The　edge　information　plays　key　role　in　the　restoration　of　depth　map.　Most　conventional　methods　assume　that　the　RGB-D　pairs　are　consistent　in　edge　areas.　In　this　paper,　firstly,　we　point　out　that　in　most　cases　the　consistency　between　normal　map　and　depth　map(N-D　pairs)　are　much　higher　than　that　between　RGB-D　pairs.　Then　we　propose　a　dual　regularization　term　to　guide　the　restoration　of　depth　map,　which　constrains　the　consistency　between　N-D　pairs　back　and　forth.　Moreover,　a　reweighted　graph　Laplacian　prior　is　incorporated　into　a　unified　optimization　framework　to　effectively　protect　piece-wise　smoothness(PWS)　characteristics　of　depth　map.　By　treating　depth　maps　as　graph　signals,　the　weight　between　two　nodes　is　adapted　according　to　its　content.　Extensive　experimental　results　demonstrate　the　superior　performance　of　our　method　compared　with　other　state-of-the-art　works　in　terms　of　objective　and　subjective　quality　evaluations.　©　2021　IEEE