High-quality　depth　information　has　been　increasingly　used　in　many　real-world　multimedia　applications　in　recent　years.　Due　to　the　limitation　of　depth　sensor　and　sensing　technology,　actually,　the　captured　depth　map　usually　has　low　resolution　and　black　holes.　In　this　paper,　inspired　by　the　geometric　relationship　between　surface　normal　of　a　3D　scene　and　their　distance　from　camera,　we　discover　that　surface　normal　map　can　provide　more　spatial　geometric　constraints　for　depth　map　reconstruction,　as　depth　map　is　a　special　image　with　spatial　information,　which　we　called　2.5D　image.　To　exploit　this　property,　we　propose　a　novel　surface　normal　data　guided　depth　recovery　method,　which　uses　surface　normal　data　and　observed　depth　value　to　estimate　missing　or　interpolated　depth　values.　Moreover,　to　preserve　the　inherent　piecewise　smooth　characteristic　of　depth　maps,　graph　Laplacian　prior　is　applied　to　regularize　the　inverse　problem　of　depth　maps　recovery　and　a　graph　Laplacian　regularizer(　GLR)　is　proposed.　Finally,　the　spatial　geometric　constraint　and　graph　Laplacian　regularization　are　integrated　into　a　unified　optimization　framework,　which　can　be　efficiently　solved　by　conjugate　gradient(CG).　Extensive　quantitative　and　qualitative　evaluations　compared　with　state-of-the-art　schemes　show　the　effectiveness　and　superiority　of　our　method.　©　2019　Association　for　Computing　Machinery.