Measuring the 3D shape of semi-transparent surfaces with projector-camera 3D scanners is a difficult task because these surfaces weakly reflect light in a diffuse manner, and transmit a large part of the incident light. The task is even harder in the presence of participating background surfaces. The two methods proposed in this paper use sinusoidal patterns, each with a frequency chosen in the frequency range allowed by the projection optics of the projector-camera system. They differ in the way in which the camera-projector correspondence map is established, as well as in the number of patterns and the processing time required. The first method utilizes the discrete Fourier transform, performed on the intensity signal measured at a camera pixel, to inventory projector columns illuminating directly and indirectly the scene point imaged by that pixel. The second method goes beyond discrete Fourier transform and achieves the same goal by fitting a proposed analytical model to the measured intensity signal. Once the one (camera pixel) to many (projector columns) correspondence is established, a surface continuity constraint is applied to extract the one to one correspondence map linked to the semi-transparent surface. This map is used to determine the 3D point cloud of the surface by triangulation. Experimental results demonstrate the performance (accuracy, reliability) achieved by the proposed methods.

We present the Frequency Shift Method, a new structured light technique allowing 3D shape acquisition in the presence of strong interreflections. The intensity signal of each camera pixel is represented by one or several peaks in the Fourier domain. If there is no interreflection, only a single peak appears, otherwise several peaks are present. Each peak represents a projector pixel participating in the illumination of the surface point imaged at the camera pixel. In the baseline version of the proposed approach, the number of patterns required is proportional to the number of projector pixels. We also propose a modification that significantly reduces the required number of patterns by subdividing and encoding the projector into multiple virtual low-resolution projectors. A method based on dynamic programming is used to separate direct and indirect illuminations. Our experimental results illustrate the effectiveness of our method compared to existing ones.

Phase-shift profilometry (PSP) is a technique for acquiring non-contact three-dimensional measurements using a projector and a camera. The technique can be used to measure 3D surfaces with high accuracy. However, it can be sensitive to motion because phase images are sequentially captured. We propose a new technique that uses residual phase errors to minimize the influence of motion on the recovered phases (and 3D points). The method minimizes residual phase error with respect to apparent phase offset variations caused by motion. Furthermore, a total variation scheme is used to minimize spatial variations of apparent phase offset variations. We demonstrate the method with different moving objects, and we also study the effect of the magnitude of the motion on the accuracy of the recovered phases. Visual artefacts as well as accuracy loss associated with motion are found to be significantly decreased.

This paper introduces a method to analyze the variability of the spine shape and of the spine shape deformations using articulated shape models. The spine shape was expressed as a vector of relative poses between local coordinate systems of neighboring vertebrae. Spine shape deformations were then modeled by a vector of rigid transformations that transforms one spine shape into another. Because rigid transformations do not naturally belong to a vector space, conventional mean and covariance could not be applied. The Fréchet mean and a generalized covariance were used instead. The spine shapes of a group of 295 scoliotic patients were quantitatively analyzed as well as the spine shape deformations associated with the Cotrel-Dubousset corrective surgery (33 patients), the Boston brace (39 patients), and the scoliosis progression without treatment (26 patients). The variability of intervertebral poses was found to be inhomogeneous (lumbar vertebrae were more variable than the thoracic ones) and anisotropic (with maximal rotational variability around the coronal axis and maximal translational variability along the axial direction). Finally, brace and surgery were found to have a significant effect on the Fréchet mean and on the generalized covariance in specific spine regions where treatments modified the spine shape.