image-structure on the deformation complex of a morphism

image-structure is shown to exist on the deformation complex of a morphism of associative algebras. The main step of the construction is the extension of a image-algebra by an associative algebra. Actions of image-algebras on associative and image-algebras are analyzed; extensions of image-algebras by associative and image-algebras that they act upon are constructed. The resulting image-algebra on the deformation complex of a morphism is shown to be quasi-isomorphic to the image-algebra on the deformation complex of the corresponding diagram algebra.