用卷积模型树森林实现图像函数的平滑拟合，可处理任意旋转和视角变化。
Convolutional Model Trees
- 通过卷积处理超平面，增强对微小畸变的鲁棒性
- 构建模型树森林提升精度，输出连续可微的近似结果
- 适合需要高精度图像函数建模的场景，如医学影像分析
本文提出一种构建模型树森林的方法，用于拟合定义在图像上的函数。步骤包括：对图像进行下采样、确定树的超平面、用卷积操作处理训练图像的小畸变，并通过构建森林提升准确率和拟合平滑度。像素、超平面系数与叶函数系数之间存在一一对应关系，使模型能够应对任意旋转或视角变化等大畸变。文中还提出一种理论上的平滑方法，使森林输出具备连续可微性，并证明了训练过程的收敛性。
原文摘要 · Abstract (English)
A method for creating a forest of model trees to fit samples of a function defined on images is described in several steps: down-sampling the images, determining a tree's hyperplanes, applying convolutions to the hyperplanes to handle small distortions of training images, and creating forests of model trees to increase accuracy and achieve a smooth fit. A 1-to-1 correspondence among pixels of images, coefficients of hyperplanes and coefficients of leaf functions offers the possibility of dealing with larger distortions such as arbitrary rotations or changes of perspective. A theoretical method for smoothing forest outputs to produce a continuously differentiable approximation is described. Within that framework, a training procedure is proved to converge.
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