Diagram (a) shows the formulation of compressive structured light for recovering inhomogeneous participating media. Coded light is emitted along the z-axis to the volume while the camera acquires images as line-integrated measurements of the volume density along the x-axis. (b) shows the image formation model for participating medium under single scattering.

Here we show the sparsity of one type of participating media we often encounter in the real world -- smoke. The volumetric data is acquired by T. Hawkins, et al. [3]. We obtained 120 volumes, each of which is of size 240x240x62. We consider each row of a volume as an individual 1D signal (of length 240). This plot shows the average reconstruction errors versus the number of elements we used for reconstruction. The two curves correspond to the reconstruction errors when the signal is represented as signal value or signal gradient, respectively.

This plot shows the results on the 1D signals of the above smoke data. The first column is the original signal. The remaining columns show reconstruction results (red dashed lines) for different methods, given the measurement cost, m/n, is equal to 1/4 (where m is the number of measurements and n is the number of unknowns). The value below each plot is the NRMSE(normalized root mean squared error) of reconstruction.

In our experiment, we use the vertical binary stripe patterns as the coded light pattern. Each frame has 128 stripes. The stripes are randomly assigned to be 0 (black) or 1 (white) according to Bernoulli distribution (with p=0.5). We also tried Hadamard codes and found that the Bernoulli random code is better.

This figure shows 3D simulation results of volume reconstruction with the proposed method. The original volume is a horse where blue means the lowest density and yellow means the highest density. The figure shows the reconstruction results of several methods under different measurement costs, m/n, where m is the number of measurements and n is the number of unknowns. It shows that CS-Gradient and CS-Both can obtain fairly good reconstruction even when m/n is as low as 1/8.

Here the figure shows the reconstruction results for the two-plane example using our system. The two planes, formed as a 'V' shape, are covered with powder (except in the regions of the letters 'EC' on the back plane and the letters 'CV' on the frontal plane) to create a simple volumetric example. (a) shows the original photograph, (b) shows one of the 24 measurements, and (c)(d) shows the reconstructed volumes under different views, with and without attenuation correction.

Similar to the two-plane example, this figure shows the reconstruction results for the face example where a 3D point cloud are etched in a glass cube to form a face. (a) shows the original photograph, (b) shows one of the 24 measurements, and (c)(d) shows the reconstructed volumes under different views, with and without attenuation correction.

Exploiting the sparsity in signal reconstruction gives us higher efficiency in acquisition. This enables us to acquire time-varying volumetric data using our current setup. This figure shows the reconstruction results of a sequence of milk drops dissolving in a water tank at different times. The results are shown at 3 different views. The left-most column shows the original video frames at the corresponding moments.

This video introduces the formulation and setup for the compressive structured light method and demonstrates several simulation results as well as experimental results for reconstructing various types of inhomogeneous participating media. (Without narration)

This video shows the reconstructed 3D volume density of the milk cloud at one time instance. The volume resolution is 128*128*250. It is reconstructed from 24 images measured with the coded light patterns.

This video shows the dynamic of milk dissolving in a water tank. The left is the recorded video from the camera, and the right shows the corresponding reconstructed 3D volume density from different views. Thanks to the high efficiency in our acquisition system, we can reconstruct the dynamic volumetric phenomena up to 15fps with the volume resolution 128*128*250.

This video shows another sequence of the dynamic of milk dissolving in a water tank.

This video shows the reconstructed volume density of two glass planes. The two planes, formed as a 'V' shape, are covered with powder (except in the regions of the letters 'EC' on the back plane and the letters 'CV' on the frontal plane) to create a simple volumetric example. The image shows an photograph of the two planes and one of the measured images.

This video shows the reconstructed volume density of a 3D point cloud of a face etched in a glass cube. The image shows an photograph of the two planes and one of the measured images.