Image segmentation is a primary task in many medical applications. Recently, many deep networks derived from U-Net have been extensively used in various medical image segmentation tasks. However, in most of the cases, networks similar to U-net produce coarse and non-smooth segmentations with lots of discontinuities. To improve and refine the performance of U-Net like networks, we propose the use of parallel decoders which along with performing the mask predictions also perform contour prediction and distance map estimation. The contour and distance map aid in ensuring smoothness in the segmentation predictions. To facilitate joint training of three tasks, we propose a novel architecture called Psi-Net with a single encoder and three parallel decoders (thus having a shape of $Psi$), one decoder to learns the segmentation mask prediction and other two decoders to learn the auxiliary tasks of contour detection and distance map estimation. The learning of these auxiliary tasks helps in capturing the shape and the boundary information. We also propose a new joint loss function for the proposed architecture. The loss function consists of a weighted combination of Negative Log likelihood and Mean Square Error loss. We have used two publicly available datasets: 1) Origa dataset for the task of optic cup and disc segmentation and 2) Endovis segment dataset for the task of polyp segmentation to evaluate our model. We have conducted extensive experiments using our network to show our model gives better results in terms of segmentation, boundary and shape metrics.
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