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 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.

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.