Seminars

We present a new method of representing complex anatomical boundaries in medical images using a generalized Fourier series expansion. Anatomical boundaries that are topologically equivalent to either one or two spheres (boundaries of tumor, corpus callosum, hippocampus and human brain cortex) can be represented in this fashion.

There are three main advantages for using this new representation. The previously developed cut-and-map technique simply cuts the boundary and map the boundary in the Cartesian coordinates causing the boundary effect. The resulting statistical analysis near the boundary is not reliable. Since there is no cutting involved in our representation, there is no boundary effect. The Fourier expansion gives a natural way of data reduction and modeling. In this framework, we analyze the coefficients of the series expansion rather than the coordinates of the boundary providing a unified modeling framework. The expansion can be modeled in a linear model or the random field theory frameworks.

Shubing Wang will present 1D corpus callosum boundary modeling problem. The gradient vector flow snake (active contour) is used to segment 2D MRIs and the Fourier series expansion is used to transform the bounary coordinates to a unit circle. Then a regression tree technique is used to classify boundary curves into two groups: autism and normal controls. This is a joint work with Kim Dalton and Richard Davidson of the Waisman laboratory for brain imaging and behavior. The ultimate aim is to develop a clinical decision rule for classifying autism based on MRI and other behavioral measures.

Moo Chung will present 2D cortical boundary modeling problem. A deformable surface algorithm is used to segment 3D MRIs and the Laplace series expansion is used to transform the surface coordinates to a unit sphere. This technique is still under investigation and will discuss about the numerical implementation issues and the limitation of the Laplace series
expansion technique for very convoluted geometrical shapes. Related to the Laplace series expansion, recently developed Gauss-Weierstrass kernel smoothing technique on a unit sphere will be also presented. This should perform better than the previously developed diffusion smoothing (Chung et al., 2003) or heat kernel smoothing (Chung et al., 2005) on manifolds.