Position, rotation, and scale invariant optical correlation

All-optical geometric image transformations enabled by ultrathin metasurfaces

Image processing plays a vital role in artificial visual systems, which have diverse applications in areas such as biomedical imaging and machine vision. In particular, optical analog image processing is of great interest because of its parallel processing capability and low power consumption. Here, we present ultra-compact metasurfaces performing all-optical geometric image transformations, which are essential for image processing to correct image distortions, create special image effects, and morph one image into another. We show that our metasurfaces can realize binary image transformations by modifying the spatial relationship between pixels and converting binary images from Cartesian to log-polar coordinates with unparalleled advantages for scale- and rotation-invariant image preprocessing. Furthermore, we extend our approach to grayscale image transformations and convert an image with Gaussian intensity profile into another image with flat-top intensity profile. Our technique will potentially unlock new opportunities for various applications such as target tracking and laser manufacturing.

Elimination of optical phase sensitivity in a shift, scale, and rotation invariant hybrid opto-electronic correlator via off-axis operation

The hybrid opto-electronic correlator (HOC) uses a combination of optics and electronics to perform target recognition. Achieving a stable output from this architecture has previously presented a significant challenge due to a high sensitivity to optical phase variations, limiting the real-world feasibility of the device. Here we present a modification to the architecture that essentially eliminates the dependence on optical phases, and demonstrate verification of the proposed approach. Experimental results are shown to agree with the theory and simulations, for scale, rotation and shift invariant image recognition. This approach represents a major innovation in making the HOC viable for real-world applications.

Hologram classification of occluded and deformable objects with speckle noise contamination by deep learning

Advancements in optical, computing, and electronic technologies have enabled holograms of physical three-dimensional (3D) objects to be captured. The hologram can be displayed with a spatial light modulator to reconstruct a visible image. Although holography is an ideal solution for recording 3D images, a hologram comprises high-frequency fringe patterns that are almost impossible to recognize with traditional computer vision methods. Recently, it has been shown that holograms can be classified with deep learning based on convolution neural networks. However, the method can only achieve a high success classification rate if the image represented in the hologram is without speckle noise and occlusion. Minor occlusion of the image generally leads to a substantial drop in the success rate. This paper proposes a method known as ensemble deep-learning invariant occluded hologram classification to overcome this problem. The proposed new method attains over 95% accuracy in the classification of holograms of partially occluded handwritten numbers contaminated with speckle noise. To achieve the performance, a new augmentation scheme and a new enhanced ensemble structure are necessary. The new augmentation process includes occluded objects and simulates the worst-case scenario of speckle noise.

Thick PQ:PMMA transmission holograms for free-space optical communication via wavelength-division multiplexing

Phenantrenequinone doped poly(methyl-methacrylate) (PQ:PMMA) is a holographic substrate that can be used for angle or wavelength multiplexed Bragg gratings. However, efficient writings can be done only using a high-power, long-coherence volume laser over a limited wavelength range. This constraint makes it difficult to write gratings that would diffract several different read wavelengths into a single direction. We describe the rules for writing such gratings, taking into account the differences in the mean index seen by the write and read wavelengths. We further demonstrate the use of such a transmission hologram for wavelength-division multiplexing in a free-space optical communication system.

Image correlation by one-dimensional signatures invariant to rotation, position, and scale using the radial Hilbert transform optimized

This paper presents a new methodology for pattern recognition invariant to rotation, position, and scale. The method uses the correlation of signatures, where the signatures were created with a new equation called the radial Hilbert transform optimized (RHTO) for longer signatures. An analysis with eight non-homogeneous illumination patterns was performed with 2000 letter variants and 30 phytoplankton species. The higher confidence level was founded using the radial Hilbert optimized methodology. Also, it utilized a correlation called adaptive linear-nonlinear correlation, which gave a better discrimination performance than the nonlinear correlation function.

