An affine shape constraint for geometric active contours - Emerging Trends in Image Processing, Computer Vision, and Pattern Recognition - page 428

3 Shape Prior for Geometric Active Contours
Geometric active contours are iterative segmentation methods which use the level set ap-
proach [ 2 ] to determine the evolving front at each iteration. Several models have been pro-
posed in literature that we can classify into edge-based or region-based active contours.
In Ref. [ 4 ], the level set approach is used to model the shape of objects using an evolving
front. The evolution's equation of the level set function ∅ is
(24)
F is a speed function of the form F = F 0 + F 1 ( K ) where F 0 is a constant advection term equals to
(± 1) depends of the object inside or outside the initial contour. The second term is of the form
− εK where K is the curvature at any point and ε > 0. To detect the objects in the image, the
authors proposed to use the following function which stops the level set function's evolution
at the object boundaries.
(25)
where f is the image and G σ is a Gaussian filter with a deviation equals to σ . This stopping
function has values that are closer to zero in regions of high image gradient and values that
are closer to unity in regions with relatively constant intensity. Hence, the discrete evolution
equation is:
(26)
It's obvious that the evolution is based on the stopping function g which depends on the im-
age gradient. That's why this model leads to unsatisfactory results in presence of occlusions,
low contrast, and even noise. To make the level set function evolve in the regions of variability
between the shape of reference and the target shape, we propose the new stopping function as
follows: