Three-dimensional optical Fourier transform and correlation

Review of holographic-based three-dimensional object recognition techniques [invited]

With the advancement of computing and optical technologies, it is now possible to capture digital holograms of real-life object scenes. Theoretically, through the analysis of a hologram, the three-dimensional (3D) objects coded on the hologram can be identified. However, being different from an optical image, a hologram is composed of complicated fringes that cannot be analyzed easily with traditional computer vision methods. Over the years, numerous important research investigations have been attempted to provide viable solutions to this problem. The aim of this work is three-fold. First, we provide a quick walkthrough on the overall development of holographic-based 3D object recognition (H3DOR) in the past five decades, from film-based approaches to digital-based innovation. Second, we describe in more detail a number of selected H3DOR methods that are introduced at different timelines, starting from the late sixties and then from the seventies, where viable digital holographic-based 3D recognition methods began to emerge. Finally, we present our work on digital holographic, pose-invariant 3D object recognition that is based on a recently introduced virtual diffraction plane framework. As our method has not been reported elsewhere, we have included some experimental results to demonstrate the feasibility of the approach.

Review of three-dimensional holographic imaging by multiple-viewpoint-projection based methods

Methods of generating multiple viewpoint projection holograms of three-dimensional (3-D) realistic objects illuminated by incoherent white light are reviewed in this paper. Using these methods, it is possible to obtain holograms with a simple digital camera, operating in regular light conditions. Thus, most disadvantages characterizing conventional digital holography, namely the need for a powerful, highly coherent laser and extreme stability of the optical system, are avoided. The proposed holographic processes are composed of two stages. In the first stage, regular intensity-based images of the 3-D scene are captured from multiple points of view by a simple digital camera. In the second stage, the acquired projections are digitally processed to yield the complex digital hologram of the 3-D scene, where no interference is involved in the process. For highly reflecting 3-D objects, the resulting hologram is equivalent to an optical hologram of the objects recorded from the central point of view. We first review various methods to acquire the multiple viewpoint projections. These include the use of a microlens array and a macrolens array, as well as digitally generated projections that are not acquired optically. Next, we show how to digitally process the acquired projections to Fourier, Fresnel, and image holograms. Additionally, to obtain certain advantages over the known types of holograms, the proposed hybrid optical-digital process can yield novel types of holograms such as the modified Fresnel hologram and the protected correlation hologram. The prospective goal of these methods is to facilitate the design of a simple and portable digital holographic camera that can be useful for a variety of practical applications, including 3-D video acquisition and various types of biomedical imaging. We review several of these applications to signify the advantages of multiple viewpoint projection holography.

Image quality improvement of digital holography by superposition of reconstructed images obtained by multiple wavelengths

A method to improve the image quality of a digital holographic reconstructed image by means of speckle reduction is proposed. The size and position of the speckles are changed according to the wavelengths to record a digital hologram. By superposing reconstructed images with different wavelengths, the effect of speckle is reduced so that the image quality is improved. Optical experiments are given to confirm the proposed method.

Recognition and classification of three-dimensional phase objects by digital Fresnel holography

We demonstrate the validity of wavelet-based processing for recognition and classification of three-dimensional phase objects. One Fresnel digital hologram of each of the three-dimensional (3-D) phase objects to be classified is recorded. The electronic holograms are processed digitally to permit 3-D object information to be retrieved as two-dimensional digital complex images. We use a Mexican-hat wavelet- matched filter (WMF) to enhance the correlation peak and discriminate between the objects. The WMF performs a wavelet transform (WT) to enhance the significant features of the images and the correlation of the WT coefficients thus obtained. We compare the feasibility of a WMF-based object classifier with the matched-filter-based classifier to classify our four 3-D phase objects in a 3-D scene into true or false classes with minimal error.

Scale-invariant recognition of three-dimensional objects by use of a quasi-correlator

A method of scale-invariant recognition of three-dimensional (3-D) objects is presented. Several images of the observed scene are recorded under white-light illumination from several different points of view and compressed into a single complex two-dimensional matrix. After filtering with a single scale-invariant filter, the resultant function is then coded into a computer-generated hologram (CGH). When this CGH is coherently illuminated, a correlation space is reconstructed in which light peaks indicate the existence and location of true targets in the tested 3-D scene. The light peaks are detectable for different sizes of the true objects, as long as they are within the invariance range of the filter. Experimental results in a complete electro-optical system are presented, and comparisons with other systems are investigated by use of computer simulation.

Object recognition using three-dimensional optical quasi-correlation

A novel method of three-dimensional (3-D) object recognition is proposed. Several projections of a 3-D target are recorded under white-light illumination and fused into a single complex two-dimensional function. After proper filtering, the resulting function is coded into a computer-generated hologram. When this hologram is coherently illuminated, a correlation space is reconstructed such that light peaks indicate the existence and locations of true targets in the observed 3-D scene. Experimental results and comparisons with results of another 3-D object recognition technique are presented.

