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An affine combination of two adaptive filters (AFs) based control is developed for a three-phase single stage grid tied photo voltaic (PV) array and ultra-capacitor (UC) charging electric vehicle spot (CEVS) of a charging station (CS). This algorithm is a combination of low complexity normalized least mean square (NLMS) and improved sparse channel identification reweighted zero attracting-NLMS (RZA-NLMS) filters. This combination offers the variable sparsity identification and improves the power quality of the CS. This CS is capable of grid to vehicle (G2V), PV source to vehicle (S2V), PV source to grid (S2G) and PV source to home (S2H). This CS also incorporates the vehicle to grid (V2G) and vehicle to home (V2H) functions when solar generation is reduced due to cloud crossing or in night time and state of charge (SOC) of the battery is sufficient to discharge battery. The DC link voltage is regulated through a bidirectional converter (BDC) using a cascaded PI controller. To improve the stability of the BDC, the loop shaping method is used. The loop shaping method is incorporated using k-factor approach. The efficacy of CS is demonstrated through the simulated results using MATLAB Simulink Library.

The goal of our paper is to semantically edit parts of an image matching a given text that describes desired attributes (e.g., texture, colour, and background), while preserving other contents that are irrelevant to the text. To achieve this, we propose a novel generative adversarial network (ManiGAN), which contains two key components: text-image affine combination module (ACM) and detail correction module (DCM). The ACM selects image regions relevant to the given text and then correlates the regions with corresponding semantic words for effective manipulation. Meanwhile, it encodes original image features to help reconstruct text-irrelevant contents. The DCM rectifies mismatched attributes and completes missing contents of the synthetic image. Finally, we suggest a new metric for evaluating image manipulation results, in terms of both the generation of new attributes and the reconstruction of text-irrelevant contents. Extensive experiments on the CUB and COCO datasets demonstrate the superior performance of the proposed method. Code is available at https://github.com/mrlibw/ManiGAN., Comment: CVPR 2020

In this paper, we introduce a Bayesian framework to perform model selection for nonlinear acoustic echo cancellation. This is especially important for scenarios where the functional form of the underlying nonlinear distortion is time-varying and/or is unknown, e.g., nonlinear distortions that vary with the volume level of the loudspeakers. To this end, the proposed method evaluates the model probabilities, or what is known as the evidence density, in a Bayesian manner. Thus, unlike convex and affine combination schemes of adaptive filters, the proposed method optimizes both the model complexity as well as the model performance by a single criterion. Moreover, by using the significance-aware principle, the proposed framework is realized in a computationally efficient way. The method is validated by three experiments using synthesized time-invariant nonlinearities, synthesized time-varying nonlinearities, and using real recorded nonlinearities.

This work presents a data driven control strategy able to track a set point without steady state error. The control sequence is computed as an affine combination of past control signals, which belong to a set of past closed loop trajectories stored in a process historian database. This affine combination is computed so that the variance of the tracking error is minimized. It is shown that offset free control (zero mean tracking error) is achieved under the assumption that the underlying dynamics are linear and the closed loop trajectories of the database are in turn offset free. That is, the proposed strategy inherits the offset free tracking capability of the stored past closed loop trajectories. No prior or subsequent knowledge about the process dynamics is required. The procedure to build the database is to store only the best trajectories that meet a design criteria, chosen from a series of iteratively tuned controllers. In this way the proposed controller will learn how to obtain a well tuned control in spite of the different operating conditions.

In adaptive feedback cancellation (AFC) methods, the step-size plays an important role in controlling the convergence speed of an adaptive filter in the feedback canceller path. The selection of this step-size provides a compromise between a low steady-state error and a fast convergence rate. The use of a variable step-size (VSS) is a potential solution to achieve both fast convergence and low steady-state error. In this paper, we propose a frequency-domain AFC method which integrates an improved practical VSS (IPVSS) algorithm into a partitioned-block frequency-domain (PBFD) implementation of the prediction error method (PEM) for hearing aid applications. The proposed method derives benefit from the IPVSS algorithm, e.g., a better compromise solution between convergence and steady-state error, and from the PBFD-PEM, e.g., a low numerical complexity and an improved convergence. The proposed method is evaluated for different types of speech incoming signals as well as for a sudden change of the acoustic feedback path. Simulation results show that the proposed method provides a significant performance improvement compared to the PBFD affine combination approach as well as the PBFD using either the upper or the lower step-sizes which are utilised as boundaries in the IPVSS algorithm.

