The challenge in acquiring the 3D shape of translucent objects arises from the light transport within the object (see Figure2.4d). In particular, the incoming light enters the material and travels through the material where it is scattered. When we actively illuminate such translucent objects with a pattern, these non-local subsurface scattering effects induce a blurring of the observed pattern and, hence,
make e.g. a triangulation-based reconstruction from the decoded correspondences rather unreliable [LPC+00].
In [GLL+04], the authors circumvent these problems arising from the subsurface
scattering characteristics by covering the object of interest with a thin, diffuse dust before the actual 3D geometry acquisition via laser scanning is started. Later, this dust can easily be removed again.
Apart from using such tricks, surface geometry of translucent objects can also be acquired by utilizing certain material-specific characteristics of light transport. As many translucent objects also have a strong specular component, shape-from- specularity approaches can be applied where a moving light source is involved and the observed highlights can be used to estimate surface normals which is followed by a normal field integration [CGS06]. In [MHP+07], linearly polarized and circularly polarized spherical gradient illumination patterns are used and both the diffuse and the specular reflectance is considered for the estimation of surface normals. The advantage of the circularly spherical patterns can be identified in the fact that they allow the simultaneous estimation of surface normals from different viewpoints. The proposed polarized illumination schemes allow an independent estimation for both diffuse and specular normal maps. The latter have been proven to be appropriate for subsurface scattering materials in contrast to the diffuse normal estimates which are affected by the subsurface scattering. More recently, this method has also been used in [GCP+10] with circularly polarized spherical illumination for normal estimation from several viewpoints.
Furthermore, the investigations in [NKGR06] have demonstrated that specular and diffuse components of surface reflection can be separated by phase shifting of high-frequency structured light patterns. This observation has e.g. been explored
in [CLFS07], where a phase shifting based structured light approach has been
combined with a polarization-based removal of specular highlights at the surface. Based on the fact that global light transport characteristics remove the polarization of light, polarization filters are used in front of both the light source and the camera and multiple scattering effects can be separated from the structured light obser- vations. In subsequent work [CSL08], the same authors remove the dependency on polarization and instead modulate the low-frequency phase shifting patterns to separate direct and global components of light transport. By this modification, the obtained reconstruction quality is further improved in comparison to the technique
in [CLFS07].
In [GAVN11], certain structured light patterns tailored to translucent surfaces have
been proposed. While the analysis shows that high-frequency patterns are not applicable for translucent objects due to the blurring of the observed pattern, using Gray codes with a certain minimum stripe width following [GG03] shows more
2.3. THEDIVERSITY OF3D SHAPEACQUISITIONMETHODS
robustness on translucent surfaces and allows reliable reconstructions.
The recent technique presented in [DMZP14] represents an extension to conven- tional photometric stereo which enables the simultaneous estimation of both scat- tering properties and accurate surface normals for planar, homogeneous translucent objects based on observations from at least three different directional illumination configurations based on blind deconvolution. This avoids the problem of blurry nor- mal estimates that would result from an acquisition via conventional photometric stereo.
2.3.5
Techniques for Smooth Surfaces With Ideal or Near Ideal
Specular Refraction
Reconstructing the 3D shape of refractive objects (see Figure2.4e) is even more challenging in comparison to the cases mentioned in the previous sections. In general, such objects might exhibit inhomogeneous reflectance characteristics in- duced e.g. by a spatially varying refractive index or by inclusions of Lambertian or opaque material components. As pointed out in the recent survey given in [IKL+10], research has mainly been spent on solutions relying on certain simpli-
fying assumptions such as homogeneous material characteristics or considering only the reconstruction of a single surface separating the two enclosing media. The authors categorize the main approaches for the acquisition of refractive surfaces according to shape-from-distortion techniques, direct ray measurement techniques, reflectance-based techniques, techniques based on inverse ray tracing, tomography- based approaches and direct sampling techniques. In the scope of this section, we therefore group the related approaches according to these principles.
For the simpler case of acquiring a single refractive surface, shape-from-distortion techniques have been successfully applied. While this kind of methods can also be applied for specular surface reconstruction in a simpler form, refractive surface reconstruction requires considering the refractive index in addition to the surface normal in order to analyze the light path. Early work [Mur90,Mur92] has focused on reconstructing water surfaces from a single view. The movement of the water induces the a-priori unknown background pattern placed at the bottom of the liquid to be observed in a distorted way. Assuming an orthographic camera, optical flow [HS81,LK81] and a subsequent integration of the surface gradient are used to reconstruct the surface up to a certain scale. This seminal work has been extended in [MK05] by using a stereo camera system and a known pattern to estimate the refractive index, per-pixel depth and surface normals. As a further improvement, no average surface model is used in comparison to the approaches
to the normal consistency used in [NWR08] for specular surface reconstruction. Further work has been dedicated to the reconstruction of glass objects. Projecting structured light patterns into the refractive object with a projector and observing the respective distorted patterns in the camera image has been analyzed in [HSKK96].
