Regularized discriminative direction for shape difference analysis

The "discriminative direction" has been proven useful to re- veal 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, in- troducing 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 pro- vided to directly work out this direction. Experimental study shows its superior performance in detecting and localizing the difference of hip- pocampal shapes for sex. The result is supported by other independent research in the same domain.