We propose a method based on the collaborative Low-Rank Representation (LRR) and Sparse Subspace Clustering (SSC) to cluster data drawn from multiple linear subspaces in a high-dimensional space. Given a set of data vectors, Collaborative Low-Rank and Sparse Subspace Clustering(CLRS) want to seek a better representation among the candidates that represent all vectors as affine combination of the bases in a dictionary. Both theoretical and experimental results show that CLRS is a promising method for subspace segmentation.

In recent years, semantics-based crossover operators have attracted attention for efficient search in Genetic Programming (GP). Geometric Semantic Genetic Programming (GSGP) is one of the methods, in which a convex combination of two parents is used for creating an offspring. We have previously proposed an improved GSGP, Deterministic GSGP. In Deterministic GSGP, the convex combination is relaxed to an affine combination, and the optimum ratio for the affine combination is determined so that an offspring can always have better fitness than its parents. However, Deterministic GSGP has a problem that search might fall into local optima due to premature convergence. In this paper, we propose a new generation alternation model for maintaining population diversity. In the proposed model, all the individuals have opportunities to generate offspring as parents. We compared our proposed model with the conventional Deterministic GSGP in search performance, and showed its effectiveness.

we present a method based on a locally affineinvariant constraint for volumetric registration of 3D solid shapes. The core idea of this method is that an affine combination of the given point in 3D solid shapes that are directly connected to the given point, and the corresponding weight of each neighboring point can be obtained by the method of generalized least square. The input of our method is a pair of 3D solid shapes that are represented by a tetrahedral mesh and a voxelized object consisting of a set of voxel cells segmented from Digital Imaging and Communications in Medicine(DICOM) scans. To achieve the registration between the two input DICOM images, we firstly need to do some preprocessing to segment the bones out from the DICOM images and represent the segmented healthy bone and lesion bone using a generic template tetrahedral mesh and a set of voxel cells, respectively. Secondly we apply the standard Iterative Closest Point (ICP) method to briefly align the tetrahedral mesh and the voxelized object. Thirdly we execute a novel registration process that uses as much volumetric information and local geometry information as possible while deforming the generic template tetrahedral mesh of a healthy human bone towards the undelying geometry of the voxel cells. Compared with the previous methods that are based on point or surface, our method requires less auxiliary variables and can better capture the volumetric information of the 3D solid shapes, such as the thickness of the bones. Besides that, using a tetrahedral mesh to represent a solid shape can make the precision of registration greatly improved. Our experimental results demonstrate that the proposed method is robust and is of high registration accuracy.

Low complexity Normalized Least Mean Square (NLMS) adaptive algorithm is widely used in the adaptive system identification applications. To exploit the sparse impulse response of the system, different sparse penalties are introduced into the error function of the NLMS algorithm. Reweighted Zero Attracting-NLMS (RZA-NLMS) algorithm based on 11-norm relaxation offers improved performance in identifying the system with sparse echo path but when the system is non-sparse, NLMS algorithm dominates the sparse adaptive algorithm. In order to identify the system with varying sparseness, a new strategy is required. In this paper, we propose an affine combination of RZA-NLMS and NLMS filters used for system identification with variable sparsity. The robust performance of our proposed approach has been verified from the MATLAB simulations.

In this paper we propose a new regularized technique for identification of piecewise affine systems which combines the l 1 loss and the recently introduced stable spline kernel. This latter is used to define a quadratic penalty which embeds information on the stability of each isolated subsystem. Our procedure determines sequentially the complexity of each affine subsystem, and then its impulse response, estimating from data couples of hyperparameters. The algorithm involves a series of operations which promote intra-submodel regularization hence favoring subsystems detection and reconstruction. Numerical experiments involving high-order piecewise affine systems show the effectiveness of the new approach.

In this paper, we present a method for affine invariant feature description. Based on the gradient distribution of an image region we calculate two basis vectors defining an affine invariant coordinate system, used to normalize the image region. The estimated basis vectors are non-orthogonal and allow for a precise representation of the gradient distribution. The proposed method can be combined with any feature detector and descriptor. Its performance is evaluated on globally affine transformed as well as on real world images and compared to state of the art methods for affine invariant feature description. The observed results outperform the results obtained by the SIFT feature detector and are comparable to the results obtained by ASIFT while having less computational complexity and being more flexibly applicable in case of local affine modifications.

