# Active Shape Model

The ASM [1] is one of the most successful deformable models to segment a target object, or an organ/tissue, which iterates computation of displacement vectors based on edge information in an image and update of pose and shape parameters of a model according to the PDM explained in Sect. 2.3.2. Details of the segmentation process will be explained below.

An ASM requires initial location of a model which might be given by a user or an automated or semiautomated process. Once an initial boundary is given, ASM repetitively finds new suggested locations for model points and updates pose and shape parameters of a model. Typically the suggested locations for model points are searched along profiles normal to the model boundary through each model point using a statistical model for the grey-level profile about a point. Parameters of shape and pose, consisting of location, scale, and orientation, are updated to best fit the new found points according to the following equation:

where * T_{Xt} j_{t},s,e* is a function of translation

*scaling s, and rotation в around an origin. The parameters д,*

**(X**_{t}, Y_{t}/,*, and*

**V***are an average shape vector, a matrix of eigenshape vectors, and a shape vector that corresponds to a principal component vector. All these parameters are updated so that mean squared error between suggested locations and model points is minimized. In the actual update process, pose parameters are adjusted efficiently using a least-squares approach followed by an update of shape parameters based on the updated pose parameters. In practice, weighted adjustment for the update process and a multi-resolution scheme are employed to achieve higher performance.*

**a**A major limitation of the ASM is caused by a local minimum problem because it searches the best fit between edges in an image and a model using an iterative scheme starting from an initial location. If the initial shape is far from the true boundary of an organ, the searching process may fail. Another limitation is that a point distribution model does not take into account gray-level statistical variation in an organ across patients. The AAM was developed to overcome this limitation, in which a prior model is trained using not only shape but also grayscale values, and used for segmentation. Details can be found in [150].

ASM is not a solitary example of a segmentation algorithm that utilizes a PDM. A number of algorithms in which a PDM plays a major role in segmentation can be found in [142-145].