MATCHING IN 3-D

The demands for image recognition and display of three-dimensional (3-D) objects have rapidly increased in many areas, such as machine vision–based inspection or security scanning. Although researchers have investigated several methods for 3-D optical correlation, most of these suggestions are based on mapping three dimensions to two by use of several different 2-D perspectives and digital image processing techniques. Because holograms are intrinsically 3-D, a volume holographic processor offers an attractive method to recognize 3-D objects.¹ Such a system would provide high-capacity data storage and high-rate data transfer using massive parallelism.

The volume holographic recording method does not require the recording of multiple 2-D images. The object beam H interferes with an off-axis plane wave reference beam R in the Fresnel diffraction region. The resulting interference pattern is recorded in a photorefractive crystal. During the read process, the Fourier transform of the Fresnel diffraction pattern of the input image is given by where h and h' are the Fourier transform of H and H ', which are in turn the Fresnel transforms of the reference 3-D object U and the 3-D input U ', respectively. The degree of similarity between two inputs can be measured by  , where h₀ and h₀' are the Fourier transform of two inputs U and U ', respectively.

The 3-D object recognition system uses an argon-ion laser as a light source and an iron-doped lithium-niobate crystal as the recording media. In the diagram, objects labeled M are mirrors, P polarizers, L lenses, BE beam expander, PBS polarizing beam splitter, and HWP half-wave plate. CCD₂ captures the correlation peak.

In our photorefractive volume holographic 3-D object-recognition system, we use an argon-ion laser operating at 514.5 nm to record and read the holograms (see figure). We record the template of an object in a photorefractive iron-doped lithium niobate crystal (LiNbO₃:Fe), monitoring diffraction efficiency using a charge-coupled device camera (CCD₁). The lifetime of the stored hologram is long enough to perform a correlation experiment without any treatments, but for the practical application, it should be fixed by use of thermal or other fixing methods. To actually perform the correlation operation, we "read" the recorded hologram with the 3-D object beam under test. When the 3-D input object matches the template stored in the optical memory, it generates an autocorrelation peak, and the system recognizes the object as matching the template. In the case of a different input 3-D object, there is no correlation peak on the noise floor.

For comparison, we performed the correlation experiments using conventional 2-D input images of the 3-D object instead of the 3-D real object. For 2-D input images, there was no significant difference between autocorrelation and cross-correlation peaks. This shows that the discrimination capability of the 3-D recognition system is substantially better than its 2-D counterpart.

This all-optical processor can be easily combined with a massive optical data storage system to create a database system for 3-D real-object recognition. One can record many templates using various multiplexing methods, such as angle, wavelength, and shift multiplexing, or combinations of these. This processor also provides real-time operation with high capacity and high resolution. oe

References:

1. Seung-Ho Shin and Bahram Javidi, Opt. Lett. 26(15), 1161(2001).