Hyperspectral images often contain multiple intimate (nonlinear) mixtures. When attempting to unmix such datasets it is important to identify (cluster) the different mixtures present in the data and also minimize the effects of the nonlinearities in the data due to intimate mixing (embedding). Manifold clustering and embedding techniques appear to be an ideal tool for this task. Previous work in the field of manifold clustering either make simplifying assumptions or trade-off the embedding objective to improve the clustering. This is unacceptable in the case of unmixing as the embedded data is used for future processing (for e.g. abundance estimation). We discuss a low rank neighborhood representation which expresses each point as an affine combination of its neighbors on the same manifold. This ensures that the reconstruction matrix has a block diagonal structure, enabling the identification of classes by spectral clustering. The embedding of the different manifolds can also be obtained from this matrix. We will show the improved performance of this algorithm on simulated as well as real hyperspectral reflectance data of two ternary mixtures with two shared endmembers.

In this paper, we propose an affine invariant image matching algorithm, which is based on the well-known SIFT algorithm. Firstly, we use MSER algorithm to detect affine invariant feature regions. Then covariance matrix of an image patch is used to transform anisotropic patches into isotropic patches by rotating and squeezing. Finally, the affine invariant key points on isotropic patches are detected by SIFT algorithm. Experiments show that M-SIFT works well with large affine angle changes and scale changes compared with SIFT algorithm.

This paper describes methods for tracking using point and line features in affine views to provide fundamental invariance to changes of focal length. It first demonstrates how an earlier method of transfer-based tracking using spatio-temporal matching of point features in a stereo active head is indeed zoom-invariant. In order to also make use of lines the paper then illustrates how the affine tri- and quadrifocal tensors may be applied to tracking with zoom in monocular and stereo systems respectively. The usefulness of the tensors is evident from their ability to transfer a fixation point in two uncalibrated images into novel views. Whereas the trifocal tensor is already familiar and in common use for matching and reconstruction, we believe this to be the first practical application of a quadrifocal tensor. We develop expressions for affine tri- and quadrifocal tensors, and using novel affine specializations of existing projective algorithms we show how computation of the tensors is faster, simpler and more stable. Experiments on real images are presented.

The traditional affine iterative closest point (ICP) algorithm is fast and accuracy for affine registration of point sets, but it performs worse when the point sets with large outliers. This paper introduces a novel algorithm based on correntropy for affine registration of point sets with outliers. First, a novel objective function is proposed by introducing the maximum correntropy criterion (MCC) because of the outlier-rejection property of correntropy. Then, a new affine ICP algorithm is proposed to solve this energy function. This method uses a simple iterative algorithm and computes the affine transformation quickly at each iterative step. Similar to the ICP algorithm, this new algorithm converges monotonically to a local maximum for any given initial parameters. Experimental results demonstrate that our algorithm has the high speed and accuracy for affine registration with outliers compared with the traditional ICP algorithm and the state-of-the-art algorithms.

In this paper two block-sparse approximated memory improved proportionate affine projection algorithm are proposed for block sparse system identification. An approximation is used for a recently proposed family of block-sparse proportionate affine projection algorithms. It is shown that the proposed algorithms have close convergence performance to the original ones and they are less numerically complex. An investigation of the influence of their parameters is also presented.

Date of Conference: 16-19 May 2016 Conference Name: IEEE 24th Signal Processing and Communications Applications Conference, SIU 2016 In this work, we propose a new approach for mixture of adaptive filters based on set-membership filters (SMF) which is specifically designated for big data signal processing applications. By using this approach, we achieve significantly reduced computational load for the mixture methods with better performance in convergence rate and steady-state error with respect to conventional mixture methods. Finally, we approve these statements with the simulations done on produce data.

In this paper, we present a method to increase invariance against affine deformations in feature based object detection systems. We use the gradient distribution of an image region to calculate two non-orthogonal basis vectors defining an affine invariant coordinate system, which is used to normalize the image region. The proposed method is an intermediate processing step subsequent to the feature detection and can be combined with any feature detector and descriptor combination. Its performance is evaluated on locally affine transformed as well as on real world images and compared to state of the art methods for affine invariant feature description. The observed results outperform the results obtained by SIFT, ASIFT or the Harris-Affine based feature normalization method, without introducing significant additional demands on the memory requirement or the computational complexity.

