Zigzag persistent homology for processing neuronal images

Zigzag persistent homology techniques are applied to the processing of actual neuronal images.These algorithms allow us to recognize dendrites, which cross in space.Our methods have been implemented as a Fiji/ImageJ plugin, which is in production.The plugin is applicable to different kinds of neuronal images. We apply the ideas of zigzag persistence to determine the objects of interest in stacks of neuronal images, locating and marking different dendrites. In particular, this allows us to recognize some 3D properties of the objects, distinguishing dendrites that cross, but not intersect, in the ambient space. The algorithms are implemented in a Fiji/ImageJ plugin, usable on two different kinds of images.

[1]  Jeremy D. Schmahmann,et al.  Diffusion spectrum magnetic resonance imaging (DSI) tractography of crossing fibers , 2008, NeuroImage.

[2]  S. R. Cajal.  Textura del Sistema Nervioso del Hombre y de los Vertebrados, 1899–1904 , 2019 .

[3]  Gunnar E. Carlsson,et al.  Zigzag Persistence , 2008, Found. Comput. Math..

[4]  Mao-Jiun J. Wang,et al.  Image thresholding by minimizing the measures of fuzzines , 1995, Pattern Recognit..

[5]  Susumu Mori,et al.  Fiber tracking: principles and strategies – a technical review , 2002, NMR in biomedicine.

[6]  Y. Goda,et al.  Actin-Dependent Regulation of Neurotransmitter Release at Central Synapses , 2000, Neuron.

[7]  Oscar Herreras,et al.  Learning improvement after PI3K activation correlates with de novo formation of functional small spines , 2014, Front. Mol. Neurosci..

[8]  T. W. Ridler,et al.  Picture thresholding using an iterative selection method. , 1978 .

[9]  Paolo Maria Rossini,et al.  Brain excitability and connectivity of neuronal assemblies in Alzheimer's disease: From animal models to human findings , 2012, Progress in Neurobiology.

[10]  Aldo von Wangenheim,et al.  White Matter Fiber Tracking Computation Based on Diffusion Tensor Imaging for Clinical Applications , 2007, Journal of Digital Imaging.

[11]  Germán Cuesto,et al.  Phosphoinositide-3-Kinase Activation Controls Synaptogenesis and Spinogenesis in Hippocampal Neurons , 2011, The Journal of Neuroscience.

[12]  Afra Zomorodian,et al.  Computing Persistent Homology , 2005, Discret. Comput. Geom..