## 5 Conclusions and Future Work  
In this paper, a CNN-based PID-Net was proposed for dense tiny objects (yeast) counting task. The PID-Net is an end-to-end model based on an encoder-decoder structure, and we proposed a new down-sampling model consisting of pixel interval down-sampling and max-pooling, which can serve to extract the dense and sparse features in the task of dense tiny object counting. By comparing with the proposed PID-Net and classical U-Net-based yeast counting results, the evaluation indices of Accuracy, Dice, Jaccard, Precision, Counting Accuracy and Hausdorff Distance of PID-Net were 97.51%, 95.86%, 92.10%, 96.02%, 96.97% and 4.6272, which are improved by 0.04%, 0.15%, 0.26%, 0.4% and 5.7%, respectively, and the Hausdorff Distance decreased by 0.0394.  
Although the small image dataset resulted in some cases of mis-segmentation, the proposed PID-Net showed a more satisfactory segmentation performance than the other models in the task of dense tiny object counting on a small dataset.  
Figure 10: An example of incorrect segmentation results using the proposed PID-Net.  
In the future, we plan to apply PID-Net for more dense tiny object counting tasks, such as the _streptococcus_ counting task and blood-cell-counting task. We will further optimize the PID-Net for better counting performance. For instance, object separation is one of the most significant parts in object counting; therefore, the Contour Loss [84] can be used by referring to our work to distinguish inner texture and contour boundaries for more accurate counting. We also consider using Knowledge Distillation [85] to reduce the memory cost of PID-Net, which can help to deploy the model on portable equipment.  
J.Z. ([PERSON]): methodology, software, validation, formal analysis, data curation, writing--original draft preparation, review and editing and visualization; X.Z.: resources; T.J.: investigation and funding acquisition; M.M.R.: validation; Y.Y.: validation; Y.-H.L.: validation; J.Z. ([PERSON]): formal analysis; A.P.: investigation; M.G.: investigation and C.L.: conceptualization, methodology, data curation, writing--original draft preparation, writing--review and editing, supervision and project administration. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the \"National Natural Science Foundation of China\" (No. 61806047) and the \"Sichuan Science and Technology Plan\" (No. 2021 YFH0069, 2021 YFQ0057, 2022 YFS0565).  
Yeast dataset can be found at: [[https://www.epfl.ch/labs/lpbs/data-and-software/](https://www.epfl.ch/labs/lpbs/data-and-software/)]([https://www.epfl.ch/labs/lpbs/data-and-software/](https://www.epfl.ch/labs/lpbs/data-and-software/)) (accessed on 16 January 2021).  
We thank [PERSON] and [PERSON] for their important discussion.  
There is no conflict of interest in this paper.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} PID-Net & pixel interval down-sampling network \\ CNN & convolutional neural network \\ EMs & environmental microorganisms \\ SVM & support vector machine \\ PCA & principal-component analysis \\ BPNN & back propagation neural network \\ ANN & artificial neural network \\ ReLU & rectified linear unit \\ Adam & adaptive moment estimation \\ SGD & stochastic gradient descent \\ NGD & natural gradient descent \\ GT & ground truth \\ FC & fully connected \\ IoU & intersection over union \\ TP & true positive \\ TN & true negative \\ FP & false positive \\ FN & false negative \\ \end{tabular}