Our study investigated an object-detection method based on the faster region-based convolutional neural network (faster R-CNN). The method was designed to determine the center of either a concentric circle or concentric ellipse. Specifically, the central spot of the image (as the object region) can be marked by the bounding box when the circular or elliptical image is used as input data for the faster R-CNN model. The center point of the bounding box can then be calculated according to the coordinates of the upper left and lower right corners, that is, the center position of the concentric circle or concentric ellipse. It is important to determine the center coordinates when taking optical measurements, as the curvature radius of optical components can thus be obtained. The effectiveness of this method is demonstrated through simulation images. Furthermore, we can obtain the center coordinates of the actual Newton’s rings image using the above method; according to the coordinate transformation method, the curvature radius can be estimated based on the center.