在标准正则化理论中建议一类局部相互作用场和自适应正则项。局部相互作用场包括通常的误差项和一窗口函数。窗口的大小，取向和形状可以视具体的应用加以调整。自适应正则项用来处理不连续变化。这两项导致一对称的能量泛函。最简单的梯度下降算法通常在参数变化和有噪声时也很稳定，有效。

A set of local interaction field and adaptive regularizers are introduced to usual regularization theory. A local interaction field consists of a usual error term and a window function. The sizes, orientations and shapes of window functions can be made adaptive to specific applications. Adaptive regularizers are used to handle discont inuities. Theses two terms lead to asymmetrical energy functional. Even the simplest gradient algorithm is effective and stable when there are noises or algorithmic parameters change.