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Despite extensive research on content-based image retrieval, challenges such as low accuracy, incapability to handle complex queries and high time consumption persist. Initially, a preprocessing technique is introduced in this study, a technique that uses a median filter to remove noise to achieve improved accuracy and reliability. Then, Fourier and circularity descriptors are extract in an effective manner correspondent to the texture and affine shape adaptation features. In addition, various descriptors, such as color histogram, color moment, color autocorrelogram and color coherency vector, are extracted as the invariant color features. The multiple ant colony optimization (MACOBTC) approach is implemented with whole features to find relevant features. Finally, the relevant features are utilized for the greedy learning of deep Boltzmann machine classifier (GDBM). The proposed approach obtains effective performance and accurate results on four datasets and is analyzed with various parameters such as accuracy, precision, recall, Jaccard, Dice, and Kappa coefficients. The GDBM provides a 25% increase in accuracy compared with existing techniques, such as the a priori classification algorithm.

The performance analysis of the improved proportionate affine projection (IPAP) algorithm is performed in this brief. Based on the energy-conservation arguments, the steady-state analysis of the IPAP algorithm is performed, which provides a general expression of steady-state excess mean-square error for the proportionate-type affine projection algorithms. The tracking behavior is also studied and the step size that optimizes the tracking performance is provided. Simulation results confirm the accuracy of the proposed expressions under different operating scenarios.

We consider the person re-identification problem, assuming the availability of a sequence of images for each person, commonly referred to as video-based or multi-shot re-identification. We approach this problem from the perspective of learning discriminative distance metric functions. While existing distance metric learning methods typically employ the average feature vector as the data exemplar, this discards the inherent structure of the data. To overcome this issue, we describe the image sequence data using affine hulls. We show that directly computing the distance between the closest points on these affine hulls as in existing recognition algorithms is not sufficiently discriminative in the context of person re-identification. To this end, we incorporate affine hull data modeling into the traditional distance metric learning framework, learning discriminative feature representations directly using affine hulls. We perform extensive experiments on several publicly available data sets to show that the proposed approach improves the performance of existing metric learning algorithms irrespective of the feature space employed to perform metric learning. Furthermore, we advance the state of the art on iLIDS-VID, PRID, and SAIVT, with absolute rank-1 performance improvements of 6.0%, 11.4%, and 6.0% respectively.

In this paper, we study a simplified affine motion model-based coding framework to overcome the limitation of a translational motion model and maintain low-computational complexity. The proposed framework mainly has three key contributions. First, we propose to reduce the number of affine motion parameters from 6 to 4. The proposed four-parameter affine motion model can not only handle most of the complex motions in natural videos, but also save the bits for two parameters. Second, to efficiently encode the affine motion parameters, we propose two motion prediction modes, i.e., an advanced affine motion vector prediction scheme combined with a gradient-based fast affine motion estimation algorithm and an affine model merge scheme, where the latter attempts to reuse the affine motion parameters (instead of the motion vectors) of neighboring blocks. Third, we propose two fast affine motion compensation algorithms. One is the one-step sub-pixel interpolation that reduces the computations of each interpolation. The other is the interpolation-precision-based adaptive block size motion compensation that performs motion compensation at the block level rather than the pixel level to reduce the number of interpolation. Our proposed techniques have been implemented based on the state-of-the-art high-efficiency video coding standard, and the experimental results show that the proposed techniques altogether achieve, on average, 11.1% and 19.3% bits saving for random access and low-delay configurations, respectively, on typical video sequences that have rich rotation or zooming motions. Meanwhile, the computational complexity increases of both the encoder and the decoder are within an acceptable range.

Subspace clustering is an important problem in machine learning with many applications in computer vision and pattern recognition. Prior work has studied this problem using algebraic, iterative, statistical, low-rank and sparse representation techniques. While these methods have been applied to both linear and affine subspaces, theoretical results have only been established in the case of linear subspaces. For example, algebraic subspace clustering (ASC) is guaranteed to provide the correct clustering when the data points are in general position and the union of subspaces is transversal . In this paper we study in a rigorous fashion the properties of ASC in the case of affine subspaces. Using notions from algebraic geometry, we prove that the homogenization trick , which embeds points in a union of affine subspaces into points in a union of linear subspaces, preserves the general position of the points and the transversality of the union of subspaces in the embedded space, thus establishing the correctness of ASC for affine subspaces.

