In this paper, we introduce the notions of ( ∈ , ∈ ) -fuzzy positive implicative filters and ( ∈ , ∈ ∨ q ) -fuzzy positive implicative filters in hoops and investigate their properties. We also define some equivalent definitions of them, and then we use the congruence relation on hoop defined in blue[Aaly Kologani, M.; Mohseni Takallo, M.; Kim, H.S. Fuzzy filters of hoops based on fuzzy points. Mathematics. 2019, 7, 430; doi:10.3390/math7050430] by using an ( ∈ , ∈ ) -fuzzy filter in hoop. We show that the quotient structure of this relation is a Brouwerian semilattice.

Deep learning has shown potential in domains where large-scale annotated datasets are available. However, manual annotation is expensive, time-consuming, and tedious. Pixel-level annotations are particularly costly for semantic segmentation in images with dense irregular patterns of object instances, such as in plant images. In this work, we propose a method for developing high-performing deep learning models for semantic segmentation of wheat heads utilizing little manual annotation. We simulate a computationally-annotated dataset using a few annotated images, a short unannotated video clip of a wheat field, and several video clips from fields with no wheat. This dataset is then used to train a customized U-Net model for wheat head segmentation. Considering the distribution shift between the simulated and real data, we apply three domain adaptation steps to gradually bridge the domain gap. Only using two annotated images, we achieved a Dice score of 0.89 on the internal test set, i.e., images extracted from the wheat field video. The model trained using only two annotated images was evaluated on a diverse external dataset collected from 18 different domains across five countries and achieved a Dice score of 0.73. To further expose the model to images from different growth stages and environmental conditions, we incorporated two annotated images from each of the 18 domains and further fine-tuned the model. This resulted in improving the Dice score to 0.91. These promising results highlight the utility of the proposed approach in the absence of large-annotated datasets. Although the utility of the proposed method is shown on a wheat head dataset, it can be extended to other segmentation tasks with similar characteristics of irregularly repeating patterns of object instances.

Deep learning has shown potential in domains with large-scale annotated datasets. However, manual annotation is expensive, time-consuming, and tedious. Pixel-level annotations are particularly costly for semantic segmentation in images with dense irregular patterns of object instances, such as in plant images. In this work, we propose a method for developing high-performing deep learning models for semantic segmentation of such images utilizing little manual annotation. As a use case, we focus on wheat head segmentation. We synthesize a computationally annotated dataset—using a few annotated images, a short unannotated video clip of a wheat field, and several video clips with no wheat—to train a customized U-Net model. Considering the distribution shift between the synthesized and real images, we apply three domain adaptation steps to gradually bridge the domain gap. Only using two annotated images, we achieved a Dice score of 0.89 on the internal test set. When further evaluated on a diverse external dataset collected from 18 different domains across five countries, this model achieved a Dice score of 0.73. To expose the model to images from different growth stages and environmental conditions, we incorporated two annotated images from each of the 18 domains to further fine-tune the model. This increased the Dice score to 0.91. The result highlights the utility of the proposed approach in the absence of large-annotated datasets. Although our use case is wheat head segmentation, the proposed approach can be extended to other segmentation tasks with similar characteristics of irregularly repeating patterns of object instances.

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