The perceptual ability of human beings can determine the similarity of two shapes easily. However

this matter is still an open issue in computer machines. In computer vision applications

classifying and determining the similarity of shapes and providing a correspondence result with human beings in shape similarity determination are necessary. Unfortunately

these issues have not been addressed by up-to-date shape similarity determination algorithms. Geometry complex transform(GCT)

a method of transforming a geometric shape from its planar coordinates into the complex domain space of multidimensional vector

was used to transfer the similarity determination of two geometric shapes into that of two complex vectors. GCT transform is also an information-preserving method

which means that it can reconstruct the original shape of an object. GCT transform is translation

scale

and rotation invariant. Aside from being able to determine the similarity of two geometric shapes in correspondence with results generated by humans

this method can also compute rotation angle and scale factor between shapes. Theoretical proof and experiments show that GCT transform is feasible

effective

and efficient in determining the similarity for this class of shapes

which has its centroid in its inner region. Moreover

only two intersections of point exist between any line passing through its centroid with the contour of the shape. GCT can compute the similarity of two shapes with the same result as that of the human being.