4D Segmentation Algorithm with application to 3D+time Image Segmentation

TL;DR

This paper introduces a novel 4D image segmentation method based on surface evolution governed by a nonlinear PDE, utilizing parallel computing for large-scale biological microscopy data and demonstrating its effectiveness in cell tracking during embryogenesis.

Contribution

The paper presents a new 4D segmentation algorithm using a generalized subjective surface equation and develops a parallel numerical scheme for large-scale biological image analysis.

Findings

Successfully segmented 4D microscopy images of cell nuclei.

Implemented parallel algorithms that handle billion-unknown linear systems.

Achieved accurate cell trajectory tracking in embryogenesis studies.

Abstract

In this paper, we introduce and study a novel segmentation method for 4D images based on surface evolution governed by a nonlinear partial differential equation, the generalized subjective surface equation. The new method uses 4D digital image information and information from a thresholded 4D image in a local neighborhood. Thus, the 4D image segmentation is accomplished by defining the edge detector function's input as the weighted sum of the norm of gradients of presmoothed 4D image and norm of presmoothed thresholded 4D image in a local neighborhood. Additionally, we design and study a numerical method based on the finite volume approach for solving the new model. The reduced diamond cell approach is used for approximating the gradient of the solution. We use a semi-implicit finite volume scheme for the numerical discretization and show that our numerical scheme is unconditionally stable. The new 4D method was tested on artificial data and applied to real data representing 3D+time microscopy images of cell nuclei within the zebrafish pectoral fin and hind-brain. In a real application, processing 3D+time microscopy images amounts to solving a linear system with several billion unknowns and requires over $1000$ GB of memory; thus, it may not be possible to process these images on a serial machine without parallel implementation utilizing the MPI. Consequently, we develop and present in the paper OpenMP and MPI parallel implementation of designed algorithms. Finally, we include cell tracking results to show how our new method serves as a basis for finding trajectories of cells during embryogenesis.