1. A plane detecting apparatus for detecting a plane from a captured image with capturing units, comprising: a pair of image capturing units located in a predetermined positional relationship, for capturing images of a mutually overlapping area containing a plane; a parameter storing unit for storing, as parameters, a rotation matrix and a translation vector for transforming one of coordinate systems of said pair of said image capturing units into another coordinate system, internal parameters of said pair of said image capturing units, an initial value of a normal vector of said plane and an initial value of a distance from one image capturing unit of said image capturing units, as a base, to said plane; and a projection transformation matrix estimating unit for changing said initial value of said normal vector and said initial value of said distance based on a density gradient method by use of said rotation matrix, said translation vector and said internal parameters to estimate a projection transformation matrix for overlapping planes contained in a stereo image captured by said pair of said image capturing units, onto each other; and a projection transformation matrix calculating unit for calculating the projection transformation matrix, said projection transformation matrix transforming one of said images captured by one image capturing unit to overlap said plane contained in said one image onto a plane contained in another of said images captured by another image capturing unit, by use of said rotation matrix and said translation vector; wherein said plane is detected using said projection transformation matrix.