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SIFT algorithm is one of the most significant and effective algorithms to describe the features of image in the field of image matching. To implement SIFT algorithm to hardware environment is apparently considerable and difficult. In this paper, we mainly discuss the realization of Key Point Description in SIFT algorithm, along with Matching process. In Key Point Description, we have proposed a new method of generating histograms, to avoid the rotation of adjacent regions and insure the rotational invariance. In Matching, we replace conventional Euclidean distance with Hamming distance. The results of the experiments fully prove that the structure we propose is real-time, accurate, and efficient. Future work is still needed to improve its performance in harsher conditions.

The paper addresses the issue on landmark matching of images from Geosynchronous Earth Orbit (GEO) satellites. In general, satellite imagery is matched against the base image, which is predefined. When the satellite imagery rotation occurs, the accuracy of many landmark matching algorithms deteriorates. To overcome this problem, generalised Hough transform (GHT) is employed for landmark matching. At first an improved GHT algorithm is proposed to enhance rotational invariance. Secondly a global coastline is processed to generate the test image as the satellite image and the base image. Then the test image is matched against the base image using the proposed algorithm. The matching results show that the proposed algorithm is rotation invariant and works well in landmark matching.

A brief overview of the properties of the Gauss-Laguerre circular harmonic functions and the associated transform is given. Based on these properties, an efficient algorithm is developed for computing a normalized cross-correlation, in the full space of translation and rotation, between an image and template. The resulting algorithm is compared to standard spatial and frequency domain normalized cross-correlation in terms of computational complexity. The capabilities of the algorithm are illustrated in a complex scene.

The DOA (Direction Of Arrival) estimation with subspace methods such as MUSIC (MUltiple SIgnal Classification) and ESPRIT (Estimation of Signal Parameters via Rotational Invariance Technique) is based on an accurate estimation of the eigenvalues and eigenvectors of covariance matrix. QR decomposition is implemented with the Coordinate Rotation DIgital Computer (CORDIC) algorithm. QRD requires only additions and shifts [6], so it is faster and more regular than other methods. In this article the hardware architecture of an EVD (Eigen Value Decomposition) processor based on TSA (triangular systolic array) for QR decomposition is proposed. Using Xilinx System Generator (XSG), the design is implemented and the estimated logic device resource values are presented for different matrix sizes.

A new method along with Zernike moments for classify fruit shape is developed, the image is first subjected to a normalization process using its regular moments to obtain scale and translation invariance, the rotation invariant Zernike features are then extracted from the scale and translation normalized images and the numbers of features are decided by primary component analysis (PCA), at last, these features are input to support vector machine (SVM) classifier. This method performs better than traditional approaches because of their orthogonal base and rotation invariance of the defined features on them, which is verified by experiments on Zernike moments and Fourier descriptors.

This paper analyzes the spectrum influence between Radon transform and Log-polar transform when rotation effect is eliminated. The average retrieval performance of wavelet and NSCT with different retrieval parameters is also studied. Based on which, the authors design a multi-scale and multi-orientation texture transform spectrum, as well as rotationinvariant feature vector and its measurement criteria. Then a new two-level rotation-invariant texture retrieval algorithm based on no-parameter statistic features is proposed. Experiments on Brodatz image database show that the algorithm proposed in this paper is appropriate for main orientation capturing and detail information description. Besides, the combination of this two-level progressive retrieval strategy and multi-scale analysis method can effectively improve retrieval efficiency compared with traditional algorithms and ensure a high precision as well.

Scale and rotation invariant texture classification is a challenging and significant topic in texture analysis. This paper presents a scale and rotation invariant Gabor Texture Descriptor (GTD) for texture classification. Firstly, Gabor filters with different orientations and scales are carried out on an image. Secondly, to obtain a scale invariant GTD, different scale energies of these Gabor filtered images are calculated, and the optimal matching scales of the GTD are chosen by the sliding window filter with the scale energies. Thirdly, to extract a rotation invariant GTD, a new method using Discrete Fourier Transform is employed on the scale invariant GTD. At last, the distances between the GTDs of a query image and the target images are calculated for texture classification. Five different GTDs are employed for texture classification to demonstrate the effectiveness of the proposed scale and rotation invariant GTD.

