A scale-space approach for the 3D analysis of neuronal traces

Abstract

The advent of large-scale microscopy along with advances in automated image analysis algorithms 1 is currently revolutionizing neuroscience. These approaches result in rapidly increasing libraries 2 of neuron reconstructions requiring innovative computational methods to draw biological insight 3 from. Here, we propose a framework from differential geometry based on scale-space representation 4 to extract a quantitative structural readout of neurite traces seen as tridimensional (3D) curves 5 within the anatomical space. We define and propose algorithms to compute a multiscale hierarchical 6 decomposition of traced neurites according to their intrinsic dimensionality, from which we deduce 7 a local 3D scale, i.e. the scale in microns at which the curve is fully 3D as opposed to being 8 embedded in a 2D plane or a 1D line. We applied our scale-space analysis to recently published 9 data including zebrafish whole brain traces to demonstrate the importance of the computed local 3D 10 scale for description and comparison at the single arbor levels and as a local spatialized information 11 characterizing axons populations at the whole brain level. The use of this broadly applicable approach 12 is facilitated through an open-source implementation in Python available through GeNePy3D, a 13 quantitative geometry library.14 Keywords Computational neuroanatomy · scale space · quantitative geometry · python 15 1 Introduction 16 Throughout the evolution of the field of neuroscience, neuroanatomy has played a key role via the analysis of neuronal 17 arbor traces, either at single cell or gross projection levels. The NeuroMorpho.Org database (Ascoli, 2006; Ascoli et al., 18 2007), which collects and indexes neuronal tracing data, currently hosts more than one hundred thousand arbors of 19 diverse neurons from various animal species. Thanks to technological advances in microscopy, through block-face 20 electron microscopy (Helmstaedter et al., 2013) and large-scale fluorescence microscopy (Abdeladim et al., 2019), we 21 are now able to image even larger tissue volumes with ever increasing resolution and contrast modalities. Crucially, the 22 coming of age of computer vision through the advent of deep learning is offering ways to automate the extraction of 23 neurite traces (Magliaro et al., 2019), a process that is both tedious and time consuming to do manually. As a result, we 24 are about to experience an exponential increase in the amount of neuronal traces extracted in diverse species, brain 25 regions, developmental stages and experimental conditions to answer key questions across neuroscience (Meinertzhagen, 26 2018). Methods from quantitative and computational geometry will play a major role in handling and analyzing the 27 A scale-space approach for 3D neuronal traces analysis growing body of neuronal reconstruction data, in its full tridimensional (3D) complexity, a requisite to linking neuronal 28 structure with development and function of brain circuits and systems. 29A vast array of geometric algorithmic met...

GeNePy3D: a quantitative geometry python toolbox for large scale bioimaging

“…Other feature are listed as optional, as they come from harder to install or less recognized sources, including the C++ library CGAL, only partially available in Python, for generic object interaction in 3D, or the optimal transport method implemented in PyEMD. Some original development available in GeNePy3d include an algorithm to compute local 3D scale we recently published 16 . Many common input/output formats are supported including SWC for Tree, CSV, XYZ for Points/Curve and STL and OFF for Surface.…”

GeNePy3D: a quantitative geometry python toolbox for bioimaging

“…Any further responses from the reviewers can be found at the end of the article sources, including the C++ library CGAL, only partially available in Python, for generic object interaction in 3D, or the optimal transport method implemented in PyEMD. Some original development available in GeNePy3d include an algorithm to compute local 3D scale we recently published 16 . Many common input/output formats are supported including SWC for Tree, CSV, XYZ for Points/Curve and STL and OFF for Surface.…”

“…Examples of decomposing the traces, computing sections inside and outside the Tectum region are shown in Figure 2B bottom. Finally, we measured within the brain regions neuronal lengths, number of branching points, tortuosities (proportion of length over distance between two end points of the curve), and local 3D scales 16 (scale at which the curve transforms to 3D).…”