Demonstration of shift, scale, and rotation invariant target recognition using the hybrid opto-electronic correlator

Previously, we had proposed a hybrid opto-electronic correlator (HOC), which can achieve the same functionality as that of a holographic optical correlator but without using any holographic medium. Here, we demonstrate experimentally that the HOC is capable of detecting objects in a scale, rotation, and shift invariant manner. First, the polar Mellin transformed (PMT) versions of two images are produced, using a combination of optical and electronic signal processing. The PMT images are then used as the reference and the query inputs for the HOC. The observed correlation signal is used to infer, with high accuracy, the relative scale and angular orientation of the original images. We also discuss practical constraints in reaching a high-speed implementation of such a system. In addition, we describe how these challenges may be overcome for producing an automated version of such a correlator.

Image registration under translation and rotation in two-dimensional planes using Fourier slice theorem

Image recognition in the presence of both rotation and translation is a longstanding problem in correlation pattern recognition. Use of log polar transform gives a solution to this problem, but at a cost of losing the vital phase information from the image. The main objective of this paper is to develop an algorithm based on Fourier slice theorem for measuring the simultaneous rotation and translation of an object in a 2D plane. The algorithm is applicable for any arbitrary object shift for full 180° rotation.

Histopathology in 3D: From three-dimensional reconstruction to multi-stain and multi-modal analysis

Light microscopy applied to the domain of histopathology has traditionally been a two-dimensional imaging modality. Several authors, including the authors of this work, have extended the use of digital microscopy to three dimensions by stacking digital images of serial sections using image-based registration. In this paper, we give an overview of our approach, and of extensions to the approach to register multi-modal data sets such as sets of interleaved histopathology sections with different stains, and sets of histopathology images to radiology volumes with very different appearance. Our approach involves transforming dissimilar images into a multi-channel representation derived from co-occurrence statistics between roughly aligned images.

Incorporation of polar Mellin transform in a hybrid optoelectronic correlator for scale and rotation invariant target recognition

In this paper, we show that our proposed hybrid optoelectronic correlator (HOC), which correlates images using spatial light modulators (SLMs), detectors, and field-programmable gate arrays (FPGAs), is capable of detecting objects in a scale and rotation invariant manner, along with the shift invariance feature, by incorporating polar Mellin transform (PMT). For realistic images, we cut out a small circle at the center of the Fourier transform domain, as required for PMT, and illustrate how this process corresponds to correlating images with real and imaginary parts. Furthermore, we show how to carry out shift, rotation, and scale invariant detection of multiple matching objects simultaneously, a process previously thought to be incompatible with PMT-based correlators. We present results of numerical simulations to validate the concepts.

Unsupervised content classification based nonrigid registration of differently stained histology images

Registration of histopathology images of consecutive tissue sections stained with different histochemical or immunohistochemical stains is an important step in a number of application areas, such as the investigation of the pathology of a disease, validation of MRI sequences against tissue images, multiscale physical modeling, etc. In each case, information from each stain needs to be spatially aligned and combined to ascertain physical or functional properties of the tissue. However, in addition to the gigabyte-size images and nonrigid distortions present in the tissue, a major challenge for registering differently stained histology image pairs is the dissimilar structural appearance due to different stains highlighting different substances in tissues. In this paper, we address this challenge by developing an unsupervised content classification method that generates multichannel probability images from a roughly aligned image pair. Each channel corresponds to one automatically identified content class. The probability images enhance the structural similarity between image pairs. By integrating the classification method into a multiresolution-block-matching-based nonrigid registration scheme (N. Roberts, D. Magee, Y. Song, K. Brabazon, M. Shires, D. Crellin, N. Orsi, P. Quirke, and D. Treanor, "Toward routine use of 3D histopathology as a research tool," Amer. J. Pathology, vol. 180, no. 5, 2012.), we improve the performance of registering multistained histology images. Evaluation was conducted on 77 histological image pairs taken from three liver specimens and one intervertebral disc specimen. In total, six types of histochemical stains were tested. We evaluated our method against the same registration method implemented without applying the classification algorithm (intensity-based registration) and the state-of-the-art mutual information based registration. Superior results are obtained with the proposed method.

