Fast image matching algorithm based on affine invariants

Feature-based image matching algorithms play an indispensable role in automatic target recognition （ATR）. In this work, a fast image matching algorithm （FIMA） is proposed which utilizes the geometry feature of extended centroid （EC） to build affine invariants. Based on at-fine invariants of the length ratio of two parallel line segments, FIMA overcomes the invalidation problem of the state-of-the-art algorithms based on affine geometry features, and increases the feature diversity of different targets, thus reducing misjudgment rate during recognizing targets. However, it is found that FIMA suffers from the parallelogram contour problem and the coincidence invalidation. An advanced FIMA is designed to cope with these problems. Experiments prove that the proposed algorithms have better robustness for Gaussian noise, gray-scale change, contrast change, illumination and small three-dimensional rotation. Compared with the latest fast image matching algorithms based on geometry features, FIMA reaches the speedup of approximate 1.75 times. Thus, FIMA would be more suitable for actual ATR applications.

Applications of new affine invariant for polytopes

To study the Schneider＇s projection problem, Lutwak, Yang and Zhang recently introduced a new .affine invariant functional U（P） for convex polytopes in R^n. In the paper, we obtain the analytic expression of the affine-invariant U（P） defined on a specific subclass of origin-symmetric convex polytopes in Rn and give an application of U（P） to the Lp-Minkowski problem.

An invariant interest point detector under image affine transformation

For vision-based mobile robot navigation, images of the same scene may undergo a general affine transformation in the case of significant viewpoint changes. So, a novel method for detecting affine invariant interest points is proposed to obtain the invariant local features, which is coined polynomial local orientation tensor(PLOT). The new detector is based on image local orientation tensor that is constructed from the polynomial expansion of image signal. Firstly, the properties of local orientation tensor of PLOT are analyzed, and a suitable tuning parameter of local orientation tensor is chosen so as to extract invariant features. The initial interest points are detected by local maxima search for the smaller eigenvalues of the orientation tensor. Then, an iterative procedure is used to allow the initial interest points to converge to affine invariant interest points and regions. The performances of this detector are evaluated on the repeatability criteria and recall versus 1-precision graphs, and then are compared with other existing approaches. Experimental results for PLOT show strong performance under affine transformation in the real-world conditions.

An Effective Image Retrieval Mechanism Using Family-based Spatial Consistency Filtration with Object Region

How to construct an appropriate spatial consistent measurement is the key to improving image retrieval performance. To address this problem, this paper introduces a novel image retrieval mechanism based on the family filtration in object region. First, we supply an object region by selecting a rectangle in a query image such that system returns a ranked list of images that contain the same object, retrieved from the corpus based on 100 images, as a result of the first rank. To further improve retrieval performance, we add an efficient spatial consistency stage, which is named family-based spatial consistency filtration, to re-rank the results returned by the first rank. We elaborate the performance of the retrieval system by some experiments on the dataset selected from the key frames of ＂TREC Video Retrieval Evaluation 2005 （TRECVID2005）＂. The results of experiments show that the retrieval mechanism proposed by us has vast major effect on the retrieval quality. The paper also verifies the stability of the retrieval mechanism by increasing the number of images from 100 to 2000 and realizes generalized retrieval with the object outside the dataset.

Invariants of Multi-Component Ermakov Systems

It is shown that certain multi-component Ermakov systems admit Lewis-Ray-Reid invariants.This extendsthe result to the two-component Ermakov system.

Objects Description and Extraction by the Use of Straight Line Segments in Digital Images

An advanced edge-based method of feature detection and extraction is developed for object description in digital images. It is useful for the comparison of different images of the same scene in aerial imagery, for describing and recognizing categories, for automatic building extraction and for finding the mutual regions in image matching. The method includes directional filtering and searching for straight edge segments in every direction and scale, taking into account edge gradient signs. Line segments are ordered with respect to their orientation and average gradients in the region in question. These segments are used for the construction of an object descriptor. A hierarchical set of feature descriptors is developed, taking into consideration the proposed straight line segment detector. Comparative performance is evaluated on the noisy model and in real aerial and satellite imagery.

