Fast training of neural trees by adaptive splitting based on cubature

Edge Detection by Adaptive Splitting II. The Three-Dimensional Case

“…Adaptive splitting procedures have been used in approximation theory (see, for example [25], and the references therein). Adaptive meshing methods for edge detection have been studied mainly in the context of image processing (discretely defined functions).…”

“…Most adaptive methods produce an image segmentation using a variant of the split and merge method [18,41]. An adaptive splitting approximation algorithm was proposed in [25]. In [24] it was proved (for d = 1 and d = 2) that the average integral used in its splitting criterion is an effective jump detector.…”