3D reconstruction of multiple stained histology images

CONTEXT

Three dimensional (3D) tissue reconstructions from the histology images with different stains allows the spatial alignment of structural and functional elements highlighted by different stains for quantitative study of many physiological and pathological phenomena. This has significant potential to improve the understanding of the growth patterns and the spatial arrangement of diseased cells, and enhance the study of biomechanical behavior of the tissue structures towards better treatments (e.g. tissue-engineering applications).

METHODS

This paper evaluates three strategies for 3D reconstruction from sets of two dimensional (2D) histological sections with different stains, by combining methods of 2D multi-stain registration and 3D volumetric reconstruction from same stain sections.

SETTING AND DESIGN

The different strategies have been evaluated on two liver specimens (80 sections in total) stained with Hematoxylin and Eosin (H and E), Sirius Red, and Cytokeratin (CK) 7.

RESULTS AND CONCLUSION

A strategy of using multi-stain registration to align images of a second stain to a volume reconstructed by same-stain registration results in the lowest overall error, although an interlaced image registration approach may be more robust to poor section quality.

Neurient: an algorithm for automatic tracing of confluent neuronal images to determine alignment

A goal of neural tissue engineering is the development and evaluation of materials that guide neuronal growth and alignment. However, the methods available to quantitatively evaluate the response of neurons to guidance materials are limited and/or expensive, and may require manual tracing to be performed by the researcher. We have developed an open source, automated Matlab-based algorithm, building on previously published methods, to trace and quantify alignment of fluorescent images of neurons in culture. The algorithm is divided into three phases, including computation of a lookup table which contains directional information for each image, location of a set of seed points which may lie along neurite centerlines, and tracing neurites starting with each seed point and indexing into the lookup table. This method was used to obtain quantitative alignment data for complex images of densely cultured neurons. Complete automation of tracing allows for unsupervised processing of large numbers of images. Following image processing with our algorithm, available metrics to quantify neurite alignment include angular histograms, percent of neurite segments in a given direction, and mean neurite angle. The alignment information obtained from traced images can be used to compare the response of neurons to a range of conditions. This tracing algorithm is freely available to the scientific community under the name Neurient, and its implementation in Matlab allows a wide range of researchers to use a standardized, open source method to quantitatively evaluate the alignment of dense neuronal cultures.

Masked object registration in the Fourier domain

Registration is one of the most common tasks of image analysis and computer vision applications. The requirements of most registration algorithms include large capture range and fast computation so that the algorithms are robust to different scenarios and can be computed in a reasonable amount of time. For these purposes, registration in the Fourier domain using normalized cross-correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain so that all steps of translation registration can be computed efficiently using Fast Fourier Transforms. We provide algorithms and implementation details that demonstrate the correctness of our derivations. We also demonstrate how this masked FFT registration approach can be applied to improve the Fourier-Mellin algorithm that calculates translation, rotation, and scale in the Fourier domain. We demonstrate the computational efficiency, advantages, and correctness of our algorithm on a number of images from real-world applications. Our framework enables fast, global, parameter-free registration of images with masked regions.

Real-time affine global motion estimation using phase correlation and its application for digital image stabilization

We propose a fast and robust 2D-affine global motion estimation algorithm based on phase-correlation in the Fourier-Mellin domain and robust least square model fitting of sparse motion vector field and its application for digital image stabilization. Rotation-scale-translation (RST) approximation of affine parameters is obtained at the coarsest level of the image pyramid, thus ensuring convergence for a much larger range of motions. Despite working at the coarsest resolution level, using subpixel-accurate phase correlation provides sufficiently accurate coarse estimates for the subsequent refinement stage of the algorithm. The refinement stage consists of RANSAC based robust least-square model fitting for sparse motion vector field, estimated using block-based subpixel-accurate phase correlation at randomly selected high activity regions in finest level of image pyramid. Resulting algorithm is very robust to outliers such as foreground objects and flat regions. We investigate the robustness of the proposed method for digital image stabilization application. Experimental results show that the proposed algorithm is capable of estimating larger range of motions as compared to another phase correlation method and optical flow algorithm.

