Abstract. Fully convolutional deep neural networks carry out excellent potential for fast and accurate image segmentation. One of the main challenges in training these networks is data imbalance, which is particularly problematic in medical imaging applications such as lesion segmentation where the number of lesion voxels is often much lower than the number of non-lesion voxels. Training with unbalanced data can lead to predictions that are severely biased towards high precision but low recall (sensitivity), which is undesired especially in medical applications where false negatives are much less tolerable than false positives. Several methods have been proposed to deal with this problem including balanced sampling, two step training, sample re-weighting, and similarity loss functions. In this paper, we propose a generalized loss function based on the Tversky index to address the issue of data imbalance and achieve much better trade-off between precision and recall in training 3D fully convolutional deep neural networks. Experimental results in multiple sclerosis lesion segmentation on magnetic resonance images show improved F2 score, Dice coefficient, and the area under the precision-recall curve in test data. Based on these results we suggest Tversky loss function as a generalized framework to effectively train deep neural networks.

; for the Imaging and Informatics in Retinopathy of Prematurity (i-ROP) Research Consortium IMPORTANCE Retinopathy of prematurity (ROP) is a leading cause of childhood blindness worldwide. The decision to treat is primarily based on the presence of plus disease, defined as dilation and tortuosity of retinal vessels. However, clinical diagnosis of plus disease is highly subjective and variable. OBJECTIVE To implement and validate an algorithm based on deep learning to automatically diagnose plus disease from retinal photographs. DESIGN, SETTING, AND PARTICIPANTS A deep convolutional neural network was trained using a data set of 5511 retinal photographs. Each image was previously assigned a reference standard diagnosis (RSD) based on consensus of image grading by 3 experts and clinical diagnosis by 1 expert (ie, normal, pre-plus disease, or plus disease). The algorithm was evaluated by 5-fold cross-validation and tested on an independent set of 100 images. Images were collected from 8 academic institutions participating in the Imaging and Informatics in ROP (i-ROP) cohort study. The deep learning algorithm was tested against 8 ROP experts, each of whom had more than 10 years of clinical experience and more than 5 peer-reviewed publications about ROP.

This paper investigates error-entropy-minimization in adaptive systems training. We prove the equivalence between minimization of error's Renyi entropy of order and minimization of a Csiszar distance measure between the densities of desired and system outputs. A nonparametric estimator for Renyi's entropy is presented, and it is shown that the global minimum of this estimator is the same as the actual entropy. The performance of the error-entropy-minimization criterion is compared with mean-square-error-minimization in the short-term prediction of a chaotic time series and in nonlinear system identification.

Fully convolutional deep neural networks have been asserted to be fast and precise frameworks with great potential in image segmentation. One of the major challenges in training such networks raises when data is unbalanced, which is common in many medical imaging applications such as lesion segmentation where lesion class voxels are often much lower in numbers than non-lesion voxels. A trained network with unbalanced data may make predictions with high precision and low recall, being severely biased towards the non-lesion class which is particularly undesired in most medical applications where false negatives are actually more important than false positives. Various methods have been proposed to address this problem including two step training, sample re-weighting, balanced sampling, and more recently similarity loss functions, and focal loss. In this work we trained fully convolutional deep neural networks using an asymmetric similarity loss function to mitigate the issue of data imbalance and achieve much better trade-off between precision and recall. To this end, we developed a 3D fully convolutional densely connected network (FC-DenseNet) with large overlapping image patches as input and an asymmetric similarity loss layer based on Tversky index (using Fβ scores). We used large overlapping image patches as inputs for intrinsic and extrinsic data augmentation, a patch selection algorithm, and a patch prediction fusion strategy using B-spline weighted soft voting to account for the uncertainty of prediction in patch borders. We applied this method to multiple sclerosis (MS) lesion segmentation based on two different datasets of MSSEG 2016 and ISBI longitudinal MS lesion segmentation challenge, where we achieved average Dice similarity coefficients of 69.9% and 65.74%, respectively, achieving top performance in both challenges. We compared the performance of our network trained with Fβ loss, focal loss, and generalized Dice loss (GDL) functions. Through September 2018 our network trained with focal loss ranked first according to the ISBI challenge overall score and resulted in the lowest reported lesion false positive rate among all submitted methods. Our network trained with the asymmetric similarity loss led to the lowest surface distance and the best lesion true positive rate that is arguably the most important performance metric in a clinical decision support system for lesion detection. The asymmetric similarity loss function based on Fβ scores allows training networks that make a better balance between precision and recall in highly unbalanced image segmentation. We achieved superior performance in MS lesion segmentation using a patchwise 3D FC-DenseNet with a patch prediction fusion strategy, trained with asymmetric similarity loss functions.