Edge　is　the　region　in　an　image　across　which　the　change　of　brightness　intensity　is　rapid.　The　main　and　common　approach　of　edge　extraction　is　to　compute　image　brightness　differential,　which　is　one　of　the　most　fundamental　operations　in　digital　image　processing　and　analysis.　In　order　to　provide　the　interpretation　and　understanding　of　differential　edge　extraction　method　from　geometrical　optics　perspective　as　well　as　the　theoretical　basis　for　improving　edge　extraction　method　based　on　image　brightness　differential　in　the　future,　we　analyze　the　brightness　differential　in　edge　extraction　based　on　image　brightness　model　in　this　paper.　Firstly,　we　introduce　the　digital　imaging　process　and　the　components　of　the　daylight.　Secondly,　we　discuss　the　solar　illumination　and　the　skylight　illumination　on　the　surface　of　objects　and　give　the　image　pixel　brightness　model　from　geometrical　optics　perspective.　Then,　based　on　the　image　brightness　model,　we　analyze　the　differential　edge　extraction　method　and　discuss　the　image　brightness　differential　respectively　for　different　colored　object　surfaces　under　different　illumination　conditions.　The　analysis　indicates　that　the　object　edge　intensities　will　be　very　different　when　by　using　the　differential　edge　detection　operator　for　different　color　objects　under　different　lighting　conditions　and　the　relationship　between　daylight　illumination,　object　surface　color,　and　image　brightness　differential　is　given.