Artificial Intelligence Center, SRI International, Menlo Park, CA 96025.
IEEE Trans Pattern Anal Mach Intell. 1987 Mar;9(3):341-55. doi: 10.1109/tpami.1987.4767918.
The detailed structure of intensities in the local neighborhood of an edge can often indicate the nature of the physical event givinig rise to that edge. We argue that the limit, as we approach arbitrarily close to either side of an edge, of such image parameters as type of texture, texture gradient, color, appropriate directional derivatives of intensity, etc., is a key aspect of this structure. However, the general problem of capturing this local structure is surprisingly complex. Thus, we restrict ourselves in this paper to a relatively simple domain¿one-dimensional cuts through idealized images modeled by piecewise smooth (C1) functions corrupted by Gaussian noise. Within this domain, we define local structure to be the limit of the uncorrupted intensity and of its derivatives as we approach arbitrarily close to either side of a discontinuity. We develop a technique that captures this local structure while simultaneously locating the discontinuities, and demonstrate that these tasks are in fact inseparable. The technique is an extension, using estimation theory, of the classical definition of discontinuity. It handles, in a consistent fashion, both jump discontinuities in the function and jump discontinuities in its first derivative (so-called step-edges are a special case of the former and roof-edges of the latter). It also integrates, again in a consistent fashion, information derived from a number of different neighborhood sizes.
边缘局部邻域的强度详细结构通常可以表明导致该边缘的物理事件的性质。我们认为，当我们任意接近边缘的任一侧时，图像参数（如纹理类型、纹理梯度、颜色、适当的强度方向导数等）的极限是这种结构的一个关键方面。然而，捕捉这种局部结构的一般问题非常复杂。因此，在本文中，我们将自己限制在一个相对简单的域中——通过分段光滑 (C1) 函数建模的理想化图像的一维切割，这些函数被高斯噪声污染。在这个域内，我们将局部结构定义为未污染强度及其导数在我们任意接近不连续的任一侧时的极限。我们开发了一种同时捕获局部结构和定位不连续性的技术，并证明这两个任务实际上是不可分割的。该技术是经典不连续性定义的估计理论的扩展。它以一致的方式处理函数中的跳跃不连续性和其一阶导数中的跳跃不连续性（所谓的阶跃边缘是前者的特殊情况，屋顶边缘是后者的特殊情况）。它还以一致的方式整合了来自多个不同邻域大小的信息。
