  This paper proposes a novel pixel interval down-sampling network (PID-Net)
for dense tiny object (yeast cells) counting tasks with higher accuracy. The
PID-Net is an end-to-end convolutional neural network (CNN) model with an
encoder--decoder architecture. The pixel interval down-sampling operations are
concatenated with max-pooling operations to combine the sparse and dense
features. This addresses the limitation of contour conglutination of dense
objects while counting. The evaluation was conducted using classical
segmentation metrics (the Dice, Jaccard and Hausdorff distance) as well as
counting metrics. The experimental results show that the proposed PID-Net had
the best performance and potential for dense tiny object counting tasks, which
achieved 96.97\% counting accuracy on the dataset with 2448 yeast cell images.
By comparing with the state-of-the-art approaches, such as Attention U-Net,
Swin U-Net and Trans U-Net, the proposed PID-Net can segment dense tiny objects
with clearer boundaries and fewer incorrect debris, which shows the great
potential of PID-Net in the task of accurate counting.