A Biologically Plausible Transform for Visual Recognition that is Invariant to Translation, Scale, and Rotation

Visual object recognition occurs easily despite differences in position, size, and rotation of the object, but the neural mechanisms responsible for this invariance are not known. We have found a set of transforms that achieve invariance in a neurally plausible way. We find that a transform based on local spatial frequency analysis of oriented segments and on logarithmic mapping, when applied twice in an iterative fashion, produces an output image that is unique to the object and that remains constant as the input image is shifted, scaled, or rotated.

Transformation invariant on-line target recognition

Transformation invariant automatic target recognition (ATR) has been an active research area due to its widespread applications in defense, robotics, medical imaging and geographic scene analysis. The primary goal for this paper is to obtain an on-line ATR system for targets in presence of image transformations, such as rotation, translation, scale and occlusion as well as resolution changes. We investigate biologically inspired adaptive critic design (ACD) neural network (NN) models for on-line learning of such transformations. We further exploit reinforcement learning (RL) in ACD framework to obtain transformation invariant ATR. We exploit two ACD designs, such as heuristic dynamic programming (HDP) and dual heuristic dynamic programming (DHP) to obtain transformation invariant ATR. We obtain extensive statistical evaluations of proposed on-line ATR networks using both simulated image transformations and real benchmark facial image database, UMIST, with pose variations. Our simulations show promising results for learning transformations in simulated images and authenticating out-of plane rotated face images. Comparing the two on-line ATR designs, HDP outperforms DHP in learning capability and robustness and is more tolerant to noise. The computational time involved in HDP is also less than that of DHP. On the other hand, DHP achieves a 100% success rate more frequently than HDP for individual targets, and the residual critic error in DHP is generally smaller than that of HDP. Mathematical analyses of both our RL-based on-line ATR designs are also obtained to provide a sufficient condition for asymptotic convergence in a statistical average sense.

Image processing guided analysis for estimation of bacteria colonies number by means of optical transforms

A novel method for evaluation of bacterial colonies number (Colony Forming Units--CFU), is described. Proposed algorithm, based on the Mellin transform, allows the CFU evaluation, invariant for the spatial orientation and scale changes. The proposed method involves image recording of bacteria grown in Petri dishes, calculation of the Fourier spectrum followed by coordinates transformation, and determination of the Mellin transform. It was proved that there is a high correlation between CFU and maxima of Mellin spectra. The method was practically implemented for evaluation of antibacterial activity of silver-based nanomaterials and the effect of an additional laser light irradiation.

Computation of orthogonal Fourier-Mellin moments in two coordinate systems

The computing method for orthogonal Fourier-Mellin moments in a polar coordinate system is presented in detail. The image expressed in a Cartesian system has to be transformed into a polar coordinate system first when we calculate the orthogonal Fourier-Mellin moments of the image in a polar coordinate system, which will increase both computational complexity and error. To solve the problem, a new direct computing method for orthogonal Fourier-Mellin moments in a Cartesian coordinate system is proposed, which can avoid the image transformation between two coordinate systems and eliminate the rounding error in coordinate transformation and decrease the computational complexity.

Eccentricity Estimator for Wide-Angle Fovea Vision Sensor

This paper proposes a method for estimating the eccentricity that corresponds to the incident angle to a fovea sensor. The proposed method uses the Fourier-Mellin Invariant descriptor to estimate rotation, scale, and translation, by taking both geometrical distortion and non-uniform resolution of a space-variant image from the fovea sensor into account. The following 2 points are focused on in this paper. One is to use multi-resolution images by Discrete Wavelet Transform to properly reduce noise caused by foveation. Another is to use a variable window function (although the window function is generally used for reducing DFT leakage caused by both ends of a signal) to change the effective field of view (FOV) so as not to sacrifice high accuracy. The simulation compares the root mean square (RMS) of the foveation noise between uniform and non-uniform resolutions when a resolution level and a FOV level are changed, respectively. The result shows the proposed method is suitable for the wide-angle space-variant image from the fovea sensor, and, moreover, it does not sacrifice the high accuracy in the central FOV. Another simulation is done to determine a reliable resolution level.

