Robust localisation and identification of vertebrae, jointly termed vertebrae labelling, in computed tomography (CT) images is an essential component of automated spine analysis. Current approaches for this task mostly work with 3D scans and are comprised of a sequence of multiple networks. Contrarily, our approach relies only on 2D reformations, enabling us to design an end-to-end trainable, standalone network. Our contribution includes: (1) Inspired by the workflow of human experts, a novel butterfly-shaped network architecture (termed Btrfly net) that efficiently combines information across sufficiently-informative sagittal and coronal reformations. (2) Two adversarial training regimes that encode an anatomical prior of the spine's shape into the Btrfly net, each enforcing the prior in a distinct manner. We evaluate our approach on a public benchmarking dataset of 302 CT scans achieving a performance comparable to state-of-art methods (identification rate of @math 88 ) without any post-processing stages. Addressing its translation to clinical settings, an in-house dataset of 65 CT scans with a higher data variability is introduced, where we discuss refinements that render our approach robust to such scenarios.
Notice the parallels that can be drawn between these prior encoding approaches and generative adversarial networks (GAN) @cite_10 , @cite_0 . Both of them have two networks, a primary network ( @math generator) generating a prediction and an auxiliary auto-encoding network ( @math discriminator) working on the of this prediction. Architecturally closer to the AE-like secondary network is the energy-based GAN proposed by @cite_14 that uses an AE as a discriminator and its reconstruction energy as the adversarial signal.
@cite_0 @cite_14 @cite_10
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We introduce the "Energy-based Generative Adversarial Network" model (EBGAN) which views the discriminator as an energy function that attributes low energies to the regions near the data manifold and higher energies to other regions. Similar to the probabilistic GANs, a generator is seen as being trained to produce contrastive samples with minimal energies, while the discriminator is trained to assign high energies to these generated samples. Viewing the discriminator as an energy function allows to use a wide variety of architectures and loss functionals in addition to the usual binary classifier with logistic output. Among them, we show one instantiation of EBGAN framework as using an auto-encoder architecture, with the energy being the reconstruction error, in place of the discriminator. We show that this form of EBGAN exhibits more stable behavior than regular GANs during training. We also show that a single-scale architecture can be trained to generate high-resolution images. We propose a new framework for estimating generative models via an adversarial process, in which we simultaneously train two models: a generative model G that captures the data distribution, and a discriminative model D that estimates the probability that a sample came from the training data rather than G. The training procedure for G is to maximize the probability of D making a mistake. This framework corresponds to a minimax two-player game. In the space of arbitrary functions G and D, a unique solution exists, with G recovering the training data distribution and D equal to ½ everywhere. In the case where G and D are defined by multilayer perceptrons, the entire system can be trained with backpropagation. There is no need for any Markov chains or unrolled approximate inference networks during either training or generation of samples. Experiments demonstrate the potential of the framework through qualitative and quantitative evaluation of the generated samples.