Topology-based Cost Function: a Novel Approach for Organ Delineation in Medical Images with Deep Learning Methods

Medical images segmentation plays a crucial role in diagnosis and treatment planning. Manual segmentation is a tedious and time-consuming task for experts and prone to human errors; thus, many efforts have been made to automate this process and facilitate the hardships of manual segmentation. Among these methods, deep learning approaches showed tremendous progress in the accuracy of medical image segmentation and became a dominant method. Despite these achievements, deep learning methods suffer from a defect in comprehensively learning the shape/topology of the target object. This defect cause islands of voxels, topological inconsistency, and unrealistic shapes in the final segmentation. To address this defect, an initial guess as prior knowledge for deep neural networks was proposed, and others refine the final segmentation mask to eliminate islands of voxels and fill undesired holes. In spite of these efforts, the main problem of learning topological features in neural networks is still unsolved. In this study, we proposed a novel cost function that encourages the neural network to capture the underlying shape morphology of the segmentation target in 3D medical images. The key idea of our proposed method is to constitute a shape space by vectorizing the 3D segmentation masks and extracting eigenvectors of this space through exploiting Principal Component Analysis (PCA) method. With a weighted sum of extracted eigenvectors, reconstruction of the primary segmentation mask is available. Therefore, the reconstruction weights can discriminate between realistic and unrealistic shape topology in the final output. We realized that the kurtoses of reconstruction weights for realistic shapes are higher than those of unrealistic ones. Accordingly, by penalizing the network to generate higher kurtoses of reconstruction weights for predicted segmentation, more realistic/valid shapes are generated, and networks learn to extract topology-based features. We employed an MRI hippocampus segmentation dataset and a 3D fully convolutional segmentation network to validate this approach. The network is once trained with a conventional cost function (e.g., Binary Cross-Entropy (BCE)) and once with the topology-based cost function (ours). The quantitative evaluation for the test set showed an improvement from 0.81 to 0.86 in the Dice score. Furthermore, the defects such as islands of voxels and topological inconsistency vanished when the shape/morphology-based loss function was used.