This paper is the full translation from the transactions of JSME Vol.74, No.744.

Eccentricity Compensator for Wide-Angle Fovea Vision Sensor

This paper aims at the acquisition of a robust feature for rotation, scale, and translation-invariant image matching of space-variant images from a fovea sensor. The proposed model eccentricity compensator corrects deformation in log-polar images when the fovea sensor is not centered on the target image, that is, when eccentricity exists. An image simulator in a discrete space implements this model through its geometrical formulation. This paper also proposes Unreliable Feature Omission (UFO) using the Discrete Wavelet Transform. UFO reduces local high frequency noise appearing in the space-variant image when the eccentricity changes. It discards coefficients when they are regarded as unreliable, based on digitized errors in the input image from the fovea sensor. The first simulation estimates the compensator by comparing it with other polar images. This result shows the compensator performs well, and its root mean square error (RMSE) changes only by up to 2.54% on the condition that the eccentricity is within 34.08°. The second simulation shows UFO performs well for the log-polar image remapped by the eccentricity compensator when white Gaussian noise (WGN) is added. The result from the Daubechies (7, 9) biorthogonal wavelet shows UFO reduces the RMSE by up to 0.40 %, even if the WGN is not added, when the eccentricity is within 34.08°.

This paper is the full translation from the transactions of JSME Vol.73, No.733.

A correlation-based approach to calculate rotation and translation of moving cells

We present a noniterative image cross-correlation approach to track translation and rotation of crawling cells in time-lapse video microscopy sequences. The method does not rely on extracting features or moments, and therefore does not impose specific requirements on the type of microscopy used for imaging. Here we use phase-contrast images. We calculate cell rotation and translation from one image to the next in two stages. First, rotation is calculated by cross correlating the images' polar-transformed magnitude spectra (Fourier magnitudes). Rotation of the cell about any center in the original images results in translation in this representation. Then, we rotate the first image such that the cell has the same orientation in both images, and cross correlate this image with the second image to calculate translation. By calculating the rotation and translation over each interval in the movie, and thereby tracking the cell's position and orientation in each image, we can then map from the stationary reference frame in which the cell was observed to the cell's moving coordinate system. We describe our modifications enabling application to nonidentical images from video sequences of moving cells, and compare this method's performance with that of a feature extraction method and an iterative optimization method.

Three-Dimensional Surface Topography Acquisition and Analysis for Firearm Identification

In the last decade, computer-based systems for the comparison of microscopic firearms evidence have been the subject of considerable research work because of their expected capability of supporting the firearms examiner through the automated analysis of large amounts of evidence. The Integrated Ballistics Identification System, which is based on a two-dimensional representation of the specimen surface, has been widely adopted in forensic laboratories worldwide. More recently, some attempts to develop systems based on three-dimensional (3D) representations of the specimen surface have been made, both in the literature and as industrial products, such as BulletTRAX-3D, but fundamental limitations in achieving fully automated identification remain. This work analyzes the advantages and disadvantages of a 3D-based approach by proposing an approach and a prototype system for firearms evidence comparison that is based on the acquisition and analysis of the 3D surface topography of specimens, with particular reference to cartridge cases. The concept of 3D virtual comparison microscope is introduced, whose purpose is not to provide fully automated identification, but to show how the availability of 3D shape information can provide a whole new set of verification means, some of them being described and discussed in this work, specifically, visual enhancement tools and quantitative measurement of shape properties, for supporting, not replacing, the firearm examiner in reaching the final decision.

