Real-time Implementation Within Pyramids and Discrete Approximation of Scale-normalized Derivatives
Regarding the topic of automatic scale selection based on normalized derivatives, pyramid approximations are frequently used to obtain real-time performance. The appropriateness of approximating scale-space operations within a pyramid originates from the fact that repeated cascade smoothing with generalized binomial kernels leads to equivalent smoothing kernels that under reasonable conditions approach the Gaussian. Furthermore, the binomial kernels (or more generally the class of generalized binomial kernels) can be shown to constitute the unique class of finite-support kernels that guarantee non-creation of local extrema or zero-crossings with increasing scale (see the article on multi-scale approaches for details). Special care may, however, need to be taken to avoid discretization artifacts.
Read more about this topic: Scale Space Implementation
Famous quotes containing the words pyramids and/or discrete:
“I go into my library, and all history unrolls before me. I breathe the morning air of the world while the scent of Eden’s roses yet lingered in it, while it vibrated only to the world’s first brood of nightingales, and to the laugh of Eve. I see the pyramids building; I hear the shoutings of the armies of Alexander.”
—Alexander Smith (1830–1867)
“We have good reason to believe that memories of early childhood do not persist in consciousness because of the absence or fragmentary character of language covering this period. Words serve as fixatives for mental images. . . . Even at the end of the second year of life when word tags exist for a number of objects in the child’s life, these words are discrete and do not yet bind together the parts of an experience or organize them in a way that can produce a coherent memory.”
—Selma H. Fraiberg (20th century)