Moment-Based Method to Estimate Image Affine Transform

The estimation of affine transform is a crucial problem in the image recognition field. This paper resorted to some invariant properties under translation, rotation and scaling, and proposed a simple method to estimate the affine transform kernel of the two-dimensional gray image. Maps, applying to the original, produce some correlative points that can accurately reflect the affine transform feature of the image. Furthermore, unknown variables existing in the kernel of the transform are calculated. The whole scheme only refers to one-order moment, therefore, it has very good stability.

Realization of Fractal Affine Transformation

This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its corresponding mathematical equations which are essential in fractal image construction.

AFFINE TRANSFORMATION IN RANDOM ITERATED FUNCTION SYSTEMS

Random iterated function systems (IFSs) is discussed, which is one of the methods for fractal drawing. A certain figure can be reconstructed by a random IFS. One approach is presented to determine a new random IFS, that the figure reconstructed by the new random IFS is the image of the origin figure reconstructed by old IFS under a given affine transformation. Two particular examples are used to show this approach.

Real-Time Tool for Affine Transformations of Two Dimensional IFS Fractal

This work introduces a novel tool for interactive, real-time affine transformations of two dimensional IFS fractals. The tool uses some of the nice properties of the barycentric coordinates that are assigned to the points that constitute the image ofa fractal, and thus enables any affine transformation of the affine basis, done by click-and-drag, to be immediately followed by the same affine transformation of the fractal. The barycentric coordinates can be relative to an arbitrary affine basis of ~2, but in order to have a better control over the fractal, a kind of minimal simplex that contains the fractal attractor is used.

Affine transformation of virtual 3D object using 2D localization of fingertips

Background Interactions with virtual 3D objects in the virtual reality(VR)environment using the gesture of fingers captured in a wearable 2D camera have emerging applications in real-life.Method This paper presents an approach of a two-stage convolutional neural network,one for the detection of hand and another for the fingertips.One purpose of VR environments is to transform a virtual 3D object with affine parameters by using the gesture of thumb and index fingers.Results To evaluate the performance of the proposed system,one existing,and another developed egocentric fingertip databases are employed so that learning involves large variations that are common in real-life.Experimental results show that the proposed fingertip detection system outperforms the existing systems in terms of the precision of detection.Conclusion The interaction performance of the proposed system in the VR environment is higher than that of the existing systems in terms of estimation error and correlation between the ground truth and estimated affine parameters.

WAVELET TRANSFORM ASSOCIATED TO THE AFFINE GROUP AGS,

This paper considers wavelet transforms associated to the affine group, which is more general than the paper given by R. Murenzi, and it seems more important in mathematical theory and more natural to be used to analyze signals in more than 1-dimension.

Transformation method and wave control

Transformation method provides an efficient way to control wave propagation by materials.The transformed relations for field and material during a transformation are essential to fulfill this method.We propose a systematic method to derive the transformed relations for a general physic process,the constraint conditions are obtained by considering geometrical and physical constraint during a mapping. The proposed method is applied to Navier＇s equation for elastodynamics,Helmholtz＇s equation for acoustic wave and Maxwell＇s equation for electromagnetic wave,the corresponding transformed relations are derived,which can be used in the framework of transformation method for wave control.We show that contrary to electromagnetic wave,the transformed relations are not uniquely determined for elastic wave and acoustic wave,so we have a freedom to choose them differently.Using the obtained transformed relations,we also provide some examples for device design,a concentrator for elastic wave,devices for illusion acoustic and illusion optics are conceived and validated by numerical simulations.

Image-Moment Based Affine Invariant Watermarking Scheme Utilizing Neural Networks

A new image watermarking scheme is proposed to resist rotation, scaling and translation （RST） attacks. Six combined low order image moments are utilized to represent image information on rotation, scaling and translation. Affine transform parameters are registered by feedforward neural networks. Watermark is adaptively embedded in discrete wavelet transform （DWT） domain while watermark extraction is carried out without original image after attacked watermarked image has been synchronized by making inverse transform through parameters learned by neural networks. Experimental results show that the proposed scheme can effectively register affine transform parameters, embed watermark more robustly and resist geometric attacks as well as JPEG2000 compression.

