Regularized discriminative direction for shape difference analysis.

The "discriminative direction" has been proven useful to reveal the subtle difference between two anatomical shape classes. When a shape moves along this direction, its deformation will best manifest the class difference detected by a kernel classifier. However, we observe that such a direction cannot maintain a shape's "anatomical" correctness, introducing spurious difference. To overcome this drawback, we develop a regularized discriminative direction by requiring a shape to conform to its population distribution when it deforms along the discriminative direction. Instead of iterative optimization, an analytic solution is provided to directly work out this direction. Experimental study shows its superior performance in detecting and localizing the difference of hippocampal shapes for sex. The result is supported by other independent research in the same domain.