Let AS (2v, Fq) be a 2-dimensional affine symplectic space over finite fields Fq. In this paper, we construct a family of error-tolerant pooling designs with the incidence matrix of two types of flats (i.e., (m, s)-flats and (r, 0)-flats) over affine symplectic space AS (2v, Fq). We also discuss the error-tolerant and error-correcting properties of our designs.

We propose a method for estimating multiple-hypothesis affine regions from a keypoint by using an anisotropic Laplacian-of-Gaussian (LoG) filter. Although conventional affine region detectors, such as Hessian/Harris-Affine, iterate to find an affine region that fits a given image patch, such iterative searching is adversely affected by an initial point. To avoid this problem, we allow multiple detections from a single keypoint. We demonstrate that the responses of all possible anisotropic LoG filters can be efficiently computed by factorizing them in a similar manner to spectral SIFT. A large number of LoG filters that are densely sampled in a parameter space are reconstructed by a weighted combination of a limited number of representative filters, called "eigenfilters", by using singular value decomposition. Also, the reconstructed filter responses of the sampled parameters can be interpolated to a continuous representation by using a series of proper functions. This results in efficient multiple extrema searching in a continuous space. Experiments revealed that our method has higher repeatability than the conventional methods.

Scale Invariant Feature Transform (SIFT) is a method to detect and match invariant feature points on images, and is robust against contrast, rotation, and scale changes. However, SIFT cannot find many correct matching points between affine transformed images because this method employs Gaussian function for scale parameter which specifies a circle area on image planes. In this paper, we propose a method to use Bi-dimensional Empirical Mode Decomposition (BEMD) for keypoint detection, where a given image is decomposed into Intrinsic Mode Functions (IMFs). Our method also employs Affine Moment Invariants (AMIs) instead of SIFT's feature values. As a result, the proposed method detects more matching points than SIFT in a steep affine transformed image.

In this paper we present an affine combination strategy for two adaptive filters. One filter is designed to handle sparse impulse responses and the other one performs better if impulse response is dispersive. Filter outputs are combined using an adaptive mixing parameter and the resulting output shows better performance than each of the combining filters separately. We also demonstrate that affine combination results in faster convergence than convex combination of two adaptive filters.

A new method dealing with recognition of partially occluded and affine distortion objects is presented. The method is designed for objects with smooth curved boundary. It divides an object into affine-invariant parts based on the feature point. And a new approach for matching each part is presented in this paper. Robust Hausdorff distance (RHD) is introduced to measure the similarity between feature points set of model and that of target. In terms of the new RHD, the optimal affine transform can be estimated. And then the sub-curve match pairs are calculated based on the optimal affine transformation. The experimental results show proposed algorithm are capable of coping with partial occlusion and affine transformation.

This paper gives sufficient conditions for controllability of one-input affine control systems evolving on finite-dimensional real (matrix) simple Lie groups. A class of one-input invariant control affine systems evolving on the special linear group SL(n, R) is studied.

In this paper, we present an affine invariant feature descriptor, which is based on the well known Scale Invariant Feature Transform algorithm. The descriptor is a weighted histogram of gradient orientations and invariant against scale, in-plane rotation, stretch and skew. To cover the geometrical distortions introduced by an affine image transformation, we create a suiting, affine transformed coordinate system and perform all mathematical calculations in it. Furthermore, we propose to adapt the shape of the described region in order to gain invariance against affine transformations. We use elliptical respectively quadrangular regions instead of circular or quadratic regions. Based on synthetically transformed images we evaluate the matching performance of our descriptor in the case of available perfect knowledge about the image transformation, as well as for employing estimated transformation matrices. The results demonstrate that the proposed descriptor is capable of describing affine transformed regions well, even in case of strong affine image distortions.

Establishing visual correspondence is one of the most fundamental tasks in many applications of computer vision fields. In this paper we propose a robust image matching to address the affine variation problems between two images taken under different viewpoints. Unlike the conventional approach finding the correspondence with local feature matching on fully affine transformed-images, which provides many outliers with a time consuming scheme, our approach is to find only one global correspondence and then utilizes the local feature matching to estimate the most reliable inliers between two images. In order to estimate a global image correspondence very fast as varying affine transformation in affine space of reference and query images, we employ a Bhattacharyya similarity measure between two images. Furthermore, an adaptive tree with affine transformation model is employed to dramatically reduce the computational complexity. Our approach represents the satisfactory results for severe affine transformed-images while providing a very low computational time. Experimental results show that the proposed affine-invariant image matching is twice faster than the state-of-the-art methods at least, and provides better correspondence performance under viewpoint change conditions.

