Light Field Measurement of Reflective Interfaces

Light Field Measurement of Reflective Interfaces

Tadd Truscott, Department of Mechanical and Aerospace Engineering, Utah State University, Logan, UT, USA

Jesse Belden, Naval Undersea Warfare Center, Newport, RI, USA

Alexander Jafek, Department of Mechanical Engineering, University of Utah, Salt Lake City, UT, USA

Introduction

The geometric reconstruction of a diffuse surface can be accomplished with a simple projector-camera system [1]. However, in the case of specular objects - such as a gas-liquid interface (GLI) - these same methods fail to uniquely define surface location and orientation. Several methods have been demonstrated for recovering specular surface geometry including: using multiple cameras with diffuse scene points [2, 3], using one camera with images of a calibration target in two or more locations [4] and resolving the distortion of known geometry imaged by one camera [5, 6]. We seek a method that uses a single lenslet-based light field (LF) camera and one projector to reconstruct a GLI. This setup is attractive for situations that require the hardware to be small to perform measurements in confined spaces.

Methods

The geometry of our proposed LF camera-projector system is shown in figure 1 for one light ray. The angle φ of each ray is assumed to be known, as are the camera extrinsic parameters and location of the laser source relative to the global X-Y-Z coordinate system; the camera fixed coordinate system is x-y-z. The specular surface is locally parameterized by the distance D and the angle β relative the X-axis. The angle that the reflected ray makes with the Y-axis is given as

(1)

In our system model, all rays are traced exactly until they strike the surface at point (Xs,Ys). The paraxial approximation is then employed to trace the reflected rays to the main lens of the LF camera (point (XL, YL)). If the camera is angled, then the location and angle at which the ray hits the lens are converted to local camera coordinates,

(2)

(3)

where (XC,YC) are the coordinates of the camera center. The angle of the ray inside the camera is computed as

(4)

Combined with the distance sl, this angle determines which lenslet the ray hits. It is then assumed that the lenlsets are focused at infinity and the main lens is at infinity, so the chief ray is traced through the lenlset to determine the pixels the ray strikes, as shown in figure 1. In our system, we assume that the image formed on each pixel can be paired with the angle of the light ray that formed it.

Figure 1.Schematic of the LF imaging arrangement used to resolve local GLI location and orientation.

When the pixel-lenlset association is known, the angle of the light ray is uniquely defined (with some resolution set by the LF camera). Using equations 1-3, this ray can then be traced backwards through the lenslet, main lens and free- space and the intersection with the source ray can be found. This intersection point fixes the location of the surface and the constraints on angles fixes the orientation of the surface. A Matlab simulation demonstrates the ability of the LF camera-projector system to accurately define local surface orientation and location using this approach. Figure 2 shows two rays hitting an angled specular surface; the estimated surface is the average of the location and orientation found from backward tracing of these two rays; the accuracy on location is <2 mm and the accuracy on angle is <1 degree.

Figure 2.Schematic of the LF imaging arrangement used to resolve local GLI location and orientation.

References

[1]Douglas Lanman and Gabriel Taubin. Build your own 3d scanner: 3d photography for beginners. In ACM SIGGRAPH 2009 Courses, page 8. ACM, 2009.

[2]ThomasBonfortandPeterSturm.Voxelcarvingforspecularsurfaces.InComputer Vision, 2003. Proceedings. Ninth IEEE International Conference on, pages 591-596. IEEE, 2003.

[3]Yuanyuan Ding, Feng Li, Yu Ji, and Jingyi Yu. Dynamic fluid surface acquisition using a camera array. In Computer Vision (ICCV), 2011 IEEE International Conference on, pages 2478–2485. IEEE, 2011.

[4]Thomas Bonfort, Peter Sturm, and Pau Gargallo. General specular surface triangulation. In Computer Vision–ACCV 2006, pages 872–881. Springer, 2006.

[5]Silvio Savarese, Min Chen, and PietroPerona. Local shape from mirror reflections. International Journal of Computer Vision, 64(1):31–67, 2005.

[6]Yuanyuan Ding, Jingyi Yu, and Peter Sturm. Recovering specular surfaces using curved line images. In Computer Vision and Pattern Recognition, 2009. CVPR 2009. IEEE Conference on, pages 2326–2333. IEEE, 2009.