A novel target detection method based on affine invariant interest point detection, feature encoding, and large-margin dimensionality reduction (LDR) is proposed for optical remote sensing images. First, four types of interest point detectors are introduced, and their performance in extracting low-level affine invariant descriptors using affine shape estimation is compared. Such a description can deal with significant affine transformations, including viewpoints. Second, feature encoding, which extends bag-of-words (BOW) by encoding high-order statistics, is selected to generate mid-level representation. Finally, LDR based on the large-margin constraint and stochastic subgradient is introduced to make the high-dimensional mid-level representation applicable for target detection. The experiments on aircraft and vehicle detections illustrate the effectiveness of the affine invariant description and LDR (compared with principal component analysis) in improving the detection performance. The experiments also demonstrate the effectiveness of the proposed method compared with popular approaches including Gabor, HOG, LBP, BOW, and R-CNN.

Mismatch removal is a key step in many computer vision problems. In this paper, we handle the mismatch removal problem by adopting shape interaction matrix (SIM). Given the homogeneous coordinates of the two corresponding point sets, we first compute the SIMs of the two point sets. Then, we detect the mismatches by picking out the most different entries between the two SIMs. Even under strong affine transformations, outliers, noises, and burstiness, our method can still work well. Actually, this paper is the first non-iterative mismatch removal method that achieves affine invariance. Extensive results on synthetic 2D points matching data sets and real image matching data sets verify the effectiveness, efficiency, and robustness of our method in removing mismatches. Moreover, when applied to partial-duplicate image search, our method reaches higher retrieval precisions with shorter time cost compared with the state-of-the-art geometric verification methods.

Rolling shutter distortions degrade the quality of videos captured by hand-held cameras. This letter proposes an affine motion model for removing rolling shutter distortions. The model represents the image motion during image capture as a sequence of affine transformations and computes the composition of these affine transformations precisely. Because an affine transformation can be represented by a neural network with one layer of linear neurons, the motion model can be represented by a multilayer neural network of linear neurons. Thus, the backpropagation algorithm can be used to improve the efficiency of the optimization process that estimates the model parameters. The proposed model is calibration-free. It is more general than other rolling shutter motion models because it only assumes that the velocity of the image during image acquisition is piecewise constant. Experimental results demonstrate that the model is more accurate than two state-of-the-art models and that the model parameters can be estimated efficiently.

The development of a virtual environments is desirable in many engineering applications for several reasons. For example, it can reduce the number of dangerous operations during the virtual inspection of mines, pipes for gas, water and sewer to inspect its current condition and identify possible failures. The proposal in this paper is an alternative solution to this problem obtaining a virtual image through the reconstruction of the inner pipe for assessment and fault detection. The proposed method employs regions with affine transformations used as dense correspondence, which are calculated through local correspondences, such as the detector/descriptor SIFT (Scale-invariant feature transform). The SIFT is required to obtain the position and orientation of the camera in the captured positions to get the structure of the scene through correspondences and to create a 3D reconstruction.

Local features offer high repeatability, which supports efficient matching between images, but they do not provide sufficient discriminative power. Imposing a geometric coherence constraint on local features improves the discriminative power but makes the matching sensitive to anisotropic transformations. We propose a novel feature representation approach to solve the latter problem. Each image is abstracted by a set of tuples of local features. We revisit affine shape adaptation and extend its conclusion to characterize the geometrically stable feature of each tuple. The representation thus provides higher repeatability with anisotropic scaling and shearing than found in previous research. We develop a simple matching model by voting in the geometrically stable feature space, where votes arise from tuple correspondences. To make the required index space linear as regards the number of features, we propose a second approach called a centrality-sensitive pyramid to select potentially meaningful tuples of local features on the basis of their spatial neighborhood information. It achieves faster neighborhood association and has a greater robustness to errors in interest point detection and description. We comprehensively evaluated our approach using Flickr Logos 32, Holiday, Oxford Buildings, and Flickr 100 K benchmarks. Extensive experiments and comparisons with advanced approaches demonstrate the superiority of our approach in image retrieval tasks.

