Multichannel single-output color pattern recognition by use of a joint-transform correlator

A novel method for performing color image recognition by the use of the coherent joint-transform correlator is introduced. The input plane of the proposed method is a spatial rearrangement of the separation into color channels of both the color input scene and the color target. This input plane is gray scaled and monochromatic, thus it can be displayed by the use of amplitude spatial light modulators to achieve real-time operation. The system provides a single output-plane result of the optical coherent addition of the separate channels' correlation outputs. At the output plane no electronic postprocessing is needed, and the detection decision is achieved simply by the application of threshold detection. Experimental results and computer simulations are presented to demonstrate the abilities of this system.     

Rotationally invariant pattern recognition by use of linear and nonlinear cascaded filters

We discuss the merits of using single-layer (linear and nonlinear) and multiple-layer (nonlinear) filters for rotationally invariant and noise-tolerant pattern recognition. The capability of each approach is considered with reference to a two-class, rotation-invariant, character recognition problem. The minimum average correlation energy (MACE) filter is a linear filter that is generally accepted to be optimal for detecting signals that are free from noise. Here it is found that an optimized MACE filter cannot differentiate between the characters E and F in a rotation-invariant manner. We have found, however, that this task is possible when a single optimized linear filter is used to achieve the required response when a nonlinear threshold function is included after the filter. We show that this structure can be cascaded to form a multiple-layer, cascaded filter and that the capability of such a system is enhanced by its increased noise tolerance in the character recognition problem. Finally, we show the capability of a two-layer cascade as a means to detect different species of bacteria in images obtained from a phase-contrast microscope.     

Windowed Fourier transform for fringe pattern analysis

Fringe patterns in optical metrology systems need to be demodulated to yield the desired parameters. Time-frequency analysis is a useful concept for fringe demodulation, and a windowed Fourier transform is chosen for the determination of phase and phase derivative. Two approaches are developed: the first is based on the concept of filtering the fringe patterns, and the second is based on the best match between the fringe pattern and computer-generated windowed exponential elements. I focus on the extraction of phase and phase derivatives from either phase-shifted fringe patterns or a single carrier fringe pattern. Principles as well as examples are given to show the effectiveness of the proposed methods.     

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.     

Wavelet-transform-based composite filters for invariant pattern recognition

A wavelet-transformation-based optical processor for performing invariant pattern recognition is suggested. It contains a composite filter that consists of several wavelet daughter functions derived from the reference object. The intensity of the correlation peak is determined to be invariant to various deformations of the reference object. Computer simulations show explicitly the promising capability of the new technique. Laboratory experimental results are given.     

Near-field Fourier transform polarimetry by use of a discrete space-variant subwavelength grating

We present a unique method for real-time polarization measurement by use of a discrete space-variant subwavelength grating. The formation of the grating is done by discrete orientation of the local subwavelength grooves. The complete polarization analysis of the incident beam is determined by spatial Fourier transform of the near-field intensity distribution transmitted through the discrete subwavelength dielectric grating followed by a subwavelength metal polarizer. We discuss a theoretical analysis based on Stokes-Mueller formalism, as well as on Jones calculus, and experimentally demonstrate our approach with polarization measurements of infrared radiation at a wavelength of 10.6 microm.     

Gridding-based direct Fourier inversion of the three-dimensional ray transform

We describe a fast and accurate direct Fourier method for reconstructing a function f of three variables from a number of its parallel beam projections. The main application of our method is in single particle analysis, where the goal is to reconstruct the mass density of a biological macromolecule. Typically, the number of projections is extremely large, and each projection is extremely noisy. The projection directions are random and initially unknown. However, it is possible to determine both the directions and f by an iterative procedure; during each stage of the iteration, one has to solve a reconstruction problem of the type considered here. Our reconstruction algorithm is distinguished from other direct Fourier methods by the use of gridding techniques that provide an efficient means to compute a uniformly sampled version of a function g from a nonuniformly sampled version of Fg, the Fourier transform of g, or vice versa. We apply the two-dimensional reverse gridding method to each available projection of f, the function to be reconstructed, in order to obtain Ff on a special spherical grid. Then we use the three-dimensional gridding method to reconstruct f from this sampled version of Ff. This stage requires a proper weighting of the samples of Ff to compensate for their nonuniform distribution. We use a fast method for computing appropriate weights that exploits the special properties of the spherical sampling grid for Ff and involves the computation of a Voronoi diagram on the unit sphere. We demonstrate the excellent speed and accuracy of our method by using simulated data.     

双色正弦投影傅里叶变换轮廓术方法研究

提出双色正弦条纹投影方法来提高 FTP 的测量范围并保持其实时特点。只需采集一帧双色变形条纹,从中分离出两个有 π 位相差的分量,通过背景和对比度校正,得到一帧消零频的变形条纹图,并且自动生成物体轮廓的二元模板。此模板结合调制度信息相可以生成可靠性模板,指导相位展开,避免物体轮廓以外相位展开误差的传递;结合参考条纹可以完成变形条纹的扩充,提高频域的分辨率。     

Modification of Karhunen-Loeve transform for pattern recognition

Application of the Karhunen-Loeve transform in pattern recognition problems necessitates knowledge of the mean vectors for the training sets of different classes for construction of the respective covariance matrices. This modality poses problems for recognizing an unknown signal in a multi-class environment and for its on-line implementation. This is becausea priori it is unknown which mean vector of the several classes is to be subtracted from an unknown input signal. To remove this difficulty a global mean approach has been proposed. The proposed method has been applied to synthetic and experimentally observed acoustic signals successfully and its performance with respect to pattern recognition and data compression has been compared with the conventional method.     

