On the Quantization of Control Points for 2D and 3D Blending Surfaces

"Blending surfaces are extensively used for graphics modeling. Recently, we proposed a still image coding using these surfaces. These surfaces are completely defined by their control points. The usual approach is to partition an image or a 3D object into regions of same shape. Each region is represented by one blending surface. However, a surface shares control points with the neighboring regions. This results in a dependence problem which cannot be addressed by traditional techniques like Loyd-Max quantization or Laplacian optimization. We describe an iterative greedy algorithm to address this problem and efficiently quantize these control points. It has a computational time complexity of O(n.log(n)), for n control points. Examples of application of the algorithm are provided for still image coding and encoding of VRML files. We achieved an excellent tradeoff between bit-rate and distortion as illustrated by comparisons to uniform quantization."