Understanding　the　characteristics　of　high-quality　stereoscopic　3D　(S3D)　images　has　great　significance　for　S3D　image　classification,　quality　assessment,　and　quality　enhancement.　Existing　works　assess　the　quality　of　an　S3D　image　from　a　single　perspective　and　use　databases　with　subjective　opinion　scores　obtained　by　conducting　subjective　experiments　in　labs.　So　the　performance　of　these　works　in　real　applications　is　unclear　and　questionable.　In　this　paper,　we　propose　an　S3D　image　quality　assessment　index　based　on　two　important　factors,　namely　DisTortion　and　DisParity　(DTDP).　Distortion　reflects　the　extent　of　distortion　of　each　view　of　an　S3D　image,　respectively.　Disparity　is　a　distinguishing　factor　for　an　S3D　image　as　compared　with　a　monocular　image.　We　design　some　features　to　represent　these　two　factors　and　use　a　random　forest　regression　(RFR)　to　learn　the　mapping　between　the　features　and　subjective　opinion　scores.　The　database　we　choose　is　the　NVIDIA　3D　VISION　LIVE　Highest　Rated　database　which　is　from　real　application.　The　images　and　the　subjective　opinion　scores　are　directly　come　from　the　website　viewers　all　over　the　world.　Experimental　results　demonstrate　a　superior　performance　of　the　proposed　DTDP　index　as　compared　to　the　existing　methods.　©　2018　IEEE.