Concave Bowl on a Marble Slab

Concave bowl on a marble slab. There are inter-reflections inside the concave bowl and sub-surface scattering on the translucent marble slab.
Image captured with a low-frequency projected pattern. Due to inter-reflections, scene points that are not directly lit have a large radiance. This results in structured light decoding errors.
Image captured with a high-frequency projected pattern. Due to sub-surface scattering on the marble slab, the high frequency pattern is blurred. Consequently, this image are not decoded accurately.
3D Reconstruction Comparison
Conventional Gray Codes
(11 images)
Modulated Phase Shifting
(162 images)
Our Code Ensemble
(42 images)
Using conventional Gray codes results in errors due to inter-reflections. Modulated phase shifting relies on explicitly separating the direct and the global illumination components. Hence, it suffers from low signal to noise ratio due to low direct component on the marble slab. Our result using an ensemble of codes has significantly fewer errors.
Designing patterns for preventing errors due to interreflections
Interreflections result in errors for structured light patterns with low spatial frequencies (see paper for details). To prevent errors due to interreflections, structured light patterns with only high spatial frequencies must be used. Existing patterns (phase shifting, conventional Gray codes) have patterns with a range of spatial frequencies. We show that by using simple logical operations, codes with only high spatial frequencies can be constructed. Below we show an example with a V-groove scene (see paper for details).
Local effects such as sub-surface scattering and defocus result in blurring of incident illumination. For such effects, patterns with low spatial frequencies must be used. We used tools from combinatorial mathematics literature to design binary patterns with high minimum stripe width (low spatial frequencies) as shown below. Note the distribution of stripe widths for different codes.
Handling scenes with multiple global illumination effects
Designing patterns for sub-surface scattering and defocus
For most scenes, we do not have a priori knowledge of the form of global illumination effects. Moreover, many scenes can have both interreflections (long-range) and local effects. For such scenes, we project an ensemble of codes and perform a simple consistency check.

For example, we project four codes - two sets of logical codes (optimized for interreflections) and two sets optimized for local effects.

For each scene point, we get four different depth values (as shown below). The key idea is that if the codes make errors, they are random errors. However, if any two agree, with high probability they will agree on the correct value.