In this paper, we propose a novel coding scheme for the geometry of the triangular mesh model. The geometry coding schemes can be classified into two groups: schemes with perfect reconstruction property that maintains their connectivity, and schemes without it in which the remeshing procedure is performed to change the mesh to semi-regular or regular mesh. The former schemes have good coding performance at higher coding rate, while the latter give excellent coding performance at lower coding rate. We propose a geometry coding scheme that maintains the connectivity and has a perfect reconstruction property. We apply a method that successively structures on 2-D plane the surrounding vertices obtained by expanding vertex sequences neighboring the previous layer. Non-separable component decomposition is applied, in which 2-D structured data are decomposed into four components depending on whether their location was even or odd on the horizontal and vertical axes in the 2-D plane. And a prediction and update are performed for the decomposed components. In the prediction process the predicted value is obtained from the vertices, which were not processed, neighboring the target vertex in the 3-D space. And the zero-tree coding is introduced in order to remove the redundancies between the coefficients at similar positions in different resolution levels. SFQ (Space-Frequency Quantization) is applied, which gives the optimal combination of coefficient pruning for the descendant coefficients of each tree element and a uniform quantization for each coefficient. Experiments applying the proposed method to several polygon meshes of different resolutions show that the proposed method gives a better coding performance at lower bit rate when compared to the conventional schemes.

This paper presents data coding techniques for a stable single-bit noise-shaping quantizer, which has a cascade structure of a multi-bit ΣΔ modulator and a binary interpolator. The binary interpolator chooses a pre-optimized binary vector for each input sample and successively generates the chosen binary vector as an output bit stream. The binary vectors can have different lengths. The paper also proposes two methods to evaluate and bound output errors of a binary interpolator. A multi-bit ΣΔ modulator is designed to cause no overload for all possible input signals whose amplitudes are bounded to a specified level, and thus the ΣΔ modulator rigorously guarantees the stability condition. In design examples, we have evaluated Signal-to-Noise and Distortion Ratios (SNDRs) and noise spectra and then confirmed that our stable quantizers can sharply shape output noise spectra.