Automatic and accurate segmentation of the left atrial (LA) cavity and scar can be helpful for the diagnosis and prognosis of patients with atrial fibrillation. However, automating the segmentation can be difficult due to the poor image quality, variable LA shapes, and small discrete regions of LA scars. In this paper, we proposed a fully-automatic method to segment LA cavity and scar from Late Gadolinium Enhancement (LGE) MRIs. For the loss functions, we propose two different losses for each task. To enhance the segmentation of LA cavity from the multicenter dataset, we present a hybrid loss that leverages Dice loss with a polynomial version of cross-entropy loss (PolyCE). We also utilize different data augmentations that include histogram matching to increase the variety of the dataset. For the more difficult LA scar segmentation, we propose a loss function that uses uncertainty information to improve the uncertain and inaccurate scar segmentation results. We evaluate the proposed method on the Left Atrial and Scar Quantification and Segmentation (LAScarQS 2022) Challenge dataset. It achieves a Dice score of 0.8897 and a Hausdorff distance (HD) of 16.91mm for LA cavity and a Dice score of 0.6406 and sensitivity of 0.5853 for LA scar. From the results, we notice that for LA scar segmentation, which has small and irregular shapes, the proposed loss that utilizes the uncertainty estimates generated by the scar yields the best result compared to the other loss functions. For the multi-center LA cavity segmentation, we observe that combining the region-based Dice loss with the pixelwise PolyCE can achieve a good result by enhancing the segmentation result in terms of both Dice score and HD. Furthermore, using moderate-level data augmentation with histogram matching improves the model's generalization capability. Our proposed method won the Left Atrial and Scar Quantification and Segmentation (LAScarQS 2022) Challenge.