Incomplete　boundary　boxes　will　be　generated　in　the　edge　of　an　image　in　most　cases,　when　covering　the　image　with　boxes　of　fixed　size.　An　effective　method　by　which　these　incomplete　boundary　boxes　can　be　taken　into　computation　has　been　proposed　to　improve　the　performance　of　computation　method　of　box　dimension,　based　on　the　digital　image　processing　function　of　MATLAB.　The　improved　computation　method　is　well　suitable　for　images　of　different　sizes　with　the　use　of　arithmetic-step　box　dividing　method.　The　calculated　results　derived　from　this　method　also　showed　a　better　accuracy　and　stability.　In　addition,　a　quantitative　discussion　was　made　about　the　factors　that　influence　the　computation　results　such　as　recursive　series　of　image　and　resolution.　Meanwhile　some　useful　control　conditions　were　proposed.　In　the　end,　the　improved　method　was　applied　to　calculate　the　fractal　dimension　of　frost　crystal　images　under　different　frosting　time　and　the　physical　meaning　of　fractal　dimension　in　describing　the　frosting　phenomenon　was　explained.