The iterative two-fork tree of perimeter and area on a modified Koch curve island is acquired

and from this

the formulae for calculating perimeter and area is obtained.It shows that the theoretical value of fractal dimension could be acquired from perimeter-maximum diameter relation for the fractal structure.It also shows the relation between that the critical nested tier of both the theoretical value of the fractal dimension and the ideal value of the fractal dimension

which meets the precision of auto-image analysis obtained from perimeter-area relation and parametersaandncould be ascertained. It is considered that the perimeter-area method is effective to obtain ideal value of fractal dimension in determenation of fractal dimension.