Convolutional Model Trees
This method addresses image function approximation with potential applications in computer vision, but appears incremental as it builds on existing model tree and forest techniques.
The paper tackles the problem of fitting functions defined on images by introducing a forest of model trees that handle small distortions through convolutions and achieve smooth fits, with a theoretical guarantee of convergence for the training procedure.
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.