Position, rotation, and scale invariant optical correlation

Position-invariant, rotation-invariant, and scale-invariant process for binary image recognition

A novel recognition process is presented that is invariant under position, rotation, and scale changes. The recognition process is based on the Fang-Häusler transform [Appl. Opt. 29, 704 (1990)] and is applied to the autoconvolved image, rather than to the image itself. This makes the recognition process sensitive not only to the image histogram but also to its detailed pattern, resulting in a more reliable process that is also applicable to binary images. The proposed recognition process is demonstrated, by use of a fast algorithm, on several types of binary images with a real transform kernel, which contains amplitude, as well as phase, information. Good recognition is achieved for both synthetic and scanned images. In addition, it is shown that the Fang-Hausler transform is also invariant under a general affine transformation of the spatial coordinates.

Decoupled automated rotational and translational registration for functional MRI time series data: the DART registration algorithm

A rapid, in-plane image registration algorithm that accurately estimates and corrects for rotational and translational motion is described. This automated, one-pass method achieves its computational efficiency by decoupling the estimation of rotation and translation, allowing the application of rapid cross-correlation and cross-spectrum techniques for the determination of displacement parameters. k-space regridding and modulation techniques are used for image correction as alternatives to linear interpolation. The performance of this method was analyzed with simulations and echo-planar image data from both phantoms and human subjects. The processing time for image registration on a Hewlett-Packard 735/125 is 7.5 s for a 128 x 128 pixel image and 1.7 s for a 64 x 64 pixel image. Imaging phantom data demonstrate the accuracy of the method (mean rotational error, -0.09 degrees; standard deviation = 0.17 degrees; range, -0.44 degrees to +0.31 degrees; mean translational error = -0.035 pixels; standard deviation = 0.054 pixels; range, -0.16 to +0.06 pixels). Registered human functional imaging data demonstrate a significant reduction in motion artifacts such as linear trends in pixel time series and activation artifacts due to stimulus-correlated motion. The advantages of this technique are its noniterative one-pass nature, the reduction in image degradation as compared to previous methods, and the speed of computation.

Pattern recognition using invariants defined from higher order spectra: 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants.

Minimum-mean-square-error filters for detecting a noisy target in background noise

A minimum-mean-square-error filter is proposed to detect a noisy target in spatially nonoverlapping background noise. In this model, both the background noise that is spatially nonoverlapping with the target and the noise that is additive to the target and the input image are considered. The criterion used to design the filter is to minimize the mean-square-error between the filter output and a delta function located at the target position in the presence of the noise. Computer-simulation results for a number of noisy input images are presented, and the performance of the filter is determined. We also test the filter discrimination against undesired objects and tolerance to target distortions, such as rotation and scaling.

Neural-network classifiers for automatic real-world aerial image recognition

We describe the application of the multilayer perceptron (MLP) network and a version of the adaptive resonance theory version 2-A (ART 2-A) network to the problem of automatic aerial image recognition (AAIR). The classification of aerial images, independent of their positions and orientations, is required for automatic tracking and target recognition. Invariance is achieved by the use of different invariant feature spaces in combination with supervised and unsupervised neural networks. The performance of neural-network-based classifiers in conjunction with several types of invariant AAIR global features, such as the Fourier-transform space, Zernike moments, central moments, and polar transforms, are examined. The advantages of this approach are discussed. The performance of the MLP network is compared with that of a classical correlator. The MLP neural-network correlator outperformed the binary phase-only filter (BPOF) correlator. It was found that the ART 2-A distinguished itself with its speed and its low number of required training vectors. However, only the MLP classifier was able to deal with a combination of shift and rotation geometric distortions.

Projection-invariant pattern recognition with a phase-only logarithmic-harmonic-derived filter

A phase-only filter based on logarithmic harmonics for projection-invariant pattern recognition is presented. This logarithmic-harmonic-derived filter is directly calculated in the Fourier plane. With respect to normal logarithmic-harmonic filters it provides a smaller variation of the correlation intensity with the projection factor of the target. Computer and optical experiments are presented.

