**3. Results**

The automatic results provided by the RENFAST method are compared herein both with manual annotations and with previously published works. For blood vessel segmentation, we compared our algorithm with the one proposed by Bevilacqua et al. [8], while we used the methods published by Tey et al. [10] and Fu et al. [11] as benchmarks for interstitial fibrosis segmentation. As datasets and manual annotations of these works are not publicly available, all the described methods were applied to the same dataset used in this paper. The processing was performed on a custom workstation with a 3.5 GHz 10-core CPU with 64 Gb of RAM (Turin, Italy).

### *3.1. Blood Vessel Detection*

Both pixel-based metrics (BalACCURACY, precision, recall, F1SCORE) and object-based metrics (DSC, HD95) were calculated to assess the performance of the RENFAST algorithm. To demonstrate the superiority of our strategy, we also evaluated the results obtained using a simple two-class CNN (background vs. vessel) and a three-class CNN without our post-processing. Tables 2 and 3 summarize the metrics calculated for blood vessel detection.


**Table 2.** Comparison between the RENFAST algorithm and the current state of the art for blood vessel segmentation (pixel-based metrics).

1 CNN with the same architecture shown in Figure 2 but trained on two classes (background vs. vessel). 2 Same deep network of the RENFAST algorithm but without post-processing (Section 2.4).

**Table 3.** Object-based metrics calculated on detected blood vessels for both the TRAIN and TEST sets.


1 CNN with the same architecture shown in Figure 2 but trained on two classes (background vs. vessel). 2 Same deep network of the RENFAST algorithm but without post-processing (Section 2.4).

Regarding pixel-based metrics, our method achieved the best BalACCURACY, recall, and F1SCORE for both the TRAIN and TEST sets. A large margin was achieved by RENFAST compared to the state-of-the-art techniques. Even more interesting, the post-processing adopted for blood vessel segmentation allowed a further increase in the overall performance of the single deep network (three-class CNN vs. RENFAST). The combination of the CNN probability map and cellular structure segmentation increased the DSC by up to 14.8% with respect to other methods. The accurate segmentation of blood vessel boundaries is also demonstrated by the lower HD95 value. Figure 7 shows a visual comparison between RENFAST and previously published works. Our approach managed to separate and correctly outline the boundaries of the blood vessels.