Extraction of affine invariant features for shape recognition based on ant colony optimization

A new approach to extraction of affine invariant features of contour image and matching strategy is proposed for shape recognition.Firstly,the centroid distance and azimuth angle of each boundary point are computed.Then,with a prior-defined angle interval,all the points in the neighbor region of the sample point are considered to calculate the average distance for eliminating noise.After that,the centroid distance ratios（CDRs） of any two opposite contour points to the barycenter are achieved as the representation of the shape,which will be invariant to affine transformation.Since the angles of contour points will change non-linearly among affine related images,the CDRs should be resampled and combined sequentially to build one-by-one matching pairs of the corresponding points.The core issue is how to determine the angle positions for sampling,which can be regarded as an optimization problem of path planning.An ant colony optimization（ACO）-based path planning model with some constraints is presented to address this problem.Finally,the Euclidean distance is adopted to evaluate the similarity of shape features in different images.The experimental results demonstrate the efficiency of the proposed method in shape recognition with translation,scaling,rotation and distortion.

AFFINE SPINOR DECOMPOSITION IN THREE-DIMENSIONAL AFFINE GEOMETRY

Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.

New Mathematical Model Based on Affine ransformation for Remote Sensing Image with High Resolution

This paper calculates the parameters of image position and orientation,proposes a mathematical model and adopts a new method with three steps of transformations based on parallel ray projection.Every step of the model is strict,and the map function of each transformation is the first order polynomials and other simple function.The final calculation of the parameters is for the linear equations with good status.As a result,the problem of the relativity of image parameter calculation is solved completely.Some experiments are carried out.

Affine A_3^((1)) N=2 Monopole as the D Module and Aftine ADHMN Sheaf

A Higgs-Yang-Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual α plane fields are holomorphic, but the right outgoing SD β plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse afiine rapidity parameters μ and μ^-1. The Dirac wave function scattering in this background also factorized respectively into the （anti）holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conformal affine massive field. We find explicit Nahm transformation matrix （Fourier Mukai transformation） between the Higgs YM BPS （fiat） bundles （1） modules） and the affinized blow up ADHMN twistors （perverse sheafs）. Thus we establish the algebra for the ＇t Hooft Hecke operators in the Hecke correspondence of the geometric Langlands program.

A NEW IMAGE REGISTRATION METHOD FOR GREY IMAGES

The proposed algorithm relies on a group of new formulas for calculating tangent slope so as to address angle feature of edge curves of image. It can utilize tangent angle features to estimate automatically and fully the rotation parameters of geometric transform and enable rough matching of images with huge rotation difference. After angle compensation, it can search for matching point sets by correlation criterion, then calculate parameters of affine transform, enable higher-precision emendation of rotation and transferring. Finally, it fulfills precise matching for images with relax-tense iteration method. Compared with the registration approach based on wavelet direction-angle features, the matching algorithm with tangent feature of image edge is more robust and realizes precise registration of various images. Furthermore, it is also helpful in graphics matching.

Multi-modality liver image registration based on multilevel B-splines free-form deformation and L-BFGS optimal algorithm

A new coarse-to-fine strategy was proposed for nonrigid registration of computed tomography(CT) and magnetic resonance(MR) images of a liver.This hierarchical framework consisted of an affine transformation and a B-splines free-form deformation(FFD).The affine transformation performed a rough registration targeting the mismatch between the CT and MR images.The B-splines FFD transformation performed a finer registration by correcting local motion deformation.In the registration algorithm,the normalized mutual information(NMI) was used as similarity measure,and the limited memory Broyden-Fletcher- Goldfarb-Shannon(L-BFGS) optimization method was applied for optimization process.The algorithm was applied to the fully automated registration of liver CT and MR images in three subjects.The results demonstrate that the proposed method not only significantly improves the registration accuracy but also reduces the running time,which is effective and efficient for nonrigid registration.

Two-stage image segmentation based on edge and region information

A two-stage method for image segmentation based on edge and region information is proposed. Different deformation schemes are used at two stages for segmenting the object correctly in image plane. At the first stage, the contour of the model is divided into several segments hierarchically that deform respectively using affine transformation. After the contour is deformed to the approximate boundary of object, a fine match mechanism using statistical information of local region to redefine the external energy of the model is used to make the contour fit the object's boundary exactly. The algorithm is effective, as the hierarchical segmental deformation makes use of the globe and local information of the image, the affine transformation keeps the consistency of the model, and the reformative approaches of computing the internal energy and external energy are proposed to reduce the algorithm complexity. The adaptive method of defining the search area at the second stage makes the model converge quickly. The experimental results indicate that the proposed model is effective and robust to local minima and able to search for concave objects.