Rotation- and scale-invariant feature extraction by a diffractive optical inner-product transform

A diffractive optical element that is capable of extracting rotation- and scale-invariant features from input images is presented. The diffractive optical element performs an inner product between the input image and a set of basis functions. This set of basis functions is derived from that used in the Fourier-Mellin transform. Simulated results from scaled and rotated versions of two input images are presented.

On the reconstructive matching of multidimensional objects

To determine a known object position and orientation within a scene is a task of fundamental importance. A scheme called reconstructive matching (RM), which is inherently invariant to shift, rotation, and optionally to scale changes is introduced. RM decomposes the matching within the source space into a set of mutually independent processes of dimensionality reduced by one. Applied to computerized tomography (CT), the approach allows CT object matching prior to their reconstruction.

An FFT-based technique for translation, rotation, and scale-invariant image registration

This correspondence discusses an extension of the well-known phase correlation technique to cover translation, rotation, and scaling. Fourier scaling properties and Fourier rotational properties are used to find scale and rotational movement. The phase correlation technique determines the translational movement. This method shows excellent robustness against random noise.

Performance of minimum-mean-square-error filters for spatially nonoverlapping target and input-scene noise

Using computer simulations, we investigate the performance of a minimum-mean-square-error filter for input-scene noise that is spatially nonoverlapping (disjoint) with a target for a limited set of images. Different input-scene-noise statistics are used to test the filter performance. We show that in the presence of spatially nonoverlapping target and input-scene noise, the output of the minimummean- square-error filter has a well-defined correlation peak, small sidelobes, and a high peak-to-correlationenergy ratio compared with other widely used filters such as the classical matched filter, the phase-only filter, and the inverse filter. We also test the robustness of the minimum-mean-square-error filter to errors in noise statistics used in the filter design. We show that, for the images tested here, the performance of the minimum-mean-square-error filter is not sensitive to errors in noise statistics and the filter can detect the target even if a considerable error exists. The discrimination capability and the illumination sensitivity of the minimum-mean-square-error filter are also tested.

Optical correlation: influence of the coding of the input image

We analyze the influence of different optical coding methods of the input image in optical correlators. The noise robustness and the optical efficiency of the correlator are investigated. We show in particular that the signal-to-noise ratio is greatly dependent on the coding method. It decreases drastically for large phase modulation.

Algorithm of invariant image description by the use of a modified Gabor transform

A scale-invariant algorithm of image description that is derived from the investigations of the neural structure of striate complex modules is proposed. First an image is preprocessed by difference-of-Gaussians functions, then the Gabor expansion in modules of different scales is used, and a group of the most excited modules is looked for with the help of scale weighting functions (SWF's). Finally, the image code is calculated as a linear combination of the output signals from the Gabor modules. The coefficients of this linear combination correspond to the SWF selected in the previous step. The scales of Gabor modules are chosen to be a logarithmic sequence with a half-octave step. Because of the SWF method, the described algorithm takes into account all the image sizes on a continuum between the minimum and the maximum scales of the Gabor modules.

Scale-invariant binary phase-only matched filter using a ferroelectric-liquid-crystal spatial light modulator

We describe the implementation of a scale-invariant binary phase-only matched filter using a 128 × 128 ferroelectric spatial light modulator. A 5-dB discrimination was obtained between a 10-image training set of highly correlated characters (E's and F's) over a scale range of 1.0 to 1.5.

Optimum filter for detection of a target in nonoverlapping scene noise

A filter function is derived for input signals containing a target that is spatially disjoint (that is, nonoverlapping) with the input scene noise. The optimization metric is the ratio of the square of the expected value of the correlation peak to the expected value of the output signal energy. In this model the effects of the nonwhiteness of the scene noise, the nonstationarity of the scene noise that is due to the limited size of the input scene, the nonoverlapping of the target and the scene noise, and the unknown variations of the target illumination are considered. We show that, for the nonoverlapping target and the scene noise, the target window and the scene-noise window strongly influence the optimum filter function.

Real filter based on Mellin radial harmonics for scale-invariant pattern recognition

Several theoretical and experimental studies are developed in order to simplify the construction of filters based on Mellin radial harmonics (MRH) for scale-invariant pattern recognition. A real filter based on MRH is designed. The impulse response of the filter is a hermitic function, obtained by a suitable modification of a MRH component. This real filter has the same scale invariance as the conventional complex MRH filters, with the main advantage of its simplicity. Both computer simulations and optical experiments are presented.

