Phase-only Correlation Research Articles

APOC-based ranging method with multipath mitigation in the NLOS environment

Asymmetric phase-only correlation (APOC) is investigated in this paper, and, for the first time, is applied into the area of ranging by separating the direct signal from multipath signals. Measurement based on the 2.45-GHz wireless signal in non-line-of-sight (NLOS) environment indicates that APOC has superior performance in mitigating multipath signals when compared with the conventional correlation method, and thus is able to increase the ranging accuracy. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 47: 318–320, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21157

BA–POC-Based Ranging Method With Multipath Mitigation

Binary asymmetric–phase-only correlation (BA–POC) is investigated in this letter, and for the first time is applied into the area of ranging to help identify the line-of-sight (LOS) signal in multipath-abundant environments. Measurements made based on the 2.45-GHz wireless signal indicate that BA–POC has superior performance in mitigating multipath signals when compared with the conventional correlation method, and thus is able to increase the ranging accuracy.

Measurement of surface roughness by speckle correlation

Measurement of the roughness of solid surfaces by digital speckle correlation of video signals is reported. Speckle patterns appearing in the diffraction field of a laser-illuminated sample are taken by a CCD before and after the change of the incident angle or the laser wavelength, and their cross-correlation is calculated from which surface roughness can be evaluated. The theoretical cross-correlation function is first derived that describes speckle displacement and decorrelation. Its peak height is then provided as a function of the change of the incident angle or the wavelength. The decorrelation curve against speckle displacement is shown to depend on the surface roughness. The derived analytical relationships were verified by numerical simulations that used two-dimensional arrays of random numbers with various maximum values representing the maximum surface roughness. The relationship between the normal correlation calculated by the theory and the phase-only correlation adopted in the experiment was also evaluated by the simulation. In experiments various roughness standards for metal were measured by using a quick processor employing the phase-only correlation algorithm. The results were compared with those obtained from a mechanical stylus, and good agreement was observed between them for root-mean-square roughnesses between several micrometers and several tens of micrometers.

Morphological phase-only correlation

We propose a modified version of morphological correlation (MC), morphological phase-only correlation (MPC), by replacing the JTC operation with phase-only filtering in the common MC implementation. The performance of MPC with noise-corrupted input scene and unknown input-scene illumination are investigated and compared with those of MC and linear correlation (LC). Simulation results show that MPC provides higher discriminability, sharper and higher correlation peaks, and better robustness in the presence of salt-and-pepper noise. MPC loses the illumination-invariant recognition of MC when input scene is brighter than reference, however its high DR is still ensured within a considerable range of illumination.

Commutative Reduced Biquaternions and Their Fourier Transform for Signal and Image Processing Applications

Digital signal and image processing using reduced biquaternions (RBs) are introduced in this paper. RBs are an extension of the complex numbers, following the doubling procedure. Two useful representations of RBs (e/sub 1/-e/sub 2/ form and matrix representation) are discussed in this paper. Besides, we propose a new representation of RBs (the polar form) to calculate the multiplication and conjugation of RBs easily. Furthermore, we define a unique and suitable RB norm and its conjugate. These definitions are similar and compatible with the complex numbers. The efficient algorithms of the discrete reduced biquaternion Fourier transform (DRBFT), convolution (DRBCV), correlation (DRBCR), and phase-only correlation are discussed in this paper. In addition, linear-time-invariant and symmetric multichannel complex systems can be easily analyzed by RBs. For color image processing, we define a simplified RB polar form to represent the color image. This representation is useful to process color images in the brightness-hue-saturation color space. Many different types of color template matching and color-sensitive edge detection (brightness, hue, saturation, and chromaticity matched edges) can be performed simultaneously by RBs.

Application of the Laser Speckle-Correlation Method for Determining the Shrinkage Vector of a Light-cured Resin

The purpose of this study was to develop a method to monitor the free-shrinkage vectors of a light-cured resin using laser speckle contrast measurement. The laser speckle contrast measurement system comprised a semiconductor laser, a speckle analyzer, and a computer-controlled data acquisition system. A light-cured resin was condensed into a glass tube and irradiated using a curing unit, the light intensity of which was adjusted to either 100 or 600 mW/cm2. The speckle patterns obtained from the lateral surface of the specimen were monitored using a CCD camera connected to a computer. The speckle images were analyzed using a phase-only correlation algorithm, and movements of the pattern were traced. The speckle pattern revealed rapid movement almost immediately after light exposure was initiated, and the orientation of free-shrinkage vectors is dependent on light intensity. When the specimens were irradiated at the lower light intensity, the free shrinkage vectors were oriented towards the light source. On the other hand, when irradiated at the higher light intensity, the free-shrinkage vectors of these specimens tended to orient towards the bottom surface. The effectiveness of the employed method to determine free-shrinkage vectors is thus proven through the results of this study.

Phase-only filtering on the three-dimensional Fourier spectrum of color images.

We propose what is to our knowledge a novel technique for filtering a two-dimensional multichannel color image based on its interpretation as a three-dimensional (3D) signal and the application of a 3D Fourier transform. The color image is considered to have the two usual spatial coordinates with the color distribution as the third dimension of the signal. This approach permits the 3D generalization of the usual phase-only filter and phase correlation, and color pattern recognition can be performed by means of a 3D correlation. We analyze two cases: whitening only along the color Fourier spectrum and whitening the whole 3D Fourier spectrum. We study the transformation induced in the color content of the image by the whitening of the color Fourier spectrum and how it affects the correlation distribution. In particular it is demonstrated that the whitening of the 3D Fourier spectrum improves the recognition performance of the correlation.

