The Block-Matching (BM) method for motion estimation in most video coding is largely discussed in the case of perspective images. The omnidirectional cameras provide images with large field of view. These images contain global information about motion and permit to remove the ambiguity present with little camera motion in perspective case. Nevertheless, these images contain significant radial distortions. The Block-Matching in these catadioptric images is not a resolved problem, and still a challenging research field. A rectangular block representing the neighborhood in BM of a point and used in the perspective images is not appropriate for catadioptric cameras. The work presented in this article concerns the local motion estimation in catadioptric videos with the Adapted Block-Matching (ABM). The ABM based on an adapted neighborhood, the local motion estimation allows successful compensation prediction in catadioptric images. The Adapted Block-Matching is obtained from the equivalence between the omnidirectional image and the projection of scene points on a unit sphere.