目的 人类的视觉能力可以轻易地判定两个几何图形形状的相似性，但是，这对于计算机来说仍是一个开问题。在计算机视觉应用中，不仅需要对图形形状进行分类和相似性判定，还需要对图形形状的相似性度量给出与人类的视觉判断一致的结果，这是目前图形形状表示和分类算法没有较好解决的问题。方法 通过GCT变换，将图形形状从实数空间的坐标表示变换到复数空间的复数特征向量表示，进而将判定两个几何形状的相似性问题转化为判定它们的复数空间特征向量的相似性问题。GCT变换不仅可以判定图形形状的相似性，它还是可逆的，它可以近似重建原图形形状。结果 GCT变换具有位移、尺度和旋转不变性，它不仅可以判定几何图形形状的相似性，给出与人类视觉判断一致的相似性结果，而且在两个几何图形形状相似的情况下，还能计算出它们的角度旋转和尺度缩放。结论 对于封闭的几何形状，如果几何形状的中心点位于几何形状的内部且过中心点的任一直线与该几何形状有且只有两个交点，理论证明和实验验证，GCT变换可以高效准确地判定这类几何图形形状的相似性，并给出与人类视觉判定一致的结果。

Objective 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. Method 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. Result 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. Conclusion 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.