The　registration　of　unitary-modality　geometric　data　has　been　successfully　explored　over　past　decades.　However,　existing　approaches　typically　struggle　to　handle　cross-modality　data　due　to　the　intrinsic　difference　between　different　models.　To　address　this　problem,　in　this　article,　we　formulate　the　cross-modality　registration　problem　as　a　consistent　clustering　process.　First,　we　study　the　structure　similarity　between　different　modalities　based　on　an　adaptive　fuzzy　shape　clustering,　from　which　a　coarse　alignment　is　successfully　operated.　Then,　we　optimize　the　result　using　fuzzy　clustering　consistently,　in　which　the　source　and　target　models　are　formulated　as　clustering　memberships　and　centroids,　respectively.　This　optimization　casts　new　insight　into　point　set　registration,　and　substantially　improves　the　robustness　against　outliers.　Additionally,　we　investigate　the　effect　of　fuzzier　in　fuzzy　clustering　on　the　cross-modality　registration　problem,　from　which　we　theoretically　prove　that　the　classical　Iterative　Closest　Point　(ICP)　algorithm　is　a　special　case　of　our　newly　defined　objective　function.　Comprehensive　experiments　and　analysis　are　conducted　on　both　synthetic　and　real-world　cross-modality　datasets.　Qualitative　and　quantitative　results　demonstrate　that　our　method　outperforms　state-of-the-art　approaches　with　higher　accuracy　and　robustness.　Our　code　is　publicly　available　at　https://github.com/zikai1/CrossModReg.