M.I.T Artificial Intelligence Laboratory, 545 Technology Square, Cambridge, MA 02139.
IEEE Trans Pattern Anal Mach Intell. 1986 Feb;8(2):129-39. doi: 10.1109/tpami.1986.4767767.
Image analysis problems, posed mathematically as variational principles or as partial differential equations, are amenable to numerical solution by relaxation algorithms that are local, iterative, and often parallel. Although they are well suited structurally for implementation on massively parallel, locally interconnected computational architectures, such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements. Hence, they converge extremely slowly when confronted by the large representations of early vision. Application of multigrid methods can overcome this drawback, as we showed in previous work on 3-D surface reconstruction. In this paper, we develop multiresolution iterative algorithms for computing lightness, shape-from-shading, and optical flow, and we examine the efficiency of these algorithms using synthetic image inputs. The multigrid methodology that we describe is broadly applicable in early vision. Notably, it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill-posed image analysis problems.
图像分析问题，从数学角度来看，可以通过松弛算法来解决，这些算法是局部的、迭代的，并且通常是并行的。虽然它们在结构上非常适合于在大规模并行、局部互连的计算架构上实现，但这些分布式算法在传播广泛分离的处理元素之间的约束方面存在固有的效率低下，因此，当遇到早期视觉的大型表示时，它们的收敛速度非常慢。正如我们之前在三维表面重建的工作中所展示的那样，多网格方法的应用可以克服这一缺点。在本文中，我们开发了用于计算亮度、阴影形状和光流的多分辨率迭代算法，并使用合成图像输入来检查这些算法的效率。我们描述的多网格方法在早期视觉中具有广泛的适用性。值得注意的是，它是一种很有吸引力的策略，可以与正则化分析结合使用，以有效地解决各种病态图像分析问题。
