In　the　field　of　computer　vision,　object　colocalization　problem　is　a　relatively　new　branch　of　object　detection.　The　state-of-the-art　methods　mainly　focus　on　supervised　learning　and　non-traditional　approaches.　However,　supervised　learning　certainly　has　better　performance　in　detecting　a　conspicuous　object,　but　a　mass　of　images　with　manual　annotation　is　indispensable,　which　is　a　heavy　burden　for　obtaining　training　images.　This　paper　presents　a　general　co-localization　framework　and　introduces　a　traditional　approach　which　is　based　on　mathematical　optimization,　for　narrowing　the　gap　of　performance　between　the　unsupervised　and　supervised　methods　in　co-localization.　The　localization　technique　we　adopted　is　based　on　multiple　saliency　map　fusion　and　mathematical　optimization　strategies.　By　extracting　the　co-saliency　map　from　a　set　of　images　with　multiple　methods　and　merging　them　at　image　level　or　superpixel　level,　we　derive　the　object　co-saliency　fusion　maps　that　the　performance　is　better　than　single　saliency　method.　This　representation　overcomes　the　problem　of　foreground　ambiguity,　which　scales　down　the　location　area　and　improves　the　accuracy　of　object　colocalization.　And　we　demonstrate　the　availability　of　co-saliency　fusion　adopted　in　co-localization　problem　by　the　experimental　results　on　the　object　discovery　dataset.　©　2019　IEEE.