Uniform distribution of points on a hyper-sphere with applications to vector bit-plane encoding

In vector bit-plane encoding schemes, codebooks must be uniformly distributed on a hyper-sphere. Shells of regular lattices are often used, but they provide only a limited choice of number of vectors K and dimension N. The authors propose a method to generate codebooks in dimension N with arbitrary number K of vectors, almost uniformly distributed on a hyper-sphere. The uniform distribution of an arbitrary number of points on the surface of a hyper-sphere is still an open problem. Some mathematicians indeed consider it one of the mathematical challenges of the 21st century. The proposed method uses a combination of geometric and stochastic approaches to generate approximate solutions. The generated codebooks are tested in vector bit-plane encoding schemes. The results show that the proposed method is effective in generating codebooks almost uniformly distributed on a hyper-sphere.