In this paper, we introduce a new algorithm to register images with rotation and image blurring. The characteristic of this approach is that a set of Legendre moment invariants are used to establish the correspondence of corner points between the reference image and the distorted image, after these points are extracted by Harris corner detector. Transformation parameters can be estimated from those matched points.

This paper presents a novel texture description approach, which is robust to variances in rotation, scale and illumination in images, to classify the texture of images. A limitation with traditional methods is that they are more or less sensitive to the mentioned changes in images. To overcome this problem, we propose a novel Local Haar Binary Pattern (LHBP) based framework to ensure invariance in global rotation, scale, and light change. Our method consists of two components: feature extraction and scale self-adaptive classification. The global rotation invariant LHBP histogram features are extracted against the variances of illumination and global rotation, and the scale self-adaptive strategy is used for optimizing the classification of different scale textures. Evaluation results on Outex and Brodatz databases illustrate the significant advantages of the proposed approach over existing algorithms.

Different-source image matching is still a difficult problem in computer vision. In this paper, we propose a novel algorithm based on edge information, shape context descriptor and graph matching to make a good performance in the different-source image matching field, especially optical and infrared image. First, as the edge information is a relatively stable in these two kinds of images, we detect the feature point based on the edge information which can reflect the construction information. Then shape context descriptor, which is rotation invariant, scale invariant and translation invariant, is adapted to describe the feature point. Finally, the graph matching algorithm is used for the image matching to eliminate the false matching point. From experimental results, our algorithm is efficient in different-source image matching.

Image-based medical diagnosis typically relies on the (poorly reproducible) subjective classification of textures in order to differentiate between diseased and healthy pathology. Clinicians claim that significant benefits would arise from quantitative measures to inform clinical decision making. The first step in generating such measures is to extract local image descriptors - from noise corrupted and often spatially and temporally coarse resolution medical signals - that are invariant to illumination, translation, scale and rotation of the features. The Dual-Tree Complex Wavelet Transform (DT-CWT) provides a wavelet multiresolution analysis (WMRA) tool e.g. in 2D with good properties, but has limited rotational selectivity. Also, it requires computationally-intensive steering due to the inherently 1D operations performed. The monogenic signal, which is defined in n >= 2D with the Riesz transform gives excellent orientation information without the need for steering. Recent work has suggested the Monogenic Riesz-Laplace wavelet transform as a possible tool for integrating these two concepts into a coherent mathematical framework. We have found that the proposed construction suffers from a lack of rotational invariance and is not optimal for retrieving local image descriptors. In this paper we show: 1. Local frequency and local phase from the monogenic signal are not equivalent, especially in the phase congruency model of a "feature", and so they are not interchangeable for medical image applications. 2. The accuracy of local phase computation may be improved by estimating the denoising parameters while maximizing a new measure of "featureness".

Rotation of targets pose great a challenge for the design of an automatic image-based target detection system.In this paper, we propose a target detection algorithm that is robust to rotation of targets. Our key ideais to use rotation invariant features as the input for the classi“er. For an image in Radon transform space,namely R (b, ), taking the magnitude of 1-D Fourier transform on ,weget|F {R (b, )}|. It was proved thatthe coec ients of the combined Radon and 1-D Fourier transform, |F {R (b, )}| is invariant to rotation of theimage. These coecients are used as the input to a maximum-margin classi“er based on I-RELIEF featureweighting technique. Its objective is to maximize the margin between two classes and improve the robustness ofthe classi“er against uncertainties. For each pixel of a sample SAR image, a feature vector can be extracted froma sub image centered at that pixel. Then our classi“er decides whether the pixel is target or non-target. Thisproduces a binary-valued image. We further improve the detection performance by co nnectivity analysis, imagedierencing and diversity combining. We evaluate the performance of our proposed algorithm, using the dataset collected by Swedish CARABAS-II systems, and the e xperimental results show that our proposed algorithmachieves superior performance over the benchmark algorithm.Keywords: VHF SAR, rotation invariant transform, target detection, I-RELIEF