Invariant optical-pattern recognition based on a contour bank

We propose a new optical pattern-recognition method that is invariant to shift, rotation, and scale changes. By means of a zero-order circular-harmonic filter the input object can be transformed into a correlation peak whose outline retains a shape similar to the outline of the input object. After multilevel thresholding and binarization, a bank composed of many contours with different sizes is formed. The invariant recognition can be obtained by a small contour line being taking as a reference and its second-order circular-harmonic component being taken as a filter. In addition to the scale invariance the correlation peak is superior to the classical circular-harmonic filter and the phase-only circular-harmonic filter in terms of peak intensity, half-maximum width, and peak-to-sidelobe ratio.

Nonlinear joint-transform correlation: an optimal solution for adaptive image discrimination and input noise robustness

We develop a processor for pattern recognition that is optimum in terms of discrimination and is tolerant to variations of the object to be recognized. This optimum processor is found to be adaptive nonlinear joint-transform correlator.

Optical processing for semiautonomous terminal navigation and docking

An optical cross correlator that recognizes a single object is suitable for performing a single-vision function, such as pattern recognition for semiautonomous navigation, landing, and docking of vehicles to a predesignated landing mark. The optical cross correlator, with a video input from a simple imaging system and the output of the optical correlation plane processed with standard star tracker software, produces sufficient information for a spacecraft's terminal homing navigation system to complete a docking maneuver. We describe the application of the optical cross correlator to a landing on a simulated space station.

Automatic spatial frequency selection algorithm for pattern recognition by correlation

We describe an approach to compute filters that automatically performs a spatial frequency selection to improve interclass discrimination and to reduce intraclass sensitivity. This approach is achieved by using as input to the filter synthesis a set of reference images to compute the filters and a set of distorted images to introduce the distortion or noise model of the reference images. Simulation results of correlation examples are provided for two pattern-recognition problems and are compared with the ones obtained with the standard minimum average correlation energy filters.

Invariant pattern recognition using angular signature functions

A new concept for invariant pattern recognition is presented that uses object contour information. First, an angular signature of the object contour is obtained by a nonlinear operation applied to two-dimensional directional convolutions with a long, narrow kernel. The angular signature function is normalized by either its area or its energy to achieve quasi-invariance to scale. The resulting signature is then compared with template signatures for the invariant recognition for which an angular similarity measure is obtained from a one-dimensional correlation between the two signatures. Numerical experiments demonstrate that the method discussed exhibits invariance to shift and angular orientation and quasi-invariance to scale.

Optimality of trade-off filters

We compare the optimal trade-off approach for synthetic discriminant function filters and an approach introduced recently, the minimum noise and correlation energy filter, using an objective quantitative figure of merit. A new general definition of multicriteria optimal trade-off correlation filters is introduced based on this comparison.

3-D repositioning and differential images of volumetric CT measurements

In quantitative computed tomography (QCT), time serial measurements are performed to detect a global bone density loss or to identify localized bone density changes. A prerequisite for an unambiguous analysis is the comparison of identical bone volumes. Usually, manual repositioning is too coarse. A mathematical procedure that allows matching two three-dimensional image volumes is presented. The algorithm is based on correlation techniques. The procedure has been optimized and applied to computer-tomographic 3-D images of the human knee. It has been tested with both artificially created and in vivo measured image data. Typical differential images calculated from real bone measurements are presented.

Theoretical framework for the design of purely real synthetic-discriminant-function-type correlation filters

A general algorithm for synthesizing purely real correlation filters in the frequency domain is developed by using the method of Lagrange multipliers. This method can be applied to filters that are derived by using linearly constrained quadratic minimization. The synthesis of purely real versions of minimum average correlation energy filters, minimum-variance synthetic discriminant functions, and other synthetic-discriminant-function-type filters is discussed to illustrate this approach. Their performance is found to be somewhat less than that of the original complex filters but still adequate for practical applications. The main advantage of this approach is that optimum purely real filters can be generated that are easy to implement in spatial light modulators without holograms and that yield the correlation output on the zero-order beam.

