The active contour model (also known as snakes) is a framework that fits open or closed splines to lines or edges in an image. A snake is an energy-minimizing, deformable spline influenced by constraint, image, and internal forces. Hence, it works by minimizing an energy that is partially defined by the image and partially by the spline's shape, length, and smoothness. The constraint and image forces pull the snake toward object contours and internal forces resist the deformation. The algorithm accepts an initial snake (around the object of interest) and to fit the closed contour to the object of interest, it shrinks/expands. The minimization is done explicitly in the image energy and implicitly in the shape energy. As the number of points is constant, we need to ensure that the initial snake has enough points to capture the details of the final contour.
In the following example, taken from the scikit-image documentation, the active contour model is going to be used to segment the face of a person (the astronaut) from the rest of an image by fitting a spline to the edges of the face. The image is smoothed a bit as a pre-processing step. First, a circle is initialized around the astronaut's face and the default boundary condition bc='periodic' is used to fit a closed curve. To make the curve search toward edges (for example, the boundaries of the face), the default parameter values w_line=0, w_edge=1 are used. The next code block demonstrates how to use the active_contour() function for segmentation (which runs an iterative algorithm with a maximum number of iterations that can be specified by a parameter to the function), and shows the closed contour line obtained by running the algorithm internally for a different number of iterations:
from skimage import data
from skimage.filters import gaussian
from skimage.segmentation import active_contour
img = data.astronaut()
img_gray = rgb2gray(img)
s = np.linspace(0, 2*np.pi, 400)
x = 220 + 100*np.cos(s)
y = 100 + 100*np.sin(s)
init = np.array([x, y]).T
i = 1
pylab.figure(figsize=(20,20))
for max_it in [20, 30, 50, 100]:
snake = active_contour(gaussian(img_gray, 3), init, alpha=0.015, beta=10, gamma=0.001, max_iterations=max_it)
pylab.subplot(2,2,i), pylab.imshow(img), pylab.plot(init[:, 0], init[:, 1], '--b', lw=3)
pylab.plot(snake[:, 0], snake[:, 1], '-r', lw=3)
pylab.axis('off'), pylab.title('max_iteration=' + str(max_it), size=20)
i += 1
pylab.tight_layout(), pylab.show()
The next screenshot shows the output of the code. The initial circle to start with was the dotted blue circle. The active contour algorithm iteratively shrinks the contour (denoted by the red lines) starting from the circle toward the face, and finally, at max_iteration=100, fits itself to the boundary of the face, thereby segmenting the face out from the image:
