Scale space contours and localization property of a Gaussian derivative edge enhancement operator

One of the nice properties of the Gaussian scale space map is its well behavedness. This rather well behaved nature is somewhat deceptive, however, as portions of the map may not have any direct relationship to the features in the unfiltered image. It has been shown that not all zero-crossing surface patches can be associated with intensity changes in the unfiltered image. Zero-crossings give rise to both authentic and phantom scale map contours. Recently, we proposed an edge enhancement operator, the LWF, which is a weighted combination of the Gaussian and its second derivative. In this paper, we provide mathematical proof that the LWF produces only the authentic scale map contours. We also show that the LWF has an excellent localization property (that is the points marked by the operator is very close to center of the true edge). Performance comparison between the Laplacian of Gaussian and LWF operators with respect to the localization property is also presented with a number of computer simulations.