Phase-Only Correlation Ships and its Vision Sensing Applications

Phase-Only Correlation Ships and its Vision Sensing Applications

Tracking of Moving Object by Phase-only Correlation

A real-time tracking system that measures four-dimensional displacement of a moving object and that traces the object by directing a pair of cameras on three-axis robot is implemented and tested. In this system, the distance, rotation, and parallel displacement values of the object are measured by Phase-Only Correlation and Rotation-Invariant Phase-Only Correlation image processing techniques. It controls the pitch, roll, and yaw angles of the camera to locate the target in the stable position on the image, as well as keeps the size of the target on the image by magnifying or reducing the image, based on the measured distance using triangular surveying.

Investigation of a phase-only correlation technique for anatomical alignment of portal images in radiation therapy

A new image registration algorithm based on phase-only correlation is applied to portal images in radiation therapy to detect translational shift. The phase-only correlation shows a sharp peak in the correlation distribution as compared to the broad peak computed from conventional correlation using fast Fourier transform. In this paper, the algorithm of phase-only correlation is described and its applicability and robustness are tested when applied to portal images used in clinical radiation oncology. The results achieved give evidence that the phase-only correlation will deliver an alternative approach for image registration and image comparison, that may be applicable in routine clinical practice.

Theoretical analysis for the nonlinear frequency-selective joint-transform correlator

The theoretical analysis for a nonlinear and bipolar frequency-selective joint-transform correlator is reported without any impractical assumptions and verifield. The theoretical results are similar to those for a nonlinear and bipolar joint-transform correlator. In addition, the optimal threshold value for a bipolar frequency-selective joint-transform correlator is found to be zero. Moreover, a bipolar frequency-selective joint-transform correlator can provide a phase-only correlation signal with delta-function shape. The theoretical study for a DC-block bipolar frequency-selective joint-transform correlator is also given. It is shown that its autocorrelation peak remains the same as that without a DC block.

Adaptive real-time architectures for phase-only correlation

A video-rate correlator can be constructed with a phase-only spatial light modulator and a CCD camera. The phase of the Fourier transform of a signal and a reference image is determined by fringe-scanning interferometry. The two measured phase images are then subtracted. The optical Fourier transform of this difference produces the phase-only correlation response. This system can update both signal and reference images with live scenery. Currently, only the joint transform correlator has demonstrated this degree of adaptivity in real time. Physically compact versions of the correlator can be built with a single spatial light modulator and a Fourier-transform lens.

Gaussian–minimum average correlation energy filters

Correlation filters with sharp delta-function correlation peaks [such as phase-only filters and minimum average correlation energy (MACE) filters] do not recognize images on which they are not trained. We show that the MACE filter cannot always recognize intermediate images of true class objects (e.g., aspect views or rotations midway between two training images). New Gaussian-MACE filters offer a solution to this problem.

Binary Fourier phase-only correlation

A technique called binary Fourier phase-only correlation is proposed for an incoherent-optical-digital-electric hybrid system. This technique has the advantages of high discriminant ability, a small memory area, and a short processing time. This technique is applicable to digital computing systems.

Multifunction Nonlinear Signal Processor: Deconvolution And Correlation

We describe a multifunction nonlinear optical processor that can perform various types of operations such as image deconvolution and nonlinear correlation. This processor is joint power spectrum based and does not use any filters. In this technique both the input signal and the processing function are displayed side by side at the input plane of the processor. The joint power spectrum of the input signals is thresholded with varying nonlinearity to produce the specific operation. In image deconvolution the joint power spectrum is modified and hard clip thresholded to remove the amplitude distortion effects and to restore the correct phase of the original image. An amplitude mask averaged over an ensemble of images is assigned to the thresholded power spectrum to provide the amplitude magnitude of the restored image. In optical correlation, the Fourier transform interference intensity is thresholded to provide higher correlation peak intensity and a better defined correlation spot. We show that various types of correlation signals can be produced simply by varying the severity of the nonlinearity and without the need to synthesize the specific matched filter. For example, a phase-only correlation signal is produced by selecting the appropriate nonlinearity. An analysis of the nonlinear processor for image deconvolution is presented. Computer simulation of the proposed technique for a linearly smeared image is provided.

Rotation invariant phase-only and binary phase-only correlation

Phase-only circular harmonic filters and binary phase-only circular harmonic filters are proposed. Both filters have full rotation invariance and excellent performance for discrimination between objects and against background noise. Their properties have been studied and implemented for computer applications. The binary filters are appropriate for real-time applications using spatial light modulators.

Design elements of binary phase-only correlation filters

The basic design elements of binary phase-only filters (BPOFs) include the angle of a thresholding line in the complex plane and the offset from a center reference point of the pattern transformed in constructing the filter. These factors are analyzed, and a general formalism for the threshold-line angle variation is presented and related to the special cases of cosine-, sine-, and Hartley-BPOFs and to the general characteristics of the BPOF impulse response. The effects of these elements on correlation performance are investigated using computer simulations with realistic target and clutter patterns. The results indicate significant, but not major, variations of correlation performance for the cases studied.

Additional Properties Of The Phase-Only Correlation Filter

Computer simulations of the scaling and rotation sensitivity of a phase-only filter were performed, showing that it is much more sensitive to such input variations than is a classical matched filter. Values of the peak correlation spot power versus both rotation angle and scale factor are presented for both filter types. Several theorems are derived for calculating the optical efficiency of any filter in both input space and frequency space.