3D Motion Estimation and Motion Fusion by Affine Region Matching

In this paper,a new method is presented for 3D motion estimation by image region correspon- dences using stereo cameras.Under the weak perspectivity assumption,we first employ the moment tensor theory(Cyganski and Orr)to compute the monocular affine transformations relating images taken by the same camera at different time instants and the binocular affine transformations relating images taken by different cameras at the same time instant.We then show that 3D motion can he recovered from these 2D transformations.A space-time fusion strategy is proposed to aim at robust results.No knowledge of point correspondences is required in the above processes and the computa- lions involved are linear.To find corresponding image regions,new affine invariants,which show stronger invariance,are derived in term of tensor contraction theory.Experiments on real motion images are conducted to verify the proposed method.

Illumination Invariant Recognition of Three-Dimensional Texture in Color Images

In this paper, illumination-affine invariant methods are presented based onaffine moment normalization techniques, Zernike moments, and multiband correlation functions. Themethods are suitable for the illumination invariant recognition of 3D color texture. Complex valuedmoments (i.e., Zernike moments) and affine moment normalization are used in the derivation ofillumination affine invariants where the real valued affine moment invariants fail to provide affineinvariants that are independent of illumination changes. Three different moment normalizationmethods have been used, two of which are based on affine moment normalization technique and thethird is based on reducing the affine transformation to a Euclidian transform. It is shown that fora change of illumination and orientation, the affinely normalized Zernike moment matrices arerelated by a linear transform. Experimental results are obtained in two tests: the first is usedwith textures of outdoor scenes while the second is performed on the well-known CUReT texturedatabase. Both tests show high recognition efficiency of the proposed recognition methods.

Computing knots by quadratic and cubic polynomial curves

A new method is presented to determine parameter values(knot)for data points for curve and surface generation.With four adjacent data points,a quadratic polynomial curve can be determined uniquely if the four points form a convex polygon.When the four data points do not form a convex polygon,a cubic polynomial curve with one degree of freedom is used to interpolate the four points,so that the interpolant has better shape,approximating the polygon formed by the four data points.The degree of freedom is determined by minimizing the cubic coefficient of the cubic polynomial curve.The advantages of the new method are,firstly,the knots computed have quadratic polynomial precision,i.e.,if the data points are sampled from a quadratic polynomial curve,and the knots are used to construct a quadratic polynomial,it reproduces the original quadratic curve.Secondly,the new method is affine invariant,which is significant,as most parameterization methods do not have this property.Thirdly,it computes knots using a local method.Experiments show that curves constructed using knots computed by the new method have better interpolation precision than for existing methods.

Dual mean Minkowski measures of symmetry for convex bodies

We introduce and study a sequence of geometric invariants for convex bodies in finite-dimensional spaces, which is in a sense dual to the sequence of mean Minkowski measures of symmetry proposed by the second author. It turns out that the sequence introduced in this paper shares many nice properties with the sequence of mean Minkowski measures, such as the sub-arithmeticity and the upper-additivity. More meaningfully, it is shown that this new sequence of geometric invariants, in contrast to the sequence of mean Minkowski measures which provides information on the shapes of lower dimensional sections of a convex body, provides information on the shapes of orthogonal projections of a convex body. The relations of these new invariants to the well-known Minkowski measure of asymmetry and their further applications are discussed as well.

AIG Based Nonlinear Anisotropic Smoothing Strategy for Vector-Valued Images

The effects of the Rician noise on the calculated tensors are analyzed and an affine invariant gradient (AIG) based nonlinear anisotropic smoothing strategy is presented.The AIG based smoothing strategy is a development of the affine invariant nonlinear anisotropic diffusion(AINAD) restoration model,introduced by Guillermo Sapiro,and adopted to restore vector-valued data.To evaluate the efficiency of the presented AINAD model in accounting for the Rician noise introduced into the vector-valued data,the peak-to-peak signal-to-noise ratio(PSNR),signal-to-mean squared error ratio(SMSE) and Beta(parameter that stands for edge preservation) metrics are used.The experiment results acquired from the synthetic and real data prove the good performance of the presented filter.

Jordan tori for a torsion free abelian group

We classify Jordan G-tori, where G is any torsion-free abelian group. Using the Zelmanov prime structure theorem, such a class divides into three types, the Hermitian type, the Clifford type, and the Albert type. We concretely describe Jordan G-tori of each type.