A novel feature descriptor-contourlet Fourier invariant feature, which combine contourlet decomposition and Fourier transforms and is translation-, rotation-, and scale-invariant, is put forward in this paper. Firstly, the translation and rotation invariant are achieved by Fourier transform along the circles that around the mass center of the scale-normalized target. Then statistic parameters of General Gaussian density (GGD) model of each contourlet sub-bands are evaluated. GGD parameters and contourlet decomposition coefficients are both as the features, which not only with rotation, shift and scaling invariant, but also with the contourlet inherent property of multi-resolution, local and multi-direction. We present experimental results using this descriptor in infrared image recognition, and it shows this descriptor is a good choice for object recognition.

We are presenting a new method for super resolution tracking of frequency modulated sinusoids in white noise. The method is specifically designed to handle the rapid transient problem, i.e. the problem of tracking a continuous, rapidly changing instantaneous frequency contour. The proposed method employs two components: 1) an adaptive generalized scale transform 1,2 which applies a localized change of time-frequency coordinates within the given signal, and 2) an estimation of signal parameters by rotational invariance techniques3 (ESPRIT). With experiments we have shown that the proposed method provides a significantly higher estimation accuracy than conventional methods. 3 With an optimal choice of transform parameters the estimation error can be reduced dramatically. Error reductions of over 40% have been observed.

We have previously shown that the use of the fair sampling assumption in EPR experiments could be questioned on the basis of experimental data. We continue our analysis of the data from the optical EPR experimental performed by Weihs et al. in Innsbruck 1997-1998, and we discuss whether a non-rotationally invariant source can account for the experimental results.

Digital watermarks for images can be made relatively robust to luminance and chrominance changes. More challenging problems are geometric or combined intensity/geometric attacks. In this work we use an additive watermarking model, commonly used in spread spectrum, using a new spreading function. The spreading function is a 2D circular chirp that can simultaneously resist JPEG compression and image rotation. Circular chirp is derived from a block chirp by polar mapping. The resistance to compression is achieved by the available tuning parameters of a block chirp. Tuning parameters include the chirp's initial frequency and chirp rate. These two parameters can be used to perform spectral shaping to avoid JPEG compression effects. Rotational invariance is achieved by mapping the block chirp to a ring whose inner and outer diameters are selectable. The watermark is added in spatial domain but detection is performed in polar domain where rotation translates to translation.

One of the important stages of fingerprint recognition is the registration of the fingerprints with respect to the original template. This is not a straightforward task as fingerprint images may have been subject to rotations and translations. Popular techniques for fingerprint registration use a reference point to achieve alignment. The drawback of existing methods of core/reference point detection is their poor performance on rotated images. In this paper, we propose a new approach for rotation invariant and reliable reference point detection applicable to fingerprints of different quality and types. Our approach is based on the integration of a directional vector field (representing the doubled ridge orientations in fingerprints) over a closed contour. We define the reference point as the point of the highest curvature. Areas of high curvature in the fingerprint are characterized by large differences in the orientations and correspond to high curvatures in the directional vector fields. Closed contour integrals of orientation vector field, defined as above, over a circle centered around the reference point corresponds to maximal closed curve integrals, and the values associated with such integrals are rotation invariant. Experimental results prove that with the proposed approach we can locate the reference point with high accuracy. Comparison with existing methods is provided.

This paper presents a new approach to translation and rotation invariant texture feature extraction for image texture retrieval. For the rotation invariant feature extraction, we invent angular projection along angular frequency in Polar coordinate system. The translation and rotation invariant feature vector for representing texture images is constructed by the averaged magnitude and the standard deviations of the magnitude of the Fourier transform spectrum obtained by the proposed angular projection. In order to easily implement the angular projection, the Radon transform is employed to obtain the Fourier transform spectrum of images in the Polar coordinate system. Then, angular projection is applied to extract the feature vector. We present our experimental results to show the robustness against the image rotation and the discriminatory capability for different texture images using MPEG-7 data set. Our Experiment result shows that the proposed rotation and translation invariant feature vector is effective in retrieval performance for the texture images with homogeneous, isotropic and local directionality.