The recoverability reflects the capability of the system to tolerate the worst faults over a prescribed set under admissible energy constrains. In this paper, a piecewise affine (PWA) controller is designed for a piecewise affine approximation of the nonlinear dynamics, which can stabilize the original nonlinear system under some conditions. By analyzing the upper bound of the piecewise linear quadratic control performance of the PWA system, a novel fault recoverability evaluation scheme is further proposed for the nonlinear system with respect to the given limit of admissible control performance. A longitudinal flight control example is taken to show the effectiveness of the proposed method.

The paper presents an original method for Finite Time Response (FTR) control of the affine systems. The FTR property is specific to linear systems only, known in the literature as dead-beat algorithms. In this work, it is developed as a new procedure for the affine systems FTR synthesis, called the Equivalent Input Method (EIM). For this purpose it calculates an equivalent input which will determine, according to a quadratic criterion, the best approximation of the affine component. This way the system is approximated by an affine system with an input variable equal to the sum of the original input and the equivalent input, but having only a residual affine component. This residual affine component has a smaller norm than the initial affine component. Considering zero the residual affine component, a FTR linear system synthesis procedure is applied. In the real system, controlled by a FTR control law, the residual affine component creates at each step a disturbance that FTR algorithm seeks to cancel. This approach is justified by the fact that the disturbance residual affine component is much smaller in norm than the original affine component. Under certain circumstances, this residual affine component can be zero. The controllability and algorithm convergence is analyzed. The proposed EIM method can be applied also for nonlinear systems approximated by Piecewise Affine Subsystems (PWAS). An experimental platform has been designed in Matlab environment allowing implementation of various affine systems and their control algorithms. Simulation results are included to support the method presented in the paper.

Global Positioning System (GPS) is an all weather Position, Velocity and Time determination navigation system. Multipath is one of the prominent error sources in GPS. In this paper, various Least Mean Square (LMS) adaptive algorithms such as simple LMS, Normalized LMS, Variable length LMS and affine combination of two LMS filters are investigated to mitigate multipath error. Accurate step size parameter is estimated and the performance of each filter is examined critically. Affine combination of two LMS adaptive filters uses two step sizes, one for slower convergence and another for good steady state response. The results are encouraging with affine combination of two LMS filters. It has improved performance with higher computational complexity compared to other three filters. Hence, affine combination of two LMS adaptive filters is the choice best choice for multipath mitigation in GPS applications.

This paper presents a novel and reliable tracking-by detection method for image regions that undergo affine transformations such as translation, rotation, scale, dilatation and shear deformations, which span the six degrees of freedom of motion. Our method takes advantage of the intrinsic Lie group structure of the 2D affine motion matrices and imposes this motion structure on a kernelized structured output SVM classifier that provides an appearance based prediction function to directly estimate the object transformation between frames using geodesic distances on manifolds unlike the existing methods proceeding by linearizing the motion. We demonstrate that these combined motion and appearance model structures greatly improve the tracking performance while an incorporated particle filter on the motion hypothesis space keeps the computational load feasible. Experimentally, we show that our algorithm is able to outperform state-of-the-art affine trackers in various scenarios.

The research of affine scale space is to create a more general approach to the affine invariant image scale representation by modifying the corresponding Gaussian filters in order to cope with the specific change of view point. It has the purpose to retain a linear relationship with the transiting of the view point. With this linear relationship, the affine scale space could be established as a more general approach for the affine invariant image retrieval, including affine feature detection and affine feature descriptor. The scope of this paper is to discuss the accessible to the affine scale space, its performance and a practical implementation to construct it in order to cope with the high complexity brought in by the scale space and the affine adaptation.

In this paper, we enhance a recently proposed method for adaptive identification of piecewise affine systems by the use of concurrent learning. It is shown that the concurrent use of recorded and instantaneous data leads to exponential convergence of all subsystem parameters under verifiable conditions on the recorded data. A key advantage of the proposed method is that linear independence of the recorded data is sufficient, compared to the persistence of excitation assumed by previous adaptive parameter identifiers. Furthermore, the procedure tremendously improves the performance of adaptive identification for piecewise affine systems that previously suffered from slow convergence.