In [BEN03], an unknown distant background pattern is used in combination with
a known parametric model including shape and refractive index. The object of interest is moved in front of a single, static camera and features are tracked over time similar to [Mur90,Mur92]. In [AMKB04], an extension of optical flow has been proposed to track refracted scene features for which the intensity might vary due to the presence of non-ideally transparent surfaces with e.g. additional absorption.
Furthermore, refractive surfaces have also been reconstructed by directly measuring the light path. For this purpose, calibrated planar patterns in several positions with respect to the object have been used in [KS05,KS08] to measure the light rays. In their theoretical analysis [KS05,KS08], the authors consider the categorization of reconstruction techniques based on ray measurements independently performed for each pixel. The introduced notation hN, M, Ki contains the relevant information with respect to the number of views N that are required for the reconstruction as well as the number M of points on specular or refractive surfaces that are located on a piecewise linear light path and the number K of calibrated reference points on a ray exitant from the object. The authors discuss that such a reconstruction cannot be performed for more than two intersections of the light ray with specular or refractive surfaces. The number of views N and the number K of calibrated reference points on a ray do not influence this observation. Following this concept, the authors consider a h3, 2, 2i reconstruction for refractive surfaces. As a result, four surface points with attached normals can be estimated per pixel. While one such pair of point and normal is located at the front surface of the object, the remaining pairs depend on the three differently refracted viewing rays and are located at the back surface.
A reflectance-based approach has been followed in [MK07]. Dense per-pixel reflectance measurements in a static camera are observed as a result of sequentially illuminating the static object of interest with a light source at varying positions on a regular grid. As a result, a 2D slice of the BRDF is recorded. However, indirect lighting effects influence these measurements. By separating the direct and indirect components of light transport, the authors achieve high-quality reconstructions for depth and normal, even for inhomogeneous refractive objects.
Other methods rely on the principle of inverse ray tracing. The underlying idea is based on the optimization of the residual of the acquired data and synthetically generated data. In order to reconstruct the surface of time-varying water surfaces, the water has been mixed with a fluorescent dye in [IM05] and a chemilumines-
2.3. THEDIVERSITY OF3D SHAPEACQUISITIONMETHODS
cent chemical in [GILM07]. While using UV illumination makes the mixture of water and fluorescent dye self-emissive [IM05], in the case of chemiluminescence
[GILM07] a chemical process has to be used for this purpose. Assuming homo-
geneous emission, both methods use synthetic images for surface fitting via level set optimization. In [WLZ+09], the liquid to be reconstructed is dyed with an opaque white paint. As a result, patterns can be projected onto the liquid and the correspondences observed in the cameras allow the reconstruction of the surface. In addition, a physically-based fluid simulation is used in this approach.
As discussed in [IKL+10], refractive object reconstruction can be performed by
making use of certain acquisition strategies. One possibility is to consider suffi- ciently high wavelengths for the incident illumination as given for x-rays. In this spirit, computer tomography has been used for scanning objects in [KTM+02],
and the proposed approach is in principle capable of scanning glass objects. Fur- thermore, as mentioned in [IKL+10], a reconstruction of refractive objects is also possible when the refractive indices of the object and the surrounding medium are identical. In [TBH06], glass objects are immersed into a liquid with care- fully controlled refractive index. Controlling the refractive index to a value of approximately 1.55 has been achieved by adding chemicals to water. As an ideal transparent object would disappear inside a medium with identical refractive index, the surrounding medium has to be dyed, which can be omitted if the object itself is absorptive [IKL+10].
Furthermore, several methods have been proposed based on direct sampling. In [HFI+08], fluorescent immersion range scanning has been proposed to reconstruct
refractive objects. The objects are placed in a different immersing medium with known refractive index. This liquid has additionally been dyed with a fluorescent chemical. During measurement, this fluorescent liquid causes the utilized laser sheet to be rendered visible while the refractive object to be scanned remains dark. A similar strategy has been explored by observing objects in a different spectrum. Several investigations e.g. focus on scanning-from-heating. In [EAM+09], the
glass surface is first heated by the incident infrared radiation which is then measured by an infrared camera. This allows to reconstruct the glass surface. Extending this approach, the shape of the hot spots observed by the infrared camera is analyzed in [AEB+12] to derive information regarding local surface orientations. Other works consider structured patterns of infrared radiation [MSSE+10] or the polarization in the infrared domain [MRA+12] for 3D reconstruction. Furthermore, several publi-
cations focus on exploiting ultra-violet radiation. In e.g. [RSFM10b,RSFM10a], structured light in the ultra-violet domain has been explored for reconstructing glass surfaces.