(untitled) (Journal of Pure & Applied Sciences, 2023)
This paper proposes and demonstrates novel methods for compressing and reconstructing 3D surface patches typically obtained from scanners that rely on stereo vision, structured light, or time-of-flight techniques. The methods involve applying a polygon reduction to the mesh to get a set of vertices lying in structured planes of a sparse, regular grid. The data in each plane is then described parametrically, and a comparative analysis is conducted using the Discrete Fourier Transform (DFT), Discrete Cosine Transform (DCT), and Discrete Wavelet Transform (DWT). Quality factors are employed to further process the transform coefficients, resulting in substantial reductions in the amount of data saved to disk. The paper also defines file formats with the necessary parameters for a complete reconstruction of the sparse mesh. Finally, elliptic Partial Differential Equations (PDE) are used to represent the reconstructed data, and the Laplace equation is iteratively solved between adjacent planes to recover the vertex density of the original mesh. Experimental results demonstrate the effectiveness of the proposed methods, achieving compression rates of over 98% compared to the OBJ file format and over 91% compared to a list of vertices in ASCII format.