In this paper, we propose a variational approach for the affine point set matching problems under the Bayesian probabilistic framework. A directed acyclic graph is provided for the representation of the joint probability over affine transformation, random variables and the point sets. Based on the directed graph, a variational iterative algorithm is derived to approximate the posteriors of the random variables and the anisotropic Gaussian mixtures are used for the estimation of the spurious outliers instead of the frequently-used uniform distribution. Experimental results demonstrate that our method achieves good performance in terms of both robustness and accuracy and is comparable to other state-of-the-art point registration algorithms especially in the case of complicated outliers.

Current techniques for shape analysis tend to seek invariance to similarity transformations (rotation, translation, and scale), but certain imaging situations require invariance to larger groups, such as affine or projective groups. Here we present a general Riemannian framework for shape analysis of planar objects where metrics and related quantities are invariant to affine and projective groups. Highlighting two possibilities for representing object boundaries-ordered points (or landmarks) and parameterized curves-we study different combinations of these representations (points and curves) and transformations (affine and projective). Specifically, we provide solutions to three out of four situations and develop algorithms for computing geodesics and intrinsic sample statistics, leading up to Gaussian-type statistical models, and classifying test shapes using such models learned from training data. In the case of parameterized curves, we also achieve the desired goal of invariance to re-parameterizations. The geodesics are constructed by particularizing the path-straightening algorithm to geometries of current manifolds and are used, in turn, to compute shape statistics and Gaussian-type shape models. We demonstrate these ideas using a number of examples from shape and activity recognition.

Local invariant features have been successfully used in image matching to cope with viewpoint change, partial occlusion, and clutters. However, when these factors become too strong, there will be a lot of mismatches due to the limited repeatability and discriminative power of features. In this paper, we present an efficient approach to remove the false matches and propagate the correct ones for the affine invariant features which represent the state-of-the-art local invariance. First, a pair-wise affine consistency measure is proposed to evaluate the consensus of the matches of affine invariant regions. The measure takes into account both the keypoint location and the region shape, size, and orientation. Based on this measure, a geometric filter is then presented which can efficiently remove the outliers from the initial matches, and is robust to severe clutters and non-rigid deformation. To increase the correct matches, we propose a global match refinement and propagation method that simultaneously finds a optimal group of local affine transforms to relate the features in two images. The global method is capable of producing a quasi-dense set of matches even for the weakly textured surfaces that suffer strong rigid transformation or non-rigid deformation. The strong capability of the proposed method in dealing with significant viewpoint change, non-rigid deformation, and low-texture objects is demonstrated in experiments of image matching, object recognition, and image based rendering.

The so-called Affine Projection (AP) algorithm is of large interest in many adaptive filters applications due to its considerable speed-up in convergence compared to its simpler version, the LMS algorithm. While the original AP algorithm is well understood, gradient type variants of less complexity with relaxed step-size conditions called pseudo affine projection offer still unresolved problems. This contribution shows i) local robustness properties of such algorithms, ii) global properties of these, concluding l2-stability conditions that are independent of the input signal statistics, as well as iii) steady-state values of moderate to high accuracy by relatively simple terms when applied to long filters. Of particular interest is the existence of lower step-size bounds for one of the variants, a bound that has not been observed before.

This work proposes novel locally affine invariant descriptors for shape representation. The descriptors are theoretically simple and solid, derived from the matrix theories. They can be used for matching and retrieval of shapes under affine transformation, articulated motion or nonrigid deformation. Comparisons of the work with the state-of-the-art shape descriptors are performed based on synthetic and some well-known databases. The experiments validate that the proposed descriptors achieve higher retrieval accuracy and have faster running speed than most of other approaches.

This paper presents a statistical analysis of a Pseudo Affine Projection (PAP) algorithm, obtained from the Affine Projection algorithm (AP) for a step size alpha < 1 and a scalar error signal in the weight update. Deterministic recursive equations are derived for the mean weight and for the mean square error (MSE) for a large number of adaptive taps N compared to the order P of the algorithm. Simulations are presented which show good to excellent agreement with the theory in the transient and steady states. The PAP learning behavior is of special interest in applications where tradeoffs are necessary between convergence speed and steady-state misadjustment.

