Ellipse detection has a very wide range of applications in the field of industrial production, especially in the geometric detection of metallurgical hinge pins. However, the factors in industrial images, such as small object size and incomplete ellipse in the image boundary, bring challenges to ellipse detection, which cannot be solved by existing methods. This paper proposes a method for ellipse detection in industrial images, which utilizes the extended proposal operation to prevent the loss of ellipse rotation angle features during ellipse regression. Moreover, the Gaussian angle distance conforming to the ellipse axioms is adopted and combined with smooth L1 loss as the ellipse regression loss function to enhance the prediction accuracy of the ellipse rotation angle. The effectiveness of the proposed method is demonstrated on the hinge pins dataset, with experiment results showing an AP* of 80.93% and indicating superior detection performance compared to other methods. It is thus suitable for engineering applications and can provide visual guidance for the precise measurement of ellipse-like mechanical parts.