Koch C, Marroquin J, Yuille A
Proc Natl Acad Sci U S A. 1986 Jun;83(12):4263-7. doi: 10.1073/pnas.83.12.4263.
Many problems in early vision can be formulated in terms of minimizing a cost function. Examples are shape from shading, edge detection, motion analysis, structure from motion, and surface interpolation. As shown by Poggio and Koch [Poggio, T. & Koch, C. (1985) Proc. R. Soc. London, Ser. B 226, 303-323], quadratic variational problems, an important subset of early vision tasks, can be "solved" by linear, analog electrical, or chemical networks. However, in the presence of discontinuities, the cost function is nonquadratic, raising the question of designing efficient algorithms for computing the optimal solution. Recently, Hopfield and Tank [Hopfield, J. J. & Tank, D. W. (1985) Biol. Cybern. 52, 141-152] have shown that networks of nonlinear analog "neurons" can be effective in computing the solution of optimization problems. We show how these networks can be generalized to solve the nonconvex energy functionals of early vision. We illustrate this approach by implementing a specific analog network, solving the problem of reconstructing a smooth surface from sparse data while preserving its discontinuities. These results suggest a novel computational strategy for solving early vision problems in both biological and real-time artificial vision systems.
早期视觉中的许多问题都可以通过最小化一个代价函数来表述。例如从明暗恢复形状、边缘检测、运动分析、从运动恢复结构以及曲面插值等。正如波吉奥和科赫所表明的[波吉奥，T. & 科赫，C.（1985年）《伦敦皇家学会学报》，B辑226，303 - 323]，二次变分问题作为早期视觉任务的一个重要子集，可以通过线性、模拟电气或化学网络“求解”。然而，在存在不连续的情况下，代价函数是非二次的，这就引出了设计计算最优解的高效算法的问题。最近，霍普菲尔德和坦克[霍普菲尔德，J. J. & 坦克，D. W.（1985年）《生物控制论》52，141 - 152]表明，非线性模拟“神经元”网络在计算优化问题的解方面可能是有效的。我们展示了如何将这些网络进行推广，以求解早期视觉中的非凸能量泛函。我们通过实现一个特定的模拟网络来说明这种方法，该网络在保留不连续的同时，从稀疏数据重建光滑曲面的问题。这些结果为在生物和实时人工视觉系统中求解早期视觉问题提出了一种新颖的计算策略。