In recent years, affine projection algorithms have been proposed for adaptive system applications as an efficient alternative to the slow convergence speed of least mean square (LMS)-type algorithms. Whereas much attention has been focused on the development of efficient versions of affine projection algorithms for echo cancellation applications, the similar adaptive problem presented by active noise control (ANC) systems has not been studied so deeply. This paper is focused on the necessity to reduce even more the computational complexity of affine projection algorithms for real-time ANC applications. We present some alternative efficient versions of existing affine projection algorithms that do not significantly degrade performance in practice. Furthermore, while in the ANC context the commonly used affine projection algorithm is based on the modified filtered-x structure, an efficient affine projection algorithm based on the (nonmodified) conventional filtered-x structure, as well as efficient methods to reduce its computational burden, are discussed throughout this paper. Although the modified filtered-x scheme exhibits better convergence speed than the conventional filtered-x structure and allows recovery of all the signals needed in the affine projection algorithm for ANC, the conventional filtered-x scheme provides a significant computational saving, avoiding the additional filtering needed by the modified filtered-x structure. In this paper, it is shown that the proposed efficient versions of affine projection algorithms based on the conventional filtered-x structure show good performance, comparable to the performance exhibited by the efficient approaches of modified filtered-x affine projection algorithms, and also achieve meaningful computational savings. Experimental results are presented to validate the use of the algorithms introduced in the paper for practical applications.

A new approach is presented to extract more robust affine invariant features for image matching. The novelty of our approach is a hierarchical filtering strategy for affine invariant feature detection, which is based on information entropy and spatial dispersion quality constraints. The concept of spatial dispersion quality is introduced to quantify the spatial distribution of features. Moreover, an integrated algorithm combined by the filtering strategy, maximally stable extremal region (MSER) and scale invariant feature transform, is introduced for affine invariant feature extraction. Since Mikolajczyk et al. identified that MSER is the best detector in many cases, we design an experiment to compare our approach (ED-MSER) with the standard MSER. By using two stereo pairs and an image sequence with different types of imagery, the experiment indicates that ED-MSER can always get much higher repeatability and matching score compared to the standard MSER and other algorithms, thus benefiting the subsequent image matching and many other applications.

This letter proposes a novel algorithm for affine registration of point sets in the way of incorporating an affine transformation into the iterative closest point (ICP) algorithm. At each iterative step of this algorithm, a closed-form solution of the affine transformation is derived. Similar to the ICP algorithm, this new algorithm converges monotonically to a local minimum from any given initial parameters. To get the best affine registration result, good initial parameters are required which are successfully estimated by using independent component analysis (ICA). Experimental results demonstrate the robustness and high accuracy of this algorithm.

A scheme, based on Principal Component Analysis (PCA), is proposed that can be used for the recognition of 2D planar shapes under affine transformations. A PCA step is first used to map the object boundary to its canonical form, reducing the problem of the non-uniform sampling of the object contour introduced by the affine transformation. Then, a PCAbased scheme is employed to train a set of basis functions on the signals extracted from the objects’ boundaries. The derived bases are used to analyze the boundary locally. Based on the theory of invariants and local boundary analysis, an novel invariant function is constructed. The performance of the proposed framework is compared with a standard wavelet-based approach with promising results.

International audience; This paper introduces a texture representation suitable for recognizing images of textured surfaces under a wide range of transformations, including viewpoint changes and nonrigid deformations. At the feature extraction stage, a sparse set of affine Harris and Laplacian regions is found in the image. Each of these regions can be thought of as a texture element having a characteristic elliptic shape and a distinctive appearance pattern. This pattern is captured in an affine-invariant fashion via a process of shape normalization followed by the computation of two novel descriptors, the spin image and the RIFT descriptor. When affine invariance is not required, the original elliptical shape serves as an additional discriminative feature for texture recognition. The proposed approach is evaluated in retrieval and classification tasks using the entire Brodatz database and a publicly available collection of 1,000 photographs of textured surfaces taken from different viewpoints.