Modification of Karhunen-Loeve transform for pattern recognition

Application of the Karhunen-Loeve transform in pattern recognition problems necessitates knowledge of the mean vectors for the training sets of different classes for construction of the respective covariance matrices. This modality poses problems for recognizing an unknown signal in a multi-class environment and for its on-line implementation. This is becausea priori it is unknown which mean vector of the several classes is to be subtracted from an unknown input signal. To remove this difficulty a global mean approach has been proposed. The proposed method has been applied to synthetic and experimentally observed acoustic signals successfully and its performance with respect to pattern recognition and data compression has been compared with the conventional method.     

Spherical nonlinear correlations for global invariant three-dimensional object recognition

We define a nonlinear filtering based on correlations on unit spheres to obtain both rotation- and scale-invariant three-dimensional (3D) object detection. Tridimensionality is expressed in terms of range images. The phase Fourier transform (PhFT) of a range image provides information about the orientations of the 3D object surfaces. When the object is sequentially rotated, the amplitudes of the different PhFTs form a unit radius sphere. On the other hand, a scale change is equivalent to a multiplication of the amplitude of the PhFT by a constant factor. The effect of both rotation and scale changes for 3D objects means a change in the intensity of the unit radius sphere. We define a 3D filtering based on nonlinear operations between spherical correlations to achieve both scale- and rotation-invariant 3D object recognition.     

Invariant pattern recognition by use of wavelength multiplexing

Rotation-invariant pattern recognition can be achieved with circular-harmonic decomposition. A common problem with such a filter is that, because it is only a single term out of the circular decomposition, it does not contain much of the reference object's energy. Thus, the obtained correlation selectivity is low. This problem is solved by use of wavelength multiplexing. First, different harmonic terms are encoded by different wavelengths, and then they all are added incoherently in the output correlation plane. This process leads to rotation-invariant pattern recognition with a higher discrimination ability.     

Single-channel polychromatic pattern recognition by the use of a joint-transform correlator

We present a single-channel system for color image recognition that is based on a joint-transform correlator setup. The color images are encoded as phase and amplitude functions, inspired from the Munsell color representation. A real-time implementation of the new codification method can be achieved by the use of a spatial light modulator operating in phase-only modulation mode. We determine the optimal codification for a linear color-phase code. Its performance is compared with a conventional multichannel correlator by means of computer simulations. Experimental results are also presented.     

Windowed Fourier transform for fringe pattern analysis: addendum

Novel approaches based on windowed Fourier transform for demodulation of fringe patterns were previously presented [Appl. Opt. 43, 2695-2702 (2004)], where extraction of phase and phase derivatives from either phase-shifted fringe patterns or a single-carrier fringe pattern was the main focus. I show that the same methods can be applied to process a single closed-fringe pattern in either noise reduction or phase approximation, which adds to the versatility of the windowed Fourier-transform method for fringe pattern analysis.     

Modified Fourier transform method for interferogram fringe pattern analysis

A modified Fourier transform method for interferogram fringe pattern analysis is proposed. While it retains most of the advantages of the Fourier transform method, the new method overcomes some drawbacks of the previous method. It eliminates the assumptions of slowly varying phase variation in the test section and the constant spatial carrier frequency. It also extends the frequency bandwidth and avoids phase distortion caused by discreteness of the sampling frequency. Both numerical simulation and experimental examination are performed to evaluate the performance of the method.     

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.     

Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform

A novel technique that uses a fan two-dimensional (2D) continuous wavelet transform (CWT) to phase demodulate fringe patterns is proposed. The fan 2D CWT algorithm is tested by using computer generated and real fringe patterns. The result of this investigation reveals that the 2D CWT technique is capable of successfully demodulating fringe patterns. The proposed algorithm demodulates fringe patterns without the requirement of removing their background illumination prior to the demodulation process. Also, the algorithm is exceptionally robust against speckle noise. The performance of the 2D CWT technique in fringe pattern demodulation is compared with that of the 1D CWT algorithms. This comparison indicates that the 2D CWT outperforms its 1D counterpart for this application.     

Vectorial signatures for invariant recognition of position,rotation and scale pattern recognition

We investigate the development and utilization of vectorial signatures obtained from the application of properties of the scale and Fourier transform for images recognition. The signatures were applied to different input scenes. In order to find a new invariant digital system two one-dimensional vectors were calculated to achieve different mathematical transformations in the target as well as in the input scene. To recognize a target, signatures were compared, calculating the Euclidean distance between the target and the input scene. These sets are generated from two sources: alphabetical letters in Arial type and digital images of seven different copepod species. Considering the great similarity between the copepod species used in this work and between the male and female of each species the results obtained are very good.     

Color pattern recognition in white-light joint transform correlation

We first discuss the restriction on the incoherent source and the color filters in a joint transform correlation (JTC) system for white-light color pattern recognition and then report on a novel, to our knowledge, solution of channeling in a white-light JTC system, using a tricolor grating to encode the color patterns in real time. The theoretical analyses and the experimental results show not only that the restriction on the experimental condition is relieved but also that parallel channeling of the power spectra of the encoded pattern is easily performed. In addition, the zero-order power spectrum also forms a useful channel for the shape-only correlation.