A method estimates an ego-motion of an apparatus between a first image and a second image of a succession of images captured by the apparatus, in a SLAM type algorithm containing a localization part including the ego-motion estimating and a mapping part. The ego-motion comprises a 3D rotation of the apparatus and a position variation of the apparatus in the 3D space, and the ego-motion estimating comprises performing a first part and performing a second part after having performed the first part, the first part including estimating the 3D rotation of the apparatus and the second part including, the 3D rotation having been estimated, estimating the position variation of the apparatus in the 3D space.