Active contour model
Active contour model, also called snakes, is a framework in computer vision introduced by Michael Kass, Andrew Witkin, and Demetri Terzopoulos[1] for delineating an object outline from a possibly noisy 2D image.
The snakes model is popular in computer vision, and snakes are widely used in applications like object tracking, shape recognition, segmentation, edge detection and stereo matching.
A snake is an energy minimizing, deformable spline influenced by constraint and image forces that pull it towards object contours and internal forces that resist deformation.
Snakes may be understood as a special case of the general technique of matching a deformable model to an image by means of energy minimization.
[1] In two dimensions, the active shape model represents a discrete version of this approach, taking advantage of the point distribution model to restrict the shape range to an explicit domain learnt from a training set.
Rather, they depend on other mechanisms such as interaction with a user, interaction with some higher level image understanding process, or information from image data adjacent in time or space.
In computer vision, contour models describe the boundaries of shapes in an image.
Snakes in particular are designed to solve problems where the approximate shape of the boundary is known.
By being a deformable model, snakes can adapt to differences and noise in stereo matching and motion tracking.
Additionally, the method can find Illusory contours in the image by ignoring missing boundary information.
The purpose of the internal energy term is to control the deformations made to the snake, and the purpose of the external energy term is to control the fitting of the contour onto the image.
Higher weights indicate that the salient feature will have a larger contribution to the image force.
One implementation of this is A snake originating far from the desired object contour may erroneously converge to some local minimum.
Scale space continuation can be used in order to avoid these local minima.
be the image smoothed by with gradient angle unit vectors along the gradient direction and unit vectors perpendicular to the gradient direction The termination functional of energy can be represented as Some systems, including the original snakes implementation, allowed for user interaction to guide the snakes, not only in initial placement but also in their energy terms.
is the force on the snake, which is defined by the negative of the gradient of the energy field.
This avoids the problem of dominating internal energies that arise from tuning the time step.
In this case, a point in the snake would oscillate between the two pixels that neighbor this zero-crossing.
[5] The default method of snakes has various limitation and corner cases where the convergence performs poorly.
Several alternatives exist which addresses issues of the default method, though with their own trade-offs.
It implements a modification of the Mumford–Shah functional and its cartoon limit and incorporates statistical shape knowledge.
is based on training from binary images of various contours and is controlled in strength by the parameter
Contours split and merge depending on the detection of objects in the image.
These models are largely inspired by level sets, and have been extensively employed in medical image computing.
This particular form of curve evolution equation is only dependent on the velocity in the normal direction.
It therefore can be rewritten equivalently in an Eulerian form by inserting the level set function
into it as follows This simple yet powerful level-set reformation enables active contours to handle topology changes during the gradient descent curve evolution.
Although the level set method has become quite a popular tool for implementing active contours, Wang and Chan argued that not all curve evolution equations should be directly solved by it.
[10] More recent developments in active contours address modeling of regional properties, incorporation of flexible shape priors and fully automatic segmentation, etc.
Statistical models combining local and global features have been formulated by Lankton and Allen Tannenbaum.