In this paper, we describe an adaptation method for speech recognition systems that is based on a nonlinear transformation of the feature space. In contrast to most existing adaptation methods which assume some form of affine transformation of either the feature vectors or the acoustic models that model the feature vectors, our proposed method composes a general nonlinear transformation from two transformations, one of these being an affine transformation that combines the dimensions of the original feature space, and the other being a nonlinear transformation that is applied independently to each dimension of the previously transformed feature space leading to a general multidimensional nonlinear transformation of the original feature space. This method also differs from other affine techniques in the way the parameters of the transform are shared. In most previous methods, the parameters of the transformation are shared on the basis of the phonetic class, in our method, the parameters of the nonlinear transformation are shared not on the basis of the phonetic class, but rather on the location in the feature space. Experimental results show that the method outperforms affine methods providing up to a 25% relative improvement in the word error rate in an in-car speech recognition task.

We solve the 2-D affine image registration problem by curve matching and alignment. Our approach starts with a super-curve, which is formed by superimposing two affine related curves in one coordinate system. We use B-spline fusion technique to find a single B-spline approximation of the super-curve and a registration between the two curves simultaneously. This approach achieves superior accuracy and efficiency in curve matching and alignment. We then address the occlusion problem by finding partial match between the curves segmented using inflections and cusps, which are affine invariant. The combination of edge detection and curve alignment lead to accurate image registration.

Affine projection algorithms are useful adaptive filters whose main purpose is to speed the convergence of LMS-type filters. Most analytical results on affine projection algorithms assume special regression models or Gaussian regression data. The available analysis also treat different affine projection filters separately. This paper provides a unified treatment of the mean-square error, tracking, and transient performances of a family of affine projection algorithms. The treatment relies on energy conservation arguments and does not restrict the regressors to specific models or to a Gaussian distribution. Simulation results illustrate the analysis and the derived performance expressions.

The trace transform is a generalization of the Radon transform that allows one to construct image features that are invariant to a chosen group of image transformations. In this paper, we propose a methodology and appropriate functionals that can be computed from the image function and which can be used to calculate features invariant to the group of affine transforms. We demonstrate the usefulness of the constructed image descriptors in retrieving images from an image database and compare it with relevant state-of-the-art object retrieval methods.

In the field of adaptive signal processing, it is well known that affine projection algorithms or their low-computational implementations fast affine projection algorithms can produce a good tradeoff between convergence speed and computational complexity. Although these algorithms typically do not provide the same convergence speed as recursive-least-squares algorithms, they can provide a much improved convergence speed compared to stochastic gradient descent algorithms, without the high increase of the computational load or the instability often found in recursive-least-squares algorithms. In this paper, multichannel affine and fast affine projection algorithms are introduced for active noise control or acoustic equalization. Multichannel fast affine projection algorithms have been previously published for acoustic echo cancellation, but the problem of active noise control or acoustic equalization is a very different one, leading to different structures, as explained in the paper. The computational complexity of the new algorithms is evaluated, and it is shown through simulations that not only can the new algorithms provide the expected tradeoff between convergence performance and computational complexity, they can also provide the best convergence performance (even over recursive-least-squares algorithms) when nonideal noisy acoustic plant models are used in the adaptive systems.

The so-called affine projection algorithm (APA) has become a popular method in adaptive filtering applications and fast versions of it have been developed previously, such as fast affine projection (FAP) and the frequency domain block exact fast affine projection (BEFAP). While it is known that regularization is an absolute necessity in affine projection based adaptive filtering algorithms, FAP and BEFAP rely on an implicit "small regularization parameter" assumption. In this paper, a block exact affine projection algorithm (BE-APA) is derived that does not rely on the assumption of a small regularization parameter. It is an exact frequency domain translation of the original AP algorithm, and still has about the same complexity as, block exact FAR Unlike BEFAP, it can be used with strong regularization. It is then extended to incorporate an alternative to explicit regularization that is based on so-called "sparse" equations.

