Image enhancement and denoising by complex diffusion processes
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Updated: Aug 15, 2026

Quantifying Microglia Morphology from Photomicrographs of Immunohistochemistry Prepared Tissue Using ImageJ
Published on: June 5, 2018
Guy Gilboa1, Nir Sochen, Yehoshua Y Zeevi
1Department of Electrical Engineering, Technion-Israel Institute of Technology, Technion City, Haifa, Israel. gilboa@tx.technion.ac.il
Abstract:
The linear and nonlinear scale spaces, generated by the inherently real-valued diffusion equation, are generalized to complex diffusion processes, by incorporating the free Schrödinger equation. A fundamental solution for the linear case of the complex diffusion equation is developed. Analysis of its behavior shows that the generalized diffusion process combines properties of both forward and inverse diffusion. We prove that the imaginary part is a smoothed second derivative, scaled by time, when the complex diffusion coefficient approaches the real axis. Based on this observation, we develop two examples of nonlinear complex processes, useful in image processing: a regularized shock filter for image enhancement and a ramp preserving denoising process.
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