## 4 Conclusions  
In this paper, a new method for automatic segmentation of coronary arteries, based on multiscale analysis of X-ray angiograms, has been introduced. The proposed method employs the multiscale Gaussian matched filters, applied in the image domain, and the multiscale Gabor filter, applied in the frequency domain, in order to improve the contrast between vessel features and background, suppress noise in the image, and homogenize the illumination of the angiogram. Both multiscale responses are used as input layer in a four layered perceptron network. A statistical analysis has shown that the Multilayer perceptron with 9 neurons in each of the two hidden layers is the appropriate using a comparative set of configurations. Moreover, the proposed method based on an artificial neural network with multiscale analysis has performed better than eleven vessel detection methods from the state of the art by reaching an \(A_{z}=0.9775\) when applied to 30 test images. The use of a fixed threshold value of 0.87, over the multiscale response of the proposed method, has proved to be the most appropriate from fourteen segmentation techniques. Finally, according to comparative experiments with twelve state-of-the-art vessel segmentation methods, the proposed method has provided the most accurate vessel segmentation of the test set of 30 angiograms with a classification accuracy of 0.9698, and Dice coefficient of 0.6857. In addition to the experimental results, the high performance and robustness in the detection and segmentation steps have shown that the proposed method could be a potential method to be integrated in a computer decision support system to aid diagnosis in medical practice.  
Conceptualization, F.C.-S. and I.C.-A.; Data curation, M.A.H.-G. and S.E.S.-M.; Funding acquisition, A.H.-A., M.A.H.-G. and S.E.S.-M.; Investigation, F.C.-S.; Methodology, I.C.-A. and A.H.-A.; Resources, M.A.H.-G. and S.E.S.-M.; Supervision, I.C.-A. and A.H.-A.; Validation, F.C.-S., A.H.-A., M.A.H.-G. and S.E.S.-M.; Writing original draft, F.C.-S. and I.C.-A.  
This work was supported by the Mexican National Council for Science and Technology (CONACYT) under the project No. 3150-3097 and the national scholarship for doctorate studies No. 626949/332702.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{l c} \hline \hline
**Segmentation Method** & **Execution Time (s)** \\ \hline
**GMF/Entropy Maximization [8]** & **0.02** \\ GMF/Degree-based [38] & 0.03 \\ Top-hat/Background Unification [1] & 0.07 \\ GMF/Local Entropy [37] & 0.08 \\ Multiscale Top-hat/Background Unification [2] & 0.09 \\ Multiline Detector/Threshold (0.56) [25] & 0.14 \\ U-Net ([PERSON] et al.) [39] & 0.17 * \\ CNN ([PERSON] and [PERSON]) [24] & 0.19 * \\ Single-scale Gabor filters/Ostu [15] & 0.47 \\ Multiscale GMF/Ostu [17] & 0.59 \\ Hessian Matrix-based/Vessel Repair [5] & 1.22 \\ CNN ([PERSON] et al.) [23] & 1.88 * \\ Proposed method/Threshold (0.87) & 1.89 \\ \hline \hline \end{tabular}  
* NVidia K40 12 GB (GPU execution time).  
\end{table}
Table 6: Average execution time of the proposed method and the twelve vessel segmentation methods from the state of the art presented in Table 5, using the testing set of 30 images.