Haptic　data　compression　has　gradually　become　a　key　issue　for　emerging　real-time　haptic　communications　in　Tactile　Internet　(TI).　However,　it　is　challenging　to　achieve　a　tradeoff　between　high　perceptual　quality　and　compression　ratio　in　haptic　data　compression　scheme.　Inspired　by　the　perspective　of　embodied　AI,　we　propose　a　cross-modal　haptic　compression　scheme　for　haptic　communications　to　improve　the　perception　quality　on　TI　devices　in　this　paper.　Since　multimodal　fusion　is　routinely　employed　to　improve　the　ability　of　system　in　cognition,　we　assume　that　haptic　codec　is　guided　by　visual　semantics　to　optimize　parameter　settings　in　the　coding　process.　We　first　design　a　multi-dimensional　tactile　feature　fusion　network　(MTFFN)　relying　on　multi-head　attention　mechanism.　The　MTFFN　extracts　the　multi-dimensional　features　from　the　material　surface　and　maps　them　to　infer　the　coding　parameters.　Secondly,　we　provide　second-order　difference　and　linear　interpolation　to　establish　an　criterion　for　the　determination　of　optimal　codec　parameters,　which　are　customized　by　the　material　categories　so　as　to　give　high　robustness.　Finally,　the　simulation　results　reveal　that　our　compression　scheme　can　efficiently　make　a　personalized　codec　procedure　for　different　materials,　obtaining　more　than　17%　improvement　in　terms　of　compression　ratio　with　high　perceptual　quality　at　the　same　time.　　©　2025　IEEE.