The principle behind VSLAM applications like 3D object reconstruction or indoor mapping is to estimate the spatial transformation between two large clouds of points, which represent two poses of the same scene. They can further be processed to obtain detailed surfaces. Since its introduction in 1992, the standard algorithm for finding the alignment between two point clouds is ICP (Iterative Closest Point) and its variants, combined with RANSAC (RANdom SAmple Consensus). This paper presents a new approach using interval analysis. The idea is to define large intervals for the transformation parameters between the poses then to successively contract those intervals using the equations of the transformation of corresponding points between the poses. To contract those intervals faster, we added an IMU (Inertial Measurement Unit) to our system so the initial intervals of the parameters are already small before applying the contractions. We implemented our algorithm using the middleware ROS (Robot Operating System) and stated our performances.