Tomographic Reconstruction of Transparent Objects

B. Trifonov, D. Bradley, W. Heidrich,

EGSR 2006

Abstract

The scanning of 3D geometry has become a popular way of capturing the shape of real-world objects. Transparent objects, however, pose problems for traditional scanning methods. We present a visible light tomographic reconstruction method for recovering the shape of transparent objects, such as glass. Our setup is relatively simple to implement, and accounts for refraction, which can be a significant problem in visible light tomography.

Setup and Acquisition

In order to scan a transparent object we place it in a glass cylinder filled with fluid. We change the index of refraction of the fluid to match that of the object by adding potassium salt. This causes light rays inside the cylinder to pass straight through object and removes refraction. Refraction still occurs at the boundary between the cylinder and the liquid, and between the cylinder and air. We account for these by using a 2-plane calibration step. Acquisition proceeds by placing the cylinder on a turn-table with a diffuse white background and capturing a number of images during 360 degree rotation. The following is a diagram and photograph of the setup.

Colored glass objects are captured easily with this setup. In order to capture clear objects, a contrast agent (such as food coloring) is added to the liquid.

Tomographic Reconstruction

Each pixel in each captured image represents a light ray segment inside the cylinder. The value of the pixel is the line integral of the absorption along the ray. We use Algebraic Reconstruction Techniques (ART) on a voxel grid to recover densities through the volume. We then use Marching Cubes to extract the iso-surface. In the images at the top of the page, the leftmost is an example object that was acquired. The second image is one of the captured images, and the third image is the reconstructed geometry. Note that some of the support structure is visible, but this can be removed as a post-process. The last image in the sequence illustrates that the hole in the center of the object was captured correctly. Standard laser scanning acquisition methods would not be able to capture such a feature due to occlusion (additionally they require that the object be spray-painted to remove transparency and specularity).

The following images show the acquisition of a glass jar, including the fine detail of the thread for the lid.

The next image is from a capture sequence of two chess pieces. Since the chess pieces are clear, blue dye is added to the fluid. In this case, the fluid absorbs light while the object does not. The results for an entire chess set are given. Note that the cross on the King piece broke off before acquisition and was glued back on, causing the artifact that is visible in the result.