A Harmonic Analysis View on Neuroscience Imaging
After highlighting some of the current trends in neuroscience imaging, this work studies the approximation errors due to varying directional aliasing, arising when 2D or 3D images are subjected to the action of orthogonal transformations. Such errors are
- PDF / 669,025 Bytes
- 28 Pages / 439.36 x 666.15 pts Page_size
- 49 Downloads / 191 Views
bstract After highlighting some of the current trends in neuroscience imaging, this work studies the approximation errors due to varying directional aliasing, arising when 2D or 3D images are subjected to the action of orthogonal transformations. Such errors are common in 3D images of neurons acquired by confocal microscopes. We also present an algorithm for the construction of synthetic data (computational phantoms) for the validation of algorithms for the morphological reconstruction of neurons. Our approach delivers synthetic data that have a very high degree of fidelity with respect to their ground-truth specifications. Keywords Synthetic tubular data • Synthetic dendrites • Directional aliasing • Approximation error • Dendritic arbor segmentation • Confocal microscopy
1 Overture What is the substance of knowledge and memory? These fundamental questions have been at the center of philosophical debate for over three millennia, but only P. Hernandez–Herrera () • I.A. Kakadiaris Computational Biomedicine Lab, Department of Computer Science, University of Houston, Houston, TX 77204, USA e-mail: [email protected]; [email protected] D. Jim´enez • D. Labate • M. Papadakis Department of Mathematics, University of Houston, Houston, TX 77204-3008, USA e-mail: [email protected]; [email protected]; [email protected] A. Koutsogiannis Department of Mathematics, University of Athens, Greece, GR-15784 Zografou, Greece e-mail: [email protected] F. Laezza Department of Pharmacology and Toxicology, University of Texas Medical Branch, Galveston, TX 77555-1031, USA e-mail: [email protected] T.D. Andrews et al. (eds.), Excursions in Harmonic Analysis, Volume 2, Applied and Numerical Harmonic Analysis, DOI 10.1007/978-0-8176-8379-5 21, © Springer Science+Business Media New York 2013
423
424
P. Hernandez–Herrera et al.
during the last fifty years our understanding of these essential human cognitive functions is finally becoming concrete. The quest for answers takes us back to the philosopher Plato (424/423 BC–348/347 BC) who, in the dialogue “Theaetetus,” written circa 360 BC when Athens’ glory was in decline amidst the Peloponnesian war, attempts to define knowledge from a philosophical viewpoint. In the dialogue, Euclid (not the famous geometer from Alexandria) recounts a discussion between Socrates and Theaetetus aiming to discover the nature of knowledge. Around the middle of their conversation Socrates refers to knowledge as being a series of “engrams”, impressions on the “wax of the soul”: Socrates: And the origin of truth and error is as follows: When the wax in the soul of any one is deep and abundant, and smooth and perfectly tempered, then the impressions which pass through the senses and sink into the heart of the soul, as Homer says in a parable, meaning to indicate the likeness of the soul to wax (o&); K these, I say, being pure and clear, and having a sufficient depth of wax, are also lasting, and minds, such as these, easily learn and easily retain, and are not liable to confusion, but have true though
Data Loading...
