We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight distribution is determined by maximizing the associated entropy function. This approach, previously applied successfully to polynomials and spline curves, enhances the robustness of the regression model by automatically detecting and down-weighting anomalous data during the fitting process. To demonstrate the effectiveness of the method, we present applications to two image processing problems and further illustrate its potential through two synthetic examples.

翻译：本文考虑采用加权最小二乘代价函数对数据进行双变量样条回归模型拟合，其中权重求和为一以构成离散概率分布。通过应用最大熵原理，权重分布通过最大化关联熵函数确定。该方法先前已成功应用于多项式和样条曲线拟合，能够在拟合过程中自动检测异常数据并降低其权重，从而增强回归模型的鲁棒性。为验证该方法的有效性，我们展示了两个图像处理问题的应用实例，并通过两个合成算例进一步阐明其潜力。