Frequency-multiplexed profilometric phase coding for three-dimensional object recognition without 2pi pi phase ambiguity

A novel phase-coding technique based on Fourier-transform profilometry (FTP) is proposed for three-dimensional object recognition. Two spatially multiplexed grating patterns of different spatial frequencies are projected simultaneously onto the objects-target, and the phase changes in the distorted patterns are detected. An algebraic addition or subtraction of these phase values is utilized to code the two-dimensional plans of the objects-target with spatial harmonic modulations. The phase-coded plans of the objects and the target are cross correlated digitally to yield a high correlation peak at the target location. The 2pi ambiguity of the phase associated with FTP has been resolved in correlation results without recourse to phase unwrapping. Experimental results show an excellent discrimination capability for target recognition.

Neural network for three-dimensional object recognition based on digital holography

We present a two-layer neural network for processing of three-dimensional (3D) images that are obtained by digital holography. The network is trained with a real 3D object to compute the weights of the layers. Experiments are presented to illustrate the system performance. The system is designed to detect a 3D object in the presence of various distortions. As an example, experiments are presented to illustrate how the system is able to recognize a 3D object with 360 degrees out-of-plane rotation.

Shift-invariant three-dimensional object recognition by means of digital holography

We present an optoelectronic method to analyze three-dimensional (3D) scenes that is able to detect the presence, and also the position and orientation, of a reference 3D object. The data-acquisition procedure is based on digital holography. A phase-shifting interferometer records a single digital Fresnel hologram of the 3D scene with an intensity-recording device. Holographic information of the 3D reference object is also obtained with the same method. Correlation techniques are then applied to recognize the presence and position of the 3D reference object in the 3D scene. The technique also allows us to detect the 3D reference with a small out-of-plane rotation. Preliminary experimental results are presented that demonstrate the theory.

Real-time three-dimensional object recognition with multiple perspectives imaging

A novel system for recognizing three-dimensional (3D) objects by use of multiple perspectives imaging is proposed. A 3D object under incoherent illumination is projected into an array of two-dimensional (2D) elemental images by use of a microlens array. Each elemental 2D image corresponds to a different perspective of the 3D object. Multiple perspectives imaging based on integral photography has been used for 3D display. In this way, the whole set of 2D elemental images records 3D information about the input object. After an optical incoherent-to-coherent conversion, an optical processor is employed to perform the correlation between the input and the reference 3D objects. Use of micro-optics allows us to process the 3D information in real time and with a compact optical system. To the best of our knowledge this 3D processor is the first to apply the principle of integral photography to 3D image recognition. We present experimental results obtained with both a digital and an optical implementation of the system. We also show that the system can recognize a slightly out-of-plane rotated 3D object.

Three-dimensional optical correlator with general complex filters

A new type of electro-optical three-dimensional (3-D) correlator is proposed and demonstrated. A 3-D object scene, observed by multiple cameras from several points of view, is correlated with a 3-D complex computer-generated function. This correlator is a hybridization of the joint transform and the VanderLugt correlators, and, as such, it allows correlations to be made between 3-D real-world objects and 3-D general complex functions. Experimental results are presented.

Three-dimensional object recognition by use of digital holography

We present a technique for performing three-dimensional (3D) pattern recognition by use of in-line digital holography. The complex amplitude distribution generated by a 3D object at an arbitrary plane located in the Fresnel diffraction region is recorded by phase-shifting interferometry. The digital hologram contains information about the 3D object's shape, location, and orientation. This information allows us to perform 3D pattern-recognition techniques with high discrimination and to measure 3D orientation changes. Experimental results are presented.

Optical image recognition of three-dimensional objects

A three-dimensional (3-D) optical image-recognition technique is proposed and studied. The proposed technique is based on two-pupil optical heterodyne scanning and is capable of performing 3-D image recognition. A hologram of the 3-D reference object is first created and then is used to modulate spatially one of the pupils of the optical system; the other pupil is a point source. A 3-D target object to be recognized is then scanned in two dimensions by optical beams modulated by the two pupils. The result of the two-dimensional scan pattern effectively displays the correlation of the holographic information of the 3-D reference object and that of the 3-D target object. A strong correlation peak results if the two pieces of the holographic information are matched. We analyze the proposed technique and thereby lay a theoretical foundation for optical implementations of the idea. Finally, computer simulations are performed to verify the proposed idea.

Three-dimensional joint transform correlator

The three-dimensional (3-D) joint transform correlator is demonstrated with realistic targets. Three-dimensional objects observed by multiple cameras are correlated with a 3-D reference object. The number of cameras and their directions of observation are particularly considered.