The affine transformation, which consists of rotation, translation, scaling, and shearing transformations, can be considered as an approximation to the perspective transformation. Therefore, it is very important to find an effective means for establishing point correspondences under affine transformation in many applications. In this paper, we consider the point correspondence problem as a subgraph matching problem and develop an energy formulation for affine invariant matching by a Hopfield type neural network. The fourth-order network is investigated first, then order reduction is done by incorporating the neighborhood information in the data. Thus we can use the second-order Hopfield network to perform subgraph isomorphism invariant to affine transformation, which can be applied to an affine invariant shape recognition problem. Experimental results show the effectiveness and efficiency of the proposed method.

Shows how the local slant and tilt angles of regularly textured curved surfaces can be estimated directly, without the need for iterative numerical optimization. We work in the frequency domain and measure texture distortion using the affine distortion of the pattern of spectral peaks. The key theoretical contribution is to show that the directions of the eigenvectors of the affine distortion matrices can be used to estimate local slant and tilt angles of tangent planes to curved surfaces. In particular, the leading eigenvector points in the tilt direction. Although not as geometrically transparent, the direction of the second eigenvector can be used to estimate the slant direction. The required affine distortion matrices are computed using the correspondences between spectral peaks, established on the basis of their energy ordering. We apply the method to a variety of real-world and synthetic imagery.

An optimization problem with an affine feasible set is studied. By converting the affine set to a closed convex set which contains the solution, the Meyer-Polak algorithm can be used. The selection of the constraints is the key issue. A theorem has been derived for the selection of the constraints for the affine problem where the cost function is of p-norm form. Its application in a control problem is demonstrated.

An improved Monro's (1992) zero-searching fractal coding method is presented. It enables the use of only one affine transformation and sliding domain block structure to obtain the fractal approximation for each image block The method is easier and can better exploit the self-similarities between image blocks. The peak SNR can be improved by 0.6-1.1 dB under the same condition and the encoding can be carried out very fast.

A framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross-weighted moments with fractional weights is presented. The fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise. Moreover, it makes it possible to arrive at low order (zero order) affine invariants that are more robust than those derived from higher order regular moments. The affine transformation parameters are recovered from the zero and the first order cross-weighted moments without requiring any feature point correspondence information. The equations used to find the affine transformation parameters are linear algebraic. The sensitivity of the cross-weighted moment invariants to noise, missing data, and perspective effects is shown on real images.

The fractal image coding technique has attracted a degree of interest for its low bit rate. But the reconstructed image is of medium quality. This problem has prevented the fractal technique from being used practically. In order to improve the compression fidelity, a new affine transformation is proposed. Meanwhile, its contractivity requirement is analyzed, and the optimal parameters are derived using the least square method. The new affine transformation has been practically used in image coding. Experiments show that the PSNR can reach 28.7 dB at a compression ratio (CR) of 16.4 for the 256/spl times/256/spl times/8 "Lena" image. Comparison with other fractal coding schemes shows that the new affine transformation can improve the reconstructed image quality efficiently.

Describes an efficient approach to pose invariant pictorial object recognition employing spectral signatures of image patches that correspond to object surfaces which are roughly planar. Based on singular value decomposition (SVD), the affine transform is decomposed into slant, tilt, swing, scale, and 2D translation. Unlike previous log-polar representations which were not invariant to slant, our log-log sampling configuration in the frequency domain yields complete affine invariance. The images are preprocessed by a novel model-based segmentation scheme that detects and segments objects that are affine-similar to members of a model set of basic geometric shapes. The segmented objects are then recognized by their signatures using multidimensional indexing in a pictorial dataset represented in the frequency domain. Experimental results with a dataset of 26 models show 100 percent recognition rates in a wide range of 3D pose parameters and imaging degradations: 0-360/spl deg/ swing and tilt, 0-82/spl deg/ of slant, more than three octaves in scale change, window-limited translation, high noise levels (0 dB), and significantly reduced resolution (1:5).

