OP5 - A 3D-Fourier-Descriptor Approach to Compress and Classify 3D Imaging Data

SENSOR+TEST Conferences 2009
2009-05-26 - 2009-05-28
Congress Center Nürnberg
Proceedings OPTO 2009 & IRS² 2009
OPTO Poster Session
R. Schmitt, P. Fritz - RWTH Aachen University, Aachen, Germany
133 - 138


One major problem of optical 3D measurement methods like structured light projection or computer tomography is the size of the resulting scans. For example, a medium-sized CT data set with a resolution of 1000 × 1000 × 1000 voxels and a standard bit depth per voxel of 16 Bit takes 1.9 GB. Hence, much effort has to be spent to carry out the measurement, to archive the data, or to transmit the scans to other manufacturing units. A remedy for this problem is the compression of the recorded point clouds. In contrast to previous research work, where we proposed a method for lossless compression of computer tomography point clouds, this paper provides lossy compression techniques to achieve higher compression rates. Fourier Descriptors are introduced to provide a compact representation for 2-dimensional shapes. Kim adopted this method to a lossy compression scheme for 3D-digitized engineering components. The key aspect of this method is to represent a point cloud by a series of periodic base functions. For this, the 3D model is divided into N slices and each point (xn, yn) within slice n is considered as complex value. The points on each slice form a continuous 2D-shape contour. This contour is transformed from
the geometric domain to the frequency domain by applying the Fast Fourier Transform (FFT). In the frequency domain, the information of the signal is concentrated in very few elements. This implies that the absolute values of most Fourier coefficients are extremely small compared to the signal energy. Setting these coefficients to zero and keeping only values above a certain threshold implies only small changes in the signal and small compression errors. The remaining Fourier coefficients are referred to as Fourier Descriptors (FD). The method yields a distinct compression of the initial 3D shape model—Kim reported compression rates of 88.5 up to 95 percent. The initial 3D shape model can be recovered by retransforming the Fourier descriptors to the geometric domain.