A convolutional neural artistic stylization algorithm for suppressing image distortion

Aiming at the problems of image semantic content distortion and blurred foreground and background boundaries during the transfer process of convolutional neural image stylization,we propose a convolutional neural artistic stylization algorithm for suppressing image distortion.Firstly,the VGG-19 network model is used to extract the feature map from the input content image and style image and to reconstruct the content and style.Then the transfer of the input content image and style image to the output image is constrained in the local affine transformation of the color space.And the Laplacian matting matrix is constructed by combining the local affine of the input image RGB channel.For each output blocks,affine transformation maps the RGB value of the input image to the corresponding output and position,which realizes the constraint of semantic content and the control of spatial layout.Finally,the synthesized image is superimposed on the white noise image and updated iteratively with the back propagation algorithm to minimize the loss function to complete the image stylization.Experimental results show that the method can generate images with obvious foreground and background edges,clear texture,restrained semantic content-distortion,realized spatial constraint and color mapping of the transfer images,and made the stylized images visually satisfactory.

On Quasiconformal Mappings Between Hyperbolic Triangles

Quasiconformal mappings between hyperbolic triangles are considered.We give an explicit estimate of the dilation of the quasiconformal mappings,which generalizes Bishop's results.

Contrast Enhancement Based Image Detection Using Edge Preserved Key Pixel Point Filtering

In existing methods for segmented images,either edge point extraction or preservation of edges,compromising contrast images is so sensitive to noise.The Degeneration Threshold Image Detection(DTID)framework has been proposed to improve the contrast of edge filtered images.Initially,DTID uses a Rapid Bilateral Filtering process for filtering edges of contrast images.This filter decomposes input images into base layers in the DTID framework.With minimal filtering time,Rapid Bilateral Filtering handles high dynamic contrast images for smoothening edge preservation.In the DTID framework,Rapid Bilateral Filtering with Shift-Invariant Base Pass Domain Filter is insensitive to noise.This Shift-Invariant Filtering estimates value across edges for removing outliers(i.e.,noise preserving base layers of the contrast image).The intensity values are calculated in the base layer of the contrast image for accurately detecting nearby spatial locations using Shift-Invariant base Pass Domain Filter(SIDF).At last,Affine Planar Transformation is applied to detect edge filtered contrast images in the DTID framework for attaining a high quality of the image.It normalizes the translation and rotation of images.With this,Degeneration Threshold Image Detection maximizes average contrast enhancement quality and performs an experimental evaluation of factors such as detection accuracy,rate,and filtering time on contrast images.Experimental analysis shows that the DTID framework reduces the filtering time taken on contrast images by 54%and improves average contrast enhancement quality by 27%compared to GUMA,HMRF,SWT,and EHS.It provides better performance on the enhancement of average contrast enhancement quality by 28%,detection accuracy rate by 26%,and reduction in filtering time taken on contrast images by 30%compared to state-of-art methods.

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.

Affine Structures on a Ringed Space and Schemes

The author first introduces the notion of affine structures on a ringed space and then obtains several related properties.Affine structures on a ringed space,arising from complex analytical spaces of algebraic schemes,behave like differential structures on a smooth manifold.As one does for differential manifolds,pseudogroups of affine transformations are used to define affine atlases on a ringed space.An atlas on a space is said to be an affine structure if it is maximal.An affine structure is said to be admissible if there is a sheaf on the underlying space such that they are coincide on all affine charts,which are in deed affine open sets of a scheme.In a rigour manner,a scheme is defined to be a ringed space with a specified affine structure if the affine structures make a contribution to the cases such as analytical spaces of algebraic schemes.Particularly,by the whole of affine structures on a space,two necessary and sufficient conditions,that two spaces are homeomorphic and that two schemes are isomorphic,coming from the main theorems of the paper,are obtained respectively.A conclusion is drawn that the whole of affine structures on a space and a scheme,as local data,encode and reflect the global properties of the space and the scheme,respectively.