Using differential geometry in R4 to extract typical features in 3D images

A new approach is presented to extract differential characteristics of surfaces in 3-D images from the second partial derivatives of the grey level function provided by separable recursive filters. The basic idea is to consider a 3-D image as a hypersurface in R⁴ and to express the curvatures of the surface with the curvatures of the hypersurface. This yields a very compact and efficient approach where filtering is used for both edge detection and curvature extraction. Experimental results on real data can be compared with more classical approaches. It is noted that smoothing in the fourth-dimensional space could be more efficient than smoothing in the three-dimensional space