Geometric distortions are simple and effective attack to many existing watermarking methods. We propose a rotation, scaling and translation (RST) resilient watermarking method through embedding watermark in RST invariant derived from Radon transform and Fourier transform. Based on the translation and rotation properties of Radon transform and the translation invariant property of Fourier magnitude, the RST invariant is obtained. The watermark is embedded in middle frequency of RST invariant domain, and the watermarked image is obtained with the inverse procedure. In detection process, the image which need to be detected is first transformed to the translation and rotation invariant domain, the normalized correlation between the watermarked coefficients and watermark is calculated. The correlation is compared with a threshold in order to determine if the watermark is present. To resist scale attack, the scale factor need be estimated by exhaustive search. The experiment results show the scheme is robust to RST attack and JPEG compression.

Acoustic diffraction tomography (DT) is an inversion scheme that can reconstruct the spatially variant acoustic properties of a scattering object. In this work, we develop and investigate a novel reconstruction algorithm for reconstructing separate images of the density and compressibility fluctuations of nonviscoelastic scattering objects. The reconstruction algorithm is derived by identifying and exploiting tomographic symmetries and the rotational invariance of the problem. The proposed reconstruction algorithm is implemented numerically and demonstrated by use of computer-simulation studies.

The joint transform correlator (JTC) is one of two main optical image processing architectures which provide us with a highly effective way of comparing images in a wide range of applications. Traditionally an optical correlator is used to compare an unknown input scene with a pre-captured reference image library, to detect if the reference occurs within the input. There is a new class of application for the JTC where they are used as image comparators, not having a known reference image, rather frames from a video sequence form both the input and reference. The JTC input plane is formed by combining the current frame with the previous frame in a video sequence and if the frames match, then there will be a correlation peak. If the objects move then the peaks will move (tracking) and if something has changed dramatically in the scene, then the correlation between the two frames is lost. This forms the basis of a very powerful application for the JTC in Defense and Security. Any change in the scene can be recorded and with the inherent shift invariance property of the correlator, any movement of the objects in the scene can also be detected. A major limitation of the JTC is its intolerance to rotation and scale changes in images. The strength of the correlation signal decreases as the input object rotates or varies in scale relative to the reference object. We have designed a binary phase only filter using the direct binary search algorithm for rotation invariant pattern recognition to be implemented on a JTC and compared to a classical synthetic discriminant function (SDF) filter. Results show that the performance of the DBS filter is better than the SDF filter.

To achieve scale and rotation invariant pattern recognition, we implemented synthetic discriminant function (SDF) based reference image in a nonzero order Fringe-adjusted Joint Transform Correlator (FJTC) using binary random phase mask. The binary random phase mask encodes the SDF based reference image before it is introduced in the joint input image. The joint power spectrum is then multiplied by the phase mask to remove the zero-order term and false alarms that may be generated in the correlation plane due to the presence of multiple identical target or non-target objects in the input scene. Detailed analysis for the proposed SDF based nonzero order FJTC using binary random phase mask is presented. Simulation results verify the effectiveness of the proposed technique.

We propose to model satellite and aerial images using a probabilistic approach. We show how the properties of these images, such as scale invariance, rotational invariance and spatial adaptivity lead to a new general model which aims to describe a broad range of natural images. The complex wavelet transform initially proposed by Kingsbury is a simple way of taking into account all these characteristics. We build a statistical model around this transform, by defining an adaptive Gaussian model with interscale dependencies, global parameters, and hyperpriors controlling the behaviour of these parameters. This model has been successfully applied to denoising and deconvolution, for real images and simulations provided by the French Space Agency.