This paper proposes a new image smoothing method using a metric tensor for affine invariant scale space. In the field of image processing and recognition, Gaussian filtering is a common procedure for image smoothing. For example, scale space construction based on Gaussian filtering is sometimes used as a preprocessing of various image processing tasks. However Gaussian filtering is not affine invariant. This paper proposes a new method for image smoothing that is invariant under such affine transformation that does not change the area of any region in the image. It is shown that a scale space representation can be constructed collaterally with the image smoothing. Experimental results show that the proposed method is almost never affected by affine transformation different from usual Gaussian filtering. In the proposed method, processing results are expected to be not affected much by variation of the viewpoint.

Multi-resolution and wavelet analysis have generated considerable interest in the field of mesh surface representation. In this paper, we propose a backward, coarse-to-fine framework that derives a semi-regular approximation of an original mesh, and demonstrate its effectiveness on level-of-detail and scalable coding applications. The framework is flexible and simple because the position of a new vertex at a finer resolution can be derived in a closed form, based on the affine combination of a subdivision scheme, the original mesh, and “new” information about the wavelet coefficients. We report the results of experiments on both applications; and also compare the scalable coding results with those of other methods.

We present a method for two-dimensional (2D) shape detection applicable under affine transformation. The problem of affine-invariant shape detection is an important and fundamental research subject in computer vision. Although various methods have been proposed to solve this problem, most of those approaches are not well suited for the following general cases: (1) a shape to be detected is occluded by other overlapping objects, (2) a shape boundary is partially broken because of noise or other factors. We introduce a method to deal with such cases, which extends the generalized Hough transform to be an affine-invariant shape detector. This method, called the affine-GHT, utilizes pairwise parallel tangents and basic properties of an affine transformation to carry the direct computation for six parameters of an affine transformation. Experimental results demonstrate that the proposed method performs successfully and efficiently.

Sparse system identification problems often exist in many applications, such as echo interference cancellation, sparse channel estimation, and adaptive beamforming. One of popular adaptive sparse system identification (ASSI) methods is adopting only one sparse least mean square (LMS) filter. However, the adoption of only one sparse LMS filter cannot simultaneously achieve fast convergence speed and small steady-state mean state deviation (MSD). Unlike the conventional method, we propose an improved ASSI method using affine combination of two sparse LMS filters to simultaneously achieving fast convergence and low steady-state MSD. First, problem formulation and standard affine combination of LMS filters are introduced. Then an approximate optimum affine combiner is adopted for the proposed filter according to stochastic gradient search method. Later, to verify the proposed filter for ASSI, computer simulations are provided to confirm effectiveness of the proposed filter which can achieve better estimation performance than the conventional one and standard affine combination of LMS filters., Comment: 5 pages, 8 figures, submitted for VTC2014-spring

In recent years several algorithms have been developed that allow feature matching methods to operate on images with large baseline variations such as Affine-Scale Invariant Feature Transform (ASIFT) and its variants. These algorithms solve the base line problem through simulating various potential transforms between image pairs. These simulated views may be easier to match using traditional feature matching algorithms than the original wide baseline views. This paper presents a novel approach to approximating the orientation between wide baseline views. The proposed method tentatively matches affine invariant regions, normalizes and aligns the regions using whitening transforms to produce an affine transform for the scene. To increase efficiency, edge pixels are utilized rather than correlating regions. Results show that the proposed method is able to match scenes containing up to 80 degrees in vertical and horizontal perspective change. The method is superior to state-of-the-art ASIFT algorithms in terms of execution time.

This paper introduces an evolving update interval algorithm for the optimal step-size affine projection algorithm. The optimal step-size affine projection algorithm is one of numerous approaches to get better performance for the affine projection algorithm. It is suggested by analyzing the mean square deviation of fixed step-size affine projection algorithm. With the optimal step-size affine projection algorithm, in this paper, by evolving the update interval, it is able to show much better performance. From the MSD analysis, the learning curve is dived into two stage: the transient stage and the steady-state. By finding the cross point of affine projection algorithm's learning curve, the update interval is modified. By updating the weight vector for updated interval, the proposed algorithm reduces the computational complexity. With the proposed algorithm from simulations, it shows higher convergence rate and lower steady-state error.

This paper proposes a new image smoothing method invariant to affine transformation. In the field of image processing and recognition, Gaussian filtering is a common procedure for image smoothing. However Gaussian filtering is not affine invariant. This paper proposes a new method for image smoothing that is invariant under such affine transformation that does not change the area of any region in the image. Experimental results show that the proposed method is almost never affected by affine transformation different from usual Gaussian filtering. In the proposed method, processing results are expected to be not affected much by variation of the viewpoint.