Quaternion representation for similarity transformations in visual SLAM

The use of hierarchical maps has recently been proposed as an approach to make real-time visual SLAM computationally tractable in large environments. Compared to earlier work in SLAM with other sensors, local maps generated from monocular vision have one significant difference, namely, their scale is varying over different local maps. Thus, the relationship between two maps is a similarity transformation, and not an Euclidean transformation. This paper presents a novel representation of similarity transformations using quaternions. The representation is complete, is not overparameterized, does not have singularities of consequence, and its maximum likelihood estimation can be performed in real-time. The paper describes the parameterized transformation, as well as how the parameters can be optimized in real-time in a monocular visual SLAM system. Experiments presented show the validity of the approach.