Fourier transform profilometry, a well-known technique to obtain images of three-dimensional (3-D) objects, is used to achieve a real-time optical recognition of 3-D objects. A distorted grating pattern, that carries all the 3-D information of the object, is obtained from the projection of a regular fringe pattern onto the 3-D object surface. The analysis of such patterns is the basis of the optical method for recognizing 3-D objects in real time. The performance of the technique is demonstrated in two different types of correlators: the joint transform correlator and the classical convergent correlator. The proposed method is extended to the rotation-invariant and scale-invariant 3-D optical recognition. As is shown, the whole experimental setup can be constructed with simple equipment. Some experimental results, which demonstrate the ability of the method, are presented.

The paper presents two adaptive techniques, namely, the phase-only adjustment and the amplitude-phase optimization. In each case it creates multiple nulls to suppress multiple jammers. The adaptive technique is based on forward and backward smoothed ESPRIT (estimation of signal parameters via rotational invariance technique), which is capable of handling both coherent and non-coherent narrow-band multiple signals. For the amplitude-phase optimization both current amplitudes and phases are simultaneously adjusted to maximize the SIR (signal-to-interference ratio), which does not require iteration. The phase-only adaptive technique assumed fixed amplitudes while phases are adjusted, which required iterative algorithm. In both cases it is demonstrated to be effective and efficient. Computer simulations for a linear array of 32 elements and eight incoming signals have shown that the optimization technique can create wide as well as deep nulls, which correspond well to jammer widths and strengths. In each case the SIR improves substantially and the phase-amplitude optimization has much better SIR improvement than that of the phase-only adjustment.

The paper presents an adaptive technique to create multiple nulls to suppress multiple jammers. The adaptive technique is based on forward and backward smoothed ESPRIT (estimation of signal parameters via rotational invariance technique), which is capable of handling both coherent and non-coherent narrow-band multiple signals. It is demonstrated to be effective and efficient. Computer simulations for a linear array of 32 elements have shown that the optimization technique can create wide as well as deep nulls, which correspond well to jammer widths and strengths. In all cases the SIR improves substantially and converges quickly.

Our method of attack of the molecular rotation in the case when the ro-vib interaction can not be considered as a small one involves three steps. Firstly, so called effective classical energy of the molecular rotation is defined as the minimum of the exact classical ro-vib Hamilton function (it is suggested that the dependence of Hamilton function on the angular momentum components is the parametric one). The second step consists in the qualitative analysis of the classical rotational energy function using well known conception of the rotational energy surface (RES). The non- local bifurcation in rotational dynamics of isotopically substituted P 4 molecule is considered as an example. The third step consists in the construction of an effective quantum rotational Hamiltonian from the classical rotational energy function. As an example, the rotational levels of KCN molecule in the ground vibrational state are calculated.

A novel method for shape representation based on the multiresolution representation and morphological residues of the binary image is presented in this paper. A shape description method must have three properties: translation, rotation, and size invariance. The binary image which contains the object to be described is represented by multiresolution pyramid. A set of structuring elements is selected and used to compute morphological residues. The structuring elements are rotated versions of the one initial structuring element. This enables us to achieve rotational invariance of the shape description method. The morphological residue is the difference between the original image area and the eroded image area. It is a basic descriptor used in this method. The morphological residues for each of the structuring elements and each of the multiresolution pyramid levels are computed. The obtained set of morphological residues (numbers) is then sorted by order. The sort will enable comparison of rotated versions of objects. The residues for each pyramid level are normalized to enable more accurate comparison (distance measure) between object descriptors. Real vectors obtained in such a way are used as the shape descriptors. Experiments have been performed to investigate noise robustness of the proposed method, and have shown that method is not sensitive to noise. A set of twenty test images has been created and corrupted by noise. The Euclidean distance between the original and the corrupted images has been computed, and has shown that the proposed method has good shape matching properties.

Two varieties of Focal Plane Convolvers have been fabricated; the time multiplexing and the space multiplexing focal plane convolvers. They extract spacial features of a scene using parallel processing procedures at the imaging detector array site. The detailed description and operation of these devices is described. The following related areas of technology are also discussed: o Double Correlated Double Sampling o CCD Charge Transport o Equal Variance Mapping o Charge Transport Efficiency o Spacial Convolution Operators o Uniformity Issues o Local Rotational Invariance o Other Devices on the Reticle