Image registration using log-polar mappings for recovery of large-scale similarity and projective transformations

This paper describes a novel technique to recover large similarity transformations (rotation/scale/translation) and moderate perspective deformations among image pairs. We introduce a hybrid algorithm that features log-polar mappings and nonlinear least squares optimization. The use of log-polar techniques in the spatial domain is introduced as a preprocessing module to recover large scale changes (e.g., at least four-fold) and arbitrary rotations. Although log-polar techniques are used in the Fourier-Mellin transform to accommodate rotation and scale in the frequency domain, its use in registering images subjected to very large scale changes has not yet been exploited in the spatial domain. In this paper, we demonstrate the superior performance of the log-polar transform in featureless image registration in the spatial domain. We achieve subpixel accuracy through the use of nonlinear least squares optimization. The registration process yields the eight parameters of the perspective transformation that best aligns the two input images. Extensive testing was performed on uncalibrated real images and an array of 10,000 image pairs with known transformations derived from the Corel Stock Photo Library of royalty-free photographic images.

Detecting three-dimensional location and shape of noisy distorted three-dimensional objects with ladar trained optimum nonlinear filters

We propose a filtering technique that uses laser radar (ladar) data to detect a target's three-dimensional (3D) coordinates and shape within an input scene. A two-dimensional ladar range image is converted into 3D space, and then the 3D optimum nonlinear filtering technique is used to detect the 3D coordinates of targets (including the target's distance from the sensor). The 3D optimum nonlinear filter is designed to detect distorted targets (i.e., out-of-plane and in-plane rotations and scale changes) and to be noise robust. The nonlinear filter is derived to minimize the mean of the output energy in response to the input scene in the presence of disjoint background noise and additive noise and to maintain a fixed output peak for the members of the true-class target training set. The system is tested with real ladar imagery in the presence of background clutter. The background clutter used in the system evaluation includes false objects that are similar to the true targets. The correlation output of ladar images shows a dominant peak at the target's 3D coordinates.

Detection and tracking of rotated and scaled targets by use of Hilbert-wavelet transform

In a recent work, we demonstrated the usefulness of the Hilbert transform in identifying the in-plane rotation angle between two objects. Here we use the Hilbert-wavelet bases instead of the Hilbert transform in the determination of the exact angle of rotation. We describe the design of the two-dimensional Hilbert-wavelet filter based on the spectral-factorization method to generate a Hilbert-transform pair of orthogonal wavelet bases. We compare the relative performance of the Hilbert transform and the Hilbert wavelet to identify both in-plane and out-of-plane rotation angles. We demonstrate that the Hilbert wavelet offers better rotation-angle determination than the Hilbert transform. We present correlation based rotated and scaled object identification and tracking using Hilbert or Hilbert-wavelet transformed infrared image sequences. We also demonstrate reduced data handling and improved tracking of distorted objects using the Hilbert-wavelet transform.

Distortion tolerant image recognition receiver by use of a multiple-hypothesis method

A multiple-hypothesis method is used to detect a target or a reference signal in the presence of additive noise with unknown statistics. The receiver is designed to detect the target and to be tolerant of the variations in rotation and illumination of the target. A multiple-hypothesis test with unknown-noise parameters is used to locate the target position. The proposed method does not use any specific distortion-invariant-filtering technique, but it relies on a multiple-hypothesis approach. Maximum-likelihood estimates of the illumination constant and the unknown noise parameters are obtained. Computer simulations are presented to evaluate the performance of the receiver for various distorted noisy true-class targets with varying illumination and false-class objects.

Optimum nonlinear composite filter for distortion-tolerant pattern recognition

We describe a nonlinear distortion-tolerant filter for pattern recognition that is optimum in terms of tolerance to input noise and discrimination capability. This filter was derived by minimization of the output energy that is due to the overlapping additive noise and the input scene, and the output of the filter meets the design constraints obtained from the training data set. The performance of this filter was tested with an input scene containing one of the training data sets, a nontraining true target, and a false object in the presence of overlapping additive noise and nonoverlapping background noise. We carried out Monte Carlo runs to measure the statistical performance of the filter and obtained receiver operating characteristics curves to show the detection capabilities of the filter.

