Recent advances in microelectronics have produced new generations of digital cameras with variable focal lengths and pixel sizes which facilitate automatic and high-quality imaging. However, without knowing the values of these critical camera parameters, it is difficult to measure objects in images using existing algorithms. This work investigates this important problem aiming at dimensional measurements (e.g., diameter, length, width and height) of regularly shaped physical objects in a single 2-D image free from restrictive camera parameters. Traditionally, such measurements usually require determinations of the poses of a certain reference feature, i.e., the location and orientation of the feature relative to the camera, in order to establish a geometric model for the dimensional calculation. Points or lines associated with certain shapes (including triangles and rectangles) are often used as reference features for the pose estimation. However, with only a single image as the input, these methods assume the availability of 3-D spatial relationships of the points or lines, which limits the applications of these methods to practical problems where this knowledge is unavailable or difficult to estimate, such as in the problem of image-based food portion size estimation in dietary assessment. In addition to points and lines, the circle has also been used as a reference feature because it has a single elliptic perspective projection in images. However, almost all the existing approaches treat the parameters of focal length and pixel size as the necessary prior information. Here, we propose a new approach to dimensional estimation based on single image input using the circular reference feature and a pin-hole model without considering camera distortion. Without knowing the focal length and pixel size, our approach provides a closed-form solution for the orientation estimation of the circular feature. With additional information provided, such as the size of the circular reference feature, analytical solutions are provided for physical length estimation between an arbitrary pair of points on the reference plane. Studies using both synthetic and actual objects have been conducted to evaluate this new method, which exhibited satisfactory results. This method has also been applied to the measurement of food dimensions based on digital pictures of foods in circular dining plates
