# An Efficient Decomposition Framework for Discriminative Segmentation with Supermodular Losses

## TL;DR

This paper introduces an ADMM-based decomposition framework for discriminative image segmentation that enables efficient training with supermodular loss functions, improving accuracy and computational performance.

## Contribution

It presents a novel ADMM decomposition method for loss-augmented inference in structured SVMs, allowing practical use of supermodular losses in image segmentation.

## Key findings

- Improved segmentation accuracy on Grabcut and brain data.
- Enhanced computational efficiency over existing algorithms.
- Validated effectiveness of supermodular losses during training.

## Abstract

Several supermodular losses have been shown to improve the perceptual quality of image segmentation in a discriminative framework such as a structured output support vector machine (SVM). These loss functions do not necessarily have the same structure as the one used by the segmentation inference algorithm, and in general, we may have to resort to generic submodular minimization algorithms for loss augmented inference. Although these come with polynomial time guarantees, they are not practical to apply to image scale data. Many supermodular losses come with strong optimization guarantees, but are not readily incorporated in a loss augmented graph cuts procedure. This motivates our strategy of employing the alternating direction method of multipliers (ADMM) decomposition for loss augmented inference. In doing so, we create a new API for the structured SVM that separates the maximum a posteriori (MAP) inference of the model from the loss augmentation during training. In this way, we gain computational efficiency, making new choices of loss functions practical for the first time, while simultaneously making the inference algorithm employed during training closer to the test time procedure. We show improvement both in accuracy and computational performance on the Microsoft Research Grabcut database and a brain structure segmentation task, empirically validating the use of several supermodular loss functions during training, and the improved computational properties of the proposed ADMM approach over the Fujishige-Wolfe minimum norm point algorithm.