next up previous
Next: Limitations of non model-based Up: Shape Recognition Previous: Multiscale medial axis

Origin of scale

If the intensity values of an image are reinterpreted as a distribution of molecular concentration in a liquid or as a distribution of temperature in a solid, then techniques from the field of continuum mechanics can provide certain insights into the shape properties of objects in an image. For example, consider the two-dimensional, isotropic diffusion equation:

  equation306

The temporal parameter, t, in equation gif converts the problem into a dynamic system. The solution of the two-dimensional diffusion equation is

  equation314

but equation gif can also be viewed as the convolution of a Gaussian function with mean zero and variance tex2html_wrap_inline3852 ,

equation319

Viewed as a convolution process, the time varying problem becomes converted into a purely static problem,

displaymath3848

Other forms of the diffusion equation are also possible. For example, if the diffusion constant differs in the x and y directions, the material can be described by the anisotropic diffusion equation,

  equation321

If the diffusion constant varies depending on location, the material can be described by the amorphous diffusion equation

  equation327

The significance of the MMA is that it allows for a hierarchical approach to image understanding through the use of scale parameter tex2html_wrap_inline3858 . Using this hierarchical approach, the first step is to compute medial axes at largest scale of interest. Once the gross features of an object have been recognized, the smaller features can be found by reducing the scale parameter depending on the information obtained at the larger scale. This process is repeated until all the structures and features of interest have been recognized (see Figure gif). The hierarchical MMA approach is capable of recognizing large-scale features without sacrificing information contained at the finer resolutions. There are, however, several drawbacks to the MMA approach: (1) skeletal shape cannot recover the original size of the objects, (2) edge and boundary information is lost, therefore the original shape is not uniquely represented, and (3) texture and pattern information is lost. Despite these drawbacks, the MMA can provide a structural road map of objects in an image. Although the MMA can't capture all the important features of an object, it can be used to provide some high-level information that provides the context for low-level image operators.

   figure334
Figure: The multi-scale medial axis approach performs feature recognition by starting a the largest image scale of interest and then repeatedly reduces the scale until finer objects can be recognized.


next up previous
Next: Limitations of non model-based Up: Shape Recognition Previous: Multiscale medial axis

Ramani Pichumani
Mon Jul 7 10:34:23 PDT 1997