Convolutional Model Trees

TL;DR

This paper introduces a novel convolutional model tree approach that enhances image function fitting by handling distortions, smoothing outputs, and ensuring convergence, thereby improving accuracy and robustness in image analysis tasks.

Contribution

It presents a new convolutional model tree method with a theoretical framework for smoothing and convergence, advancing image function approximation techniques.

Findings

The method effectively handles image distortions like rotations and perspective changes.

A smoothing technique produces continuously differentiable forest outputs.

The training procedure is proven to converge.

Abstract

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.