Compact photorefractive correlator for robotic applications

We design, implement, and test a multichannel photorefractive optical joint transform correlator that is capable of performing sorting tasks for robotic applications. The use of mini-YAG lasers and liquid-crystal spatial light modulators, in conjunction with updatable holographic BSO crystals, results in a compact correlator (600 mm x 300 mm x 300 mm) with real-time capabilities (100-ms recognition speed). Flexibility is a built-in feature, and correlation is demonstrated for various applications. Electronic and optical preprocessing and postprocessing for improving demonstrator performances are also discussed.

Integral logarithmic transform: theory and applications

Integral logarithmic transforms (LT's) are defined for both one- and two-dimensional input functions. These have the desirable properties of linearity and invariance to scale change of the input. One of the two-dimensional LT's is additionally invariant to rotation. The LT's are conveniently inverted by simple differentiation. Also, they are amenable to optical analog implementation by using incoherent light and simple collimating lenses. As an application, the problem of noise suppression of an arbitrarily scaled image, by using Wiener filtering, is considered. Use of the LT of the image data as a preprocessing step permits the creation of a single Wiener filter optimized for use at all scales of magnification. Finally, application to a problem of character recognition and matched filtering is proposed.

Optimal trade-off filters for noise robustness, sharpness of the correlation peak, and Horner efficiency

Filters that have optimal trade-offs among the criteria of noise robustness, sharpness of the correlation peak, and Horner efficiency are presented, and an explicit mathematical expression is provided. Owing to their optimality, these filters provide a figure of merit and then permit a rigorous characterization of filter performances for optical pattern recognition.

Effective hybrid processor to compute image moments for pattern recognition

A hybrid optical-digital processor is presented for computing the invariant moments of images in real time, which consists of a holographic mask, two lenses, a charge-coupled-device detector, and a microcomputer. The processor is tested by inputting some roman letters, and the produced results show that the invariant moments of a letter are approximately independent of shift and rotation and that the moments are distinct with different letters.

Nonredundant filters for pattern recognition and orientation estimation of rotated images

We describe a method to implement the recognition and the orientation determination of in-plane rotated images by means of nonredundant correlation filters which maximize the number of discernible patterns. The filters are computed with the minimum averaged correlation energy algorithm on specifically prefiltered reference images, with a view to the foreseen application, to reduce the intraclass sensitivity and improve the interclass discrimination. Simulation results of the correlation are provided and compared with those obtained with the standard minimum averaged correlation energy filters.

Phase selection of synthetic discriminant function filters

In this paper, we address the problem of correlation peak phase selection for synthetic discriminant function filters. We show that the minimization of the output variance and the optimization of the correlation peak form are problems of the same complexity (analogous to the determination of the ground state of a magnetic disordered system). We propose a general framework and, with examples, we show that, although the variance reduction by a proper selection of the correlation peak phases can be interesting in some situations, the optimization of the sharpness of the correlation peak is often more fruitful.

Filter design for optical pattern recognition: multicriteria optimization approach

A method of constructing optimal multicriteria filters for optical pattern recognition is presented. In the particular case of synthetic discriminant function filters, this method is illustrated for double-optimization criteria, and filters that are not overspecialized are obtained, in contrast with traditional techniques. Furthermore, a rigorous comparison between different filters, with respect to the considered criteria, is provided with this approach.

Correlation filters for target detection in a Markov model background clutter

The performance of distortion-invariant correlation filters in the presence of background clutter is addressed. Background images are modeled as Markov noise processes, and a synthesis procedure for the optimal filter is described. It is shown that spatially filtering the training set images eliminates the need for the inversion of large noise covariance matrices, thus leading to a computationally efficient filter realization. The effect of errors (in the estimation of clutter correlation coefficient) on filter performance is theoretically analyzed, and a bound on the relative degradation of the SNR due to such errors is presented.

Scale invariant pattern recognition with logarithmic radial harmonic filters

A generalized approach leads to spatial filters that accept changes of scale by a factor of 4. The procedure employs phase filters with reduced tolerance requirements and achieves high discrimination capability and efficient light throughput. Computer simulations and laboratory experiments show the advantages of this novel approach.