This paper introduces a novel, data-adaptive filtering framework: affine order-statistic filters. Affine order-statistic filters operate effectively on a wide range of signal statistics, are sensitive to the dispersion of the observed data, and are therefore particularly useful in the processing of nonstationary signals. These properties result from the introduction of a tunable affinity function that measures the affinity, or closeness, of observation samples in their natural order to their corresponding order statistics. The obtained affinity measures are utilized to control the influence of individual samples in the filtering process. Depending on the spread of the affinity function, which is controlled by a single parameter /spl gamma/, affine order-statistic filters operate effectively in various environments ranging from Gaussian to impulsive. The class of affine order-statistic filters subsumes the family of weighted order-statistic (WOS) affine filters and the class of FIR affine filters. We focus on a representative of the WOS affine filter class-the median affine filter-whose behavior can be tuned from that of a linear FIR filter to that of a robust median filter by narrowing the affinity function to a process referred to as medianization. The superior performance of affine order-statistic filters is demonstrated in two applications.

We consider model-based object localization based on local geometric feature matching between the model and the image data. The method is based on geometric constraint analysis, working in transformation space. We present a formal method which guarantees finding all feasible matchings in polynomial time. From there we develop more computationally feasible algorithms based on conservative approximations of the formal method. Additionally, our formalism relates object localization, affine model indexing, and structure from multiple views to one another.

A new method is presented for identifying and comparing closed, bounded, free-form curves that are defined by even implicit polynomial (IP) equations in the X-Y Cartesian coordinates. The method provides a new expression for an IP involving a product of conic factors with unique conic factor centers. The critical points for an IP curve are also defined. The conic factor centers and the critical points are shown to be useful related points that directly map to one another under affine transformations. In particular, the explicit determination of such points implies both a canonical form for the curves and the transformation matrix which relates affine equivalent curves.

We present a multistage affine motion segmentation method that combines the benefits of the dominant motion and block-based affine modeling approaches. In particular, we propose two key modifications to a recent motion segmentation algorithm developed by Wang and Adelson (1994). 1) The adaptive k-means clustering step is replaced by a merging step, whereby the affine parameters of a block which has the smallest representation error, rather than the respective cluster center, is used to represent each layer; and 2) we implement it in multiple stages, where pixels belonging to a single motion model are labeled at each stage. Performance improvement due to the proposed modifications is demonstrated on real video frames.

A method is described to recover the three-dimensional affine structure of a scene consisting of at least five points identified in two perspective views with a relative object-camera translation in between. When compared to the results for arbitrary stereo views, a more detailed reconstruction is possible using less information. The method presented only assumes that the two images are obtained by identical cameras, but no knowledge about the intrinsic parameters of the camera(s) or about the performed translation is assumed. By the same method, affine 3D reconstruction from a single view can be achieved for parallel structures. In that case, four points suffice for affine reconstruction.

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work-including Euclidean, projective and affine-in a natural and simple way, and introduces new, extremely simple algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

We develop expressions for measuring the distance between 2D point sets, which are invariant to either 2D affine transformations or 2D similarity transformations of the sets, and assuming a known correspondence between the point sets. We discuss the image normalization to be applied to the images before their comparison so that the computed distance is symmetric with respect to the two images. We then give a general (metric) definition of the distance between images, which leads to the same expressions for the similarity and affine cases. This definition avoids ad hoc decisions about normalization. Moreover, it makes it possible to compute the distance between images under different conditions, including cases where the images are treated asymmetrically. We demonstrate these results with real and simulated images. >

This paper provides a unified analysis of the steady-state behavior of different multichannel filtered-x affine projection algorithms when used in active noise control (ANC) systems. The analysis deals with two different filtering schemes: the modified filtered-x affine projection (MFXAP) algorithm, with the modified filtered-x structure embedded, that has been studied in previous works, and the filtered-x affine projection (CFXAP) algorithm, with the conventional filtered-x structure embedded, that becomes the main contribution of this work. This study is based on energy conservation principles and does not require a specific signal distribution. The derived theoretical models allow to accurately predict the steady-state performance of the considered algorithms for moderate AP orders and low step sizes mu. Simulation results obtained in practical ANC systems validate both the analysis and the achieved expressions, showing a relative good match between theory and practice. © 2012 IEEE., This work was supported in part by PROMETEO/2009/013, CICYT grant TEC2009-13741, Generalitat Valenciana GV/2010/027, and the Universitat Politecnica de Valencia PAID-06-09.

