With　the　development　of　the　smart　city,　camera　sensors　have　attracted　more　and　more　research　interests　from　both　academic　researchers　and　industrial　engineers.　Given　a　set　of　points　of　interests　(POI)　and　a　set　of　cameras,　practical　applications　require　to　deploy　these　cameras　with　the　minimum　cost　so　that　these　POIs　can　be　fully　covered　by　these　cameras.　In　this　paper,　we　study　a　problem　called　Min-Num　LTC-CS,　which　is,　given　a　set　of　POIs　located　on　a　line　segment　and　a　set　of　cameras　distributed　on　the　plane,　to　choose　a　minimum　number　of　cameras　so　that　these　POIs　can　be　fully　covered　by　the　sensing　ranges　of　these　cameras.　We　first　propose　a　grouping　algorithm　by　grouping　the　POIs　according　to　whether　they　can　be　covered　by　the　same　camera　with　certain　rotation　angle　and　then　construct　a　graph　using　these　POI　groups.　We　show　that　there　exists　a　feasible　constrained　st-flow　if　and　only　if　there　exists　a　subset　of　cameras　that　can　completely　cover　these　POIs.　Then　we　propose　an　LP　formulation　for　the　constrained　flow　problem　and　prove　that　any　basic　solution　of　the　LP　formulation　is　integral,　which　consequently　leads　to　an　optimal　solution　to　Min-Num　LTC-CS　by　solving　this　LP　formulation.　Lastly,　extensive　numerical　experiments　are　conducted　to　demonstrate　the　practical　performance　of　our　algorithms.　©　2021,　Springer　Nature　Switzerland　AG.