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This paper proposes a modified method for training tool segmentation networks for endoscopic images by parsing training images into two disjoint sets: one for rectangular representations of endoscopic images and one for polar. Previous work [1], [2] demonstrated that certain endoscopic images may be better segmented by a U-Net network trained on the original rectangular representation of images alone, and others performed better with polar representations. This work extends that observation to the training images and seeks to intelligently decompose the aggregate training data into disjoint image sets — one ideal for training a network to segment original, rectangular endoscopic images and the other for training a polar segmentation network. The training set decomposition consists of three stages: (1) initial data split and models, (2) image reallocation and transition mechanisms with retraining, and (3) evaluation. In (2), two separate frameworks for parsing polar vs. rectangular training images were investigated, with three switching metrics utilized in both. Experiments comparatively evaluated the segmentation performance (via Sørenson Dice coefficient) of the in-group and out-of-group images between the set-decomposed models. Results are encouraging, showing improved aggregate in-group Dice scores as well as image sets trending towards convergence.