## 5 Conclusions  
In this paper, we proposed a novel interval iterative multi-thresholding segmentation algorithm based on hybrid spatial filter and region growing for medical brain MR images. Experiments show that the hybrid spatial filter can eliminate the noise in the image well while preserve the edge information of the image. It makes the segmentation effect more accurate. The algorithm makes full use of the spatial information in the original image. It quickly obtains initial thresholds by region growing, then the idea of interval iteration is adopted to optimize the thresholds. Finally, a weighting strategy is used to achieve medical image segmentation. Compared with other similar algorithms, our algorithm achieves satisfactory results. Subjectively, good visual effects are achieved, and the segmentation results have good consistency. Objectively speaking, the evaluation metric of our algorithm achieves the best results among all the test images and has a strong anti-noise performance. The time complexity of the algorithm is O(L\({}^{2}\)*W) level. Compared with the comparative algorithm PSO with the least time consumption, for processing 1 K (1024) pixels, the time consumption is about 1/10 of it. This significantly improved the running speed, which can be applied in the real-time system of clinical medicine. We achieve excellent segmentation accuracy with minimal time cost.  
Conceptualization, Y.F. and Y.L.; form analysis, Y.F. and Y.L.; methodology, Y.F. and Y.L.; software, Y.L. and Y.F.; visualization, Y.F.; writing--original draft, Y.F. and Y.L.; investigation, Y.F. and X.Z.; validation, Y.F., Z.L. and W.L.; writing--review and editing, Y.F., X.Z. and Q.Y.; data curation, Y.L., Z.L. and W.L.; supervision, Y.F., X.Z. and Q.Y.; project administration, Y.F. and X.Z.; funding acquisition, Y.F. All authors have read and agreed to the published version of the manuscript.  
The work was supported by Natural Science Foundation of Jilin Province (NO.YDZJ202201Z YTS422), Youth Growth Science and Technology Plan Project of Jilin Provincial Department of Science and Technology (NO.20210508039 RQ), \"Thirteenth Five-Year Plan\" Scientific Research Planning Project of Education Department of Jilin Province (NO.JJKH20210752 KJ, NO.JJKH20200677 KJ), Fundamental Research Funds for the Central Universities JLU (NO.93K172020K05), and National Natural Science Foundation of China (NO.61806024).  
Not applicable.  
The data described in this article can be freely and openly accessed at \"The Whole Brain Atlas\" of Harvard Medical School Image Library ([[http://www.med.harvard.edu/aanlib/home.html](http://www.med.harvard.edu/aanlib/home.html)]([http://www.med.harvard.edu/aanlib/home.html](http://www.med.harvard.edu/aanlib/home.html)) (accessed on 20 September 2021)).  
The authors would like to thank [[http://www.med.harvard.edu/aanlib/home.html](http://www.med.harvard.edu/aanlib/home.html)]([http://www.med.harvard.edu/aanlib/home.html](http://www.med.harvard.edu/aanlib/home.html)) (accessed on 20 September 2021) for providing source medical images.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Methods** & **Proposed** & **PSO** & **BF** & **ABF** & **NMS** & **RCGA** \\ \hline
1 K pixel/s & 0.008 & 0.1057 & 0.2772 & 0.3254 & 0.3548 & 0.2815 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Computation time compare with other methods.