This paper and its companion are concerned with the problems of 3-D object recognition and shape estimation from image curves using a 3-D object curve model that is invariant to affine transformation onto the image space, and a binocular stereo imaging system. The objects of interest here are the ones that have markings (e.g., characters, letters, special drawings and symbols, etc.) on their surfaces. The 3-D curves on the object are modeled as B-splines, which are characterized by a set of parameters (the control points) from which the 3-D curve can be totally generated. The B-splines are invariant under affine transformations. That means that the affine projected object curve onto the image space is a B-spline whose control points are related to the object control points through the affine transformation. Part I deals with issues relating to the curve modeling process. In particular, the authors address the problems of estimating the control points from the data curve, and of deciding on the "best" order B-spline and the "best" number of control points to be used to model the image or object curve(s). A minimum mean-square error (mmse) estimation technique which is invariant to affine transformations is presented as a noniterative, simple, and fast approach for control point estimation. The "best" B-spline is decided upon using a Bayesian selection rule. Finally, we present a matching algorithm that allocates a sample curve to one of p prototype curves when the sample curve is an a priori unknown affine transformation of one of the prototype curves stored in the data base. The approach is tried on a variety of images of real objects. >

The method of Fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation (translation, rotation, scaling, and shearing). The method is based on a parameterized boundary description which is transformed to the Fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point. Invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions, as is demonstrated by processing silhouettes of aircraft maneuvering in three-space. >

Many well-known theorems for the two-dimensional (2D) Hartley transform are encapsulated in the affine theorem which is presented here and illustrated by example. The mode of presentation permits ready visualization of the effect on the spectral makeup when an object is subjected to a particular distortion as specified by the six disposable parameters of the affine coordinate transformation and of the effects of progressive distortion. By contrast, 2D Fourier transform pairs for images do not lend themselves to visualization in the same way. Affine transformations possess considerable flexibility and generality of a useful kind that arises from the property that a single 2D spectral component transforms into another single component. >

The above paper presented a variable regularized affine projection algorithm (VR-APA). A delay coefficients-based variable regularized affine algorithm (DC-VR-APA) was presented in [2], [3]. It was shown in [1, pp. 2103, (39)] that DC-VR-APA is an equivalent and alternate manifestation of the VR-APA when the affine projection order is equal to 1. However, results pertaining to input speech signals and presence of near-end speech activity 1 were not reported in. For the same set of parameters, this letter 2 shows that DC-VR-APA is more robust to the above conditions than the VR-APA. Motivated by some of the explanations in, we present the reasons for the robustness of DC-VR-APA in the above conditions.

Affine invariant descriptors have been widely used for recognition of objects regardless of their position, size, and orientation in space. Examples of color, texture, and shape descriptors abound in the literature. However, many tasks in computer vision require looking not only at single objects or regions in images but also at their spatial relationships. In an earlier work, we showed that the relative position of two objects can be quantitatively described by a histogram of forces. Here, we study how affine transformations affect this descriptor. The position of an object with respect to another changes when the objects are affine transformed. We analyze the link between: 1) the applied affinity, 2) the relative position before transformation (described through a force histogram), and 3) the relative position after transformation. We show that any two of these elements allow the third one to be recovered. Moreover, it is possible to determine whether (or how well) two relative positions are actually related through an affine transformation. If they are not, the affinity that best approximates the unknown transformation can be retrieved, and the quality of the approximation assessed.

In the following we consider the action of the group of affine transformations on a class of patterns representable by continuous functions with compact support. It is first shown how to accomplish a reduction of the action of the affine group to that of the orthogonal group. In the two-dimensional case, it is shown how to find the particular orthogonal transformation necessary to complete a pattern match. Finally invariants under the orthogonal group are presented. Examples are given which present typical results obtained by implementing the techniques via a digital-optical scanner and minicomputer software.

New results on the realization of finite-dimensional, discrete-time, internally biaffine systems are presented in this paper. The external behavior of such systems is described by multiaffine functions and the state space is constructed via Nerode equivalance relations. We prove that the state space is an affine space. An algorithm which amounts to choosing a frame for the affine space is presented. Our algorithm reduces in the linear and bilinear case to a generalization of algorithms existing in the literature. Explicit existence criteria for span-canonical realizations as well as an affine isomorphism theorem are given.