Establishing　dense　correspondences　between　semantically　similar　images　is　a　challenging　task.　Cost　aggregation　is　a　crucial　step　in　finding　correct　dense　correspondences,　with　the　goal　of　optimizing　the　initial　correlation　map　thereby　removing　the　ambiguity　of　the　correspondences.　Current　approaches　use　transformer　architectures　for　cost　aggregation,　which　lack　local　priors　to　adequately　capture　the　local　information　contained　in　the　correlation　map.　We　propose　to　incorporate　peripheral　position　coding　into　the　transformer　to　explore　the　local　information　to　obtain　the　matching　set　and　call　it　the　Peripheral　Transformer　Matcher　(PTM).　This　coding　technique　partitions　the　overall　receptive　field　of　the　self-attention　mechanism　into　diverse　peripheral　regions,　each　with　its　own　set　of　weights.　By　doing　this,　the　proposed　PTM　gets　a　specific　local　prior　by　adding　an　inductive　bias　to　the　transformer　models　and　making　the　initial　correlation　map　less　confusing.　In　addition,　a　local　self-attention　module　is　used　to　enhance　the　image　features　and　obtain　an　enhanced　initial　correlation　map.　Comparisons　of　the　experimental　results　with　baselines　on　public　datasets　demonstrate　the　effectiveness　of　the　proposed　PTM.　©　2023　IEEE.