Cell Tracking using Coupled Active Surfaces for Nuclei and Membranes

An Insight Toolkit (ITK) processing framework for segmenting and tracking nuclei in time-lapse microscopy images using coupled active contours is presented in this paper. We implement the method of Dufour et al. [2] to segment and track cells in ﬂuoroscence microscopy images. The basic idea is to model the image as a constant intensity background with constant intensity foreground components. We utilizes our earlier submissions on the Chan and Vese algorithm [1,3] and its multiphase extension [4,5] to build our new tracking ﬁlter. The tracking ﬁlter itk::MultiphaseLevelSetTracking inputs a segmentation result (or a coarse estimate) from the previous time-point along with the feature image and generates a new segmentation output. By iteratively repeating this process across all time-points, real-time tracking is made possible. We include 2D/3D example code, parameter settings and show the results generated on a 2D zebraﬁsh embryo image series.


Introduction
Many biological experiments that involve microscopic imaging require segmentation and temporal tracking of cells as part of the analysis protocol.For example, development biologists are interested in reconstructing cell lineages during embryonic development.The migratory behavior as well as rearrangement of cells are a fascinating topic of research.Cancer researchers track cells in colonies to determine their growth kinetics and the effect of different chemical agents on them.The cell forms the fundamental biological entity of interest and their tracking is essential in these applications.One common approach for cell tracking is to use the nucleus of each cell for segmentation and tracking since nuclei tend to be simpler shapes and more distinct from their neighbors than whole cells.Problems arise when nuclei appear as overlapping or touching each other.Identifying each nucleus separately in a biologically consistent fashion is non-trivial.While some biochemical stains provide viable clues in the form of sharp color-space gradients at the boundaries, others exhibit a narrow neck at the site of overlap between two nuclei.Cells also move quite rapidly while wading through the extracellular matrix and in between densely packed clusters.
A robust solution to the tracking problem was proposed by Dufour et al. [2] using coupled active surfaces implemented using the level set methodology.In this method, each cell is represented by a unique level set function.An energy functional involving all the level set contours is defined to partition the image into a constant intensity background and constant intensity foreground components.The foreground components are regularized in terms of their area and length for smoothness.Several other properties such as continuity in their volumes and shapes across time-points is maintained.Their solution as proposed is robust and elegant for small datasets only since each cell requires a unique level set function of the same size as the image domain.
In our implementation of the method, we make use of our earlier submission on the multiphase extension [4,5] of the Chan and Vese algorithm [1,3].There are in-built performance optimizations that now make the tracking filter scale up to larger datasets with many cells.The first term represents the i-th foreground intensity fitting with scalar constant c i and weighted by λ 1,i .The second term is the background intensity fitting with scalar constant c 0 and weighted by λ 2 .Note that the background is characterized by a product of the inverse Heaviside functions of the N foregrounds.The third and fourth terms represent the length and area regularization terms for the N level sets.Finally, the last term represents the overlap penalty function.This term penalizes the level set functions in regions where they overlap and γ represents the scalar penalty constant.
The Euler-Langrange equation for the i-th level set function is as follows: Until this point, there is nothing different from the multiphase extension in [4].
In order to track the nuclei, we implement the filter itk::MultiphaseLevelSetTracking.previous time-point and a bound on its maximum possible movement.We assume the maximum permissible movement of a nuclei is less than its largest diameter.In such cases, the centroid of the segmented nucleus at the previous time-point is calculated and used to center the ROI.A signed distance map of the segmented shape is used as initialization within the ROI.
3 Implementation: Tracking filter The filter itk::MultiphaseLevelSetTracking is templated over the LevelSetImageType and FeatureIm-ageTypes.The input consists of a labelled segmentation image of the the previous time-point and the raw image at the current time-point.Each nuclei is labelled with a unique identifier (not necessarily consecutive) in the segmentation.We make use of the sparse implementation of the multiphase extension since there may be many cells to track.The filter has the same parameters as the multiphase level set segmentation filter in addition to two new parameters that preserve the continuity in volumes during tracking.NOTE: The setting of parameters takes into account the spacing in the images.Hence, if the images are in µm, then the relevant parameters also need to be in the same units.Hence, the parameter settings remain the same.We now describe each of the parameters, their range and typical values.There is no typical limit that can be set on most parameters but depends on experimentation.Note that except for the first three, the remaining constitute weights to the different energy terms.Depending on their contribution to the overall energy, these weights need to be modified so that all the terms have an influence.

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Description: Tracking filter In the multiphase case, we have N level set functions {φ 1 ,• • • , φ n } and scalar intensity constants {c 1 ,• • • , c n } respectively and c 0 represents the background intensity.The N parameters {λ 1,1 ,• • • , λ 1,n } are scalar weights of the individual object intensity fitting terms and λ 2 is the weight for the background intensity fitting term.