## 4 Conclusions  
This study implemented the detection of coaxiality for automotive brake piston components based on machine vision and image processing technology. The novelty of the proposed detection method lies in its accuracy and flexibility. The theory and experiment show that the accuracy and stability of the method can reach 99.25%, and the coaxiality of other stepped shaft parts can be measured by modifying the algorithm parameters, meeting the requirements of automated detection in enterprise. This method has advantages such as high precision, efficiency, and stable performance, showing promising application prospects and laying a foundation for online coaxiality detection of automotive brake piston components. Additionally, this research outcome provides a new method for coaxiality detection of similar parts to stepped shafts. The main contributions of this paper are as follows:  
1. Analyzing the structural characteristics of automotive brake piston components and extracting the regions of interest based on these characteristics.
2. Proposing a mathematical morphology-based edge optimization method for complex edge structures, which removes redundant pixel points and optimizes image data into an n \(\times\) n matrix (where n is the width of the image), thereby improving the accuracy of geometric feature point extraction.
3. Determining the positions of extreme points by comparing the height of pixel points with that of neighboring pixel points, thus successfully extracting the coordinates of geometric feature points.  
In summary, the non-contact detection method based on the integration of machine vision and image processing technology offers an effective solution for the online detection of coaxiality in automobile brake piston components, demonstrating practicality and feasibility. However, there is still room for further optimization and improvement to adapt to evolving production demands and technological advancements. As a future research agenda, continuous experimental validation will be considered to ensure the method's viability and stability under various conditions. Additionally, ongoing refinement and optimization of the approach will be pursued to accommodate diverse production environments and process requirements.  
Q.L.: research ideas, experimental design and data analysis; W.G.: writing manuscripts, charting, data collection, literature retrieval; H.S.: data collection, data analysis, literature retrieval; W.Z.: document retrieval, data collection, data analysis; S.Z.: experimental design, data collection, data analysis. All authors have read and agreed to the published version of the manuscript.  
We need to thank the following organization for its strong support: the Natural Science Foundation of Jilin Province--General Project, 20220201043 GX.  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Reference [4]** & **Reference [3]** & **Reference [7]** & **This Paper** \\ \hline Data collection & & & & \\ method & Laser displacement sensor & Laser scanner & Laser collimator & Industrial camera \\ Detection type & & & & \\  & & & & Automotive brake piston \\  & & & & components (modify \\  & & & & parameters for measurement \\  & & & & of other stepped shaft parts) \\ Detection & & & & \\ method & & & & \\  & & & & \\  & & & & \\  & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison with other researchers’ detection methods.  
Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy.  
The authors would like to thank the members of the project team for their dedication and effort, and the teachers and schools for their help.  
The authors declare no conflicts of interest.