Survey of Active Contour Model

The active contour model, also known as Snake, was first introduced by Kass et al. [61] in 1988. In computer vision and image/video processing, it has been used as a very effective approach to implement contour tracking and shape feature extraction of interested object, and is also regarded as a successful de-formable model in applications ranging from medical image analysis to video object manipulation. Basically, the development of active contour models has the following phases: classical Snake, geometric models, and minimal path approach models.

Roughly speaking, a Snake model can be regarded as a curve measured with an energy function. To track the contour of a desired object in an image, some points or curves must be specified near the object's boundary initially. When the algorithm is applied, the Snake will "move" gradually toward the positions where the object's contour locates under certain constraints. This deformation process is generally conducted by iteratively searching for a local minimum of an energy function. However, a well-known problem of the classical Snake model is that it may be trapped into local minimal solutions caused by noise or poor initialization [62].

Another kind of active model is called the geometric active contour model that was first proposed by Caselles in 1993 [63]. It uses a geometric approach for the Snake modeling and applies the level set theory in the optimal curve searching. During the deformation process, the object contour evolutes and expands in the normal direction under certain constraints. Heuristic procedures are used to stop the evolution process when an edge is reached. The experiments presented in [63, 64] demonstrate better results than that was done with the classical Snake model [65, 66]. In 1995, Ceselles further improved the geometric model and transformed the object boundary detection problem as a path searching for minimal weighted length. This enhanced version is also known as the "geodesic model," which experimentally outperforms both the classical Snake model and the geometric model [67].

The minimum path approach, proposed by Cohen and Kimmel in 1996, is a state of the art solution in active contour modeling. It uses a path of cost as the interpretation of the Snake curve. The main feature of this method is that, given two prespecified end points, the global minimal path can be obtained. The energy optimization process is based on a numerical method proposed by Sethian [23] to find the "shortest path" in term of the global minimum of the energy among all paths joining the two end points. Compared with its previous versions of active contour modeling, MPA has the following advantages:

(i) It overcomes the local minimum problem in energy minimizing process.

(ii) It simplifies the initialization: only two initial end points are needed.

Nevertheless, this model still has some limitations in practical application. For example, the initial points must be precisely on the boundary of desired object to ensure the best contour searching performance. Therefore, human interaction is often required to accurately locate the initial points. Also, this model cannot address problems in which the shape of the desired object has topology change.

In the rest of this section, we will have a review of classical Snake model and the minimal path approach since they present the instinct spirit of this model and the state of the art of the optimal algorithm design.

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