Image recognition in the presence of non-Gaussian noise with unknown statistics

We design receivers to detect a known pattern or a reference signal in the presence of very general and non-Gaussian types of noise. Three sources of input-noise degradation are considered: additive, multiplicative, and disjoint background. The detection process involves two steps: (1) estimation of the relevant noise parameters within the framework of hypothesis testing and (2) maximizing a certain metric that measures the likelihood of the target being at a given location. The parameter estimation portion is carried out by moment-matching techniques. Because of the number of unknown parameters and the fact that various types of input-noise processes are non-Gaussian, the methods that are used to estimate these parameters differ from the standard methods of maximizing the likelihood function. To verify the existence of the target at a certain location, we use l(p)-norm metric for p > or = 0 to measure the likelihood of the target being present at the location of interest. Computer simulations are used to show that for the images tested here, the receivers designed herein perform better than some existing receivers.

Noise robustness of nonlinear filters for image recognition

We analyze the performance of the Fourier plane nonlinear filters in terms of signal-to-noise ratio (SNR). We obtain a range of nonlinearities for which SNR is robust to the variations in input-noise bandwidth. This is shown both by analytical estimates of the SNR for nonlinear filters and by experimental simulations. Specifically, we analyze the SNR when Fourier plane nonlinearity is applied to the input signal. Using the Karhunen-Loève series expansion of the noise process, we obtain precise analytic expressions of the SNR for Fourier plane nonlinear filters in the presence of various types of additive-noise processes. We find a range of nonlinearities that need to be applied that keep the output SNR of the filter stable relative to changes in the noise bandwidth.

Optimum receivers for pattern recognition in the presence of Gaussian noise with unknown statistics

We develop algorithms to detect a known pattern or a reference signal in the presence of additive, disjoint background, and multiplicative white Gaussian noise with unknown statistics. The presence of three different types of noise processes with unknown statistics presents difficulties in estimating the unknown parameters. The standard methods such as expected-maximization-type algorithms are iterative, and in the framework of hypothesis testing they are time-consuming, because corresponding to each hypothesis one must estimate a set of parameters. Other standard methods such as setting the gradient of the likelihood function with respect to the unknown parameters will lead to a nonlinear system of equations that do not have a closed-form solution and require iterative methods. We develop an approach to overcome these handicaps and derive algorithms to detect a known object. We present new methods to estimate unknown parameters within the framework of hypothesis testing. The methods that we present are direct and provide closed-form estimates of the unknown parameters. Computer simulations are used to show that for the images tested, the receivers that we have designed perform better than existing receivers.

Image matching algorithms for breech face marks and firing pins in a database of spent cartridge cases of firearms

