The paper describes a method for measuring the similarity and symmetry of an image annotated with bounding boxes indicating image objects. The latter representation became popular recently due to the rapid development of fast and efficient deep-learning-based object-detection methods. The proposed approach allows for comparing sets of bounding boxes to estimate the degree of similarity of their underlying images. It is based on the fuzzy approach that uses the fuzzy mutual position (FMP) matrix to describe spatial composition and relations between bounding boxes within an image. A method of computing the similarity of two images described by their FMP matrices is proposed and the algorithm of its computation. It outputs the single scalar value describing the degree of content-based image similarity. By modifying the methods parameters, instead of similarity, the reflectional symmetry of object composition may also be measured. The proposed approach allows for measuring differences in objects composition of various intensities. It is also invariant to translation and scaling and - in case of symmetry detection - position and orientation of the symmetry axis. A couple of examples illustrate the method.