Parallel Processing Strategies for Cell Motility and Shape Analysis - High-Throughput Image Reconstruction and Analysis - page 54

The constant balloon force F c pushes the curve inwards or outwards depending
on its sign. The regularization term K ensures boundary smoothness, and g ( I ) is

∇ ·∇

used to stop the curve evolution at cell boundaries. The term f is used to

increase the basin of attraction for evolving the curve to the boundaries of the
objects.

g

Directed Edge Profile-Guided Level Set Active Contours
The major drawbacks of the classical edge-based active contours are the leakage
due to weak edges and stopping at local maximums in noisy images. For the spe-
cial case of cell segmentation, edge stopping functions used in regular geodesic
active contours, if initialized outside of the cells, respond to the outer edges of
phase halos and cause early stopping which produces an inaccurate segmentation.
When the curve is initialized inside the cells, the texture inside the cell also causes
premature stopping. Often phase halo is compensated by normalizing the image,
but this weakens the cell boundaries further, especially in the areas where cells
are flattened, and leads to leakage of the curve. One remedy is to enforce a shape
model, but it fails for cells with highly irregular shapes. Nucleus-based initializa-
tion and segmentation [49] is also not applicable to images such as in Figure 3.8.
To obtain an accurate segmentation, we propose an approach that exploits the
phase halo effect instead of compensating it. The intensity profile perpendicular
to the local cell boundary is similar along the whole boundary of a cell; it passes
from the brighter phase halo to the darker cell boundary. We propose to initialize
the curve outside the cell and phase halo, and guide the active contour evolution
based on the desired edge profiles which effectively lets the curve evolve through
the halos and stop at the actual boundaries. The existence of phase halo increases
the edge strength at cell boundaries. We propose the edge stopping function g d
(3.30) guided by the directed edge profile, that lets the curve evolve through the
outer halo edge and stop at the actual boundary edge. As shown in Figure 3.8, if
initialized close to the actual boundary, the first light-to-dark edge encountered in
the local perpendicular direction corresponds to the actual boundary. By choos-
ing this profile as the stopping criterion, we avoid the outer edge of phase halo.
This stopping function is obtained as follows. Normal vector N to the evolving
contour/surface can be determined directly from the level set function:

N

= − ∇

f

(3.28)

|∇

f

|

Edge profile is obtained as the intensity derivative in opposite direction to the
normal:

− N = ∇

f

| ·∇

I I (3.29)

|∇

f

Dark-to-light transitions produce positive response in I

− N . We define the edge

profile-guided edge stopping function g d as

g d ( ∇ I )= 1

−

H ( − I

− N )(

1

−

g ( ∇ I )) (3.30)