The Image Foresting Transform (IFT) is a graph-based framework to develop image operators based on optimum connectivity between a root set and the remaining nodes, according to a given path-cost function. Its applications involve a variety of tasks, such as segmentation, boundary tracking, skeletonization, filtering, among others. The Differential Image Foresting Transform (DIFT) allows multiple IFT executions for different root sets and a same monotonically incremental path-cost function, making the processing time proportional to the number of modified nodes. In this paper, we extend the DIFT algorithm for non-monotonically incremental functions with root-based increases. This proposed extension, called Generalized DIFT (GDIFT), has been successfully used as the core part of some modern superpixels methods with state-of-the-art results. Experimental results show considerable efficiency gains over the sequential flow of IFTs for the generation of superpixels, also avoiding inconsistencies in image segmentation, which could occur with the regular DIFT algorithm.

图像森林变换（IFT）是一个基于图的框架，可根据给定的路径成本函数，根据根集与其余节点之间的最佳连通性来开发图像运算符。它的应用涉及多种任务，例如分割，边界跟踪，框架化，过滤等。差分图像森林变换（DIFT）允许针对不同的根集执行多个IFT，并具有相同的单调增量路径成本函数，从而使处理时间与修改的节点数成正比。在本文中，我们将基于根的增量扩展了用于非单调增量函数的DIFT算法。这项提议的扩展名为Generalized DIFT（GDIFT），已成功用作某些现代超像素方法的核心部分，并具有最新的结果。