Traditional　feature　detection　and　description　methods,　such　as　scale-invariant　feature　transform,　are　susceptible　to　nonlinear　radiation　distortions　(NRDs)　and　geometric　distortions　(GDs),　which　in　turn　generate　a　large　number　of　outliers　or　incorrect　correspondences.　To　address　this　issue,　this　paper　proposes　a　simple　yet　effective　heterogeneous　model　fitting　(MIMF)　for　multi-source　image　correspondences.　First,　a　multi-orientation　phase　consistency　model　is　constructed,　which　fuses　phase　consistency,　image　amplitude　and　orientation　to　detect　the　correct　correspondences　of　feature　points.　This　model　effectively　reduces　the　influence　of　NRDs.　Second,　sub-region　grids　and　orientation　histograms　are　exploited　to　construct　the　log-polar　descriptors　with　variable-size　bins,　which　are　robust　to　GDs.　Finally,　a　heterogeneous　model　fitting　method　is　proposed,　which　can　effectively　estimate　the　parameters　of　the　transformation　model　for　alleviating　the　influence　of　outliers.　Experiments　are　performed　on　six　public　datasets　and　one　constructed　dataset　containing　ten　types　of　multi-source　images,　and　the　experimental　results　show　that　the　proposed　MIMF　method　outperforms　several　state-of-the-art　competing　methods　in　terms　of　matching　performance.