On the market several systems exist for collecting spent ammunition data for forensic investigation. These databases store images of cartridge cases and the marks on them. Image matching is used to create hit lists that show which marks on a cartridge case are most similar to another cartridge case. The research in this paper is focused on the different methods of feature selection and pattern recognition that can be used for optimizing the results of image matching. The images are acquired by side light images for the breech face marks and by ring light for the firing pin impression. For these images a standard way of digitizing the images used. For the side light images and ring light images this means that the user has to position the cartridge case in the same position according to a protocol. The positioning is important for the sidelight, since the image that is obtained of a striation mark depends heavily on the angle of incidence of the light. In practice, it appears that the user positions the cartridge case with +/-10 degrees accuracy. We tested our algorithms using 49 cartridge cases of 19 different firearms, where the examiner determined that they were shot with the same firearm. For testing, these images were mixed with a database consisting of approximately 4900 images that were available from the Drugfire database of different calibers.In cases where the registration and the light conditions among those matching pairs was good, a simple computation of the standard deviation of the subtracted gray levels, delivered the best-matched images. For images that were rotated and shifted, we have implemented a "brute force" way of registration. The images are translated and rotated until the minimum of the standard deviation of the difference is found. This method did not result in all relevant matches in the top position. This is caused by the effect that shadows and highlights are compared in intensity. Since the angle of incidence of the light will give a different intensity profile, this method is not optimal. For this reason a preprocessing of the images was required. It appeared that the third scale of the "à trous" wavelet transform gives the best results in combination with brute force. Matching the contents of the images is less sensitive to the variation of the lighting. The problem with the brute force method is however that the time for calculation for 49 cartridge cases to compare between them, takes over 1 month of computing time on a Pentium II-computer with 333MHz. For this reason a faster approach is implemented: correlation in log polar coordinates. This gave similar results as the brute force calculation, however it was computed in 24h for a complete database with 4900 images.A fast pre-selection method based on signatures is carried out that is based on the Kanade Lucas Tomasi (KLT) equation. The positions of the points computed with this method are compared. In this way, 11 of the 49 images were in the top position in combination with the third scale of the à trous equation. It depends however on the light conditions and the prominence of the marks if correct matches are found in the top ranked position. All images were retrieved in the top 5% of the database. This method takes only a few minutes for the complete database if, and can be optimized for comparison in seconds if the location of points are stored in files. For further improvement, it is useful to have the refinement in which the user selects the areas that are relevant on the cartridge case for their marks. This is necessary if this cartridge case is damaged and other marks that are not from the firearm appear on it.

Shift- and scale-invariant recognition of contour objects with logarithmic radial harmonic filters

The phase-only logarithmic radial harmonic (LRH) filter has been shown to be suitable for scale-invariant block object recognition. However, an important set of objects is the collection of contour functions that results from a digital edge extraction of the original block objects. These contour functions have a constant width that is independent of the scale of the original object. Therefore, since the energy of the contour objects decreases more slowly with the scale factor than does the energy of the block objects, the phase-only LRH filter has difficulties in the recognition tasks when these contour objects are used. We propose a modified LRH filter that permits the realization of a shift- and scale-invariant optical recognition of contour objects. The modified LRH filter is a complex filter that compensates the energy variation resulting from the scaling of contour objects. Optical results validate the theory and show the utility of the newly proposed method.

Automatic retinal image registration scheme using global optimization techniques

Retinal image registration is commonly required in order to combine the complementary information in different retinal modalities. In this paper, a new automatic scheme to register retinal images is presented and is currently tested in a clinical environment. The scheme considers the suitability and efficiency of different image transformation models and function optimization techniques, following an initial preprocessing stage. Three different transformation models--affine, bilinear and projective--as well as three optimization techniques--downhill simplex method, simulated annealing and genetic algorithms--are investigated and compared in terms of accuracy and efficiency. The registration of 26 pairs of Fluoroscein Angiography and Indocyanine Green Chorioangiography images with the corresponding Red-Free retinal images, showed the superiority of combining genetic algorithms with the affine and bilinear transformation models. A comparative study of the proposed automatic registration scheme against the manual method, commonly used in the clinical practice, is finally presented showing the advantage of the proposed automatic scheme in terms of accuracy and consistency.

One-dimensional logarithmic harmonic synthetic discriminant function filters for shift-, scale-, and projection-invariant pattern recognition

We introduce a new approach for shift-, scale-, and projection-invariant pattern recognition that combines the harmonic expansion and the synthetic discriminant function approaches by use of a synthetic discriminant function filter with equal-order one-dimensional logarithmic harmonic components. Because projection invariance in one direction is guaranteed by the harmonics, the required number of training images is much fewer than with classical synthetic discriminant function filters.

Evaluation of three-dimensional convolutions by use of two-dimensional filtering

A three-dimensional to two-dimensional mapping is proposed that permits the reduction of three-dimensional convolutions-correlations to two-dimensional ones and thereby lays a theoretical foundation for their optical implementation.