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.

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.

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.

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.

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.

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.

关于双曲三角形间的拟共形映射

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.

Density Map Guided Region Localization for End-to-End Small Object Detection

With the advancement of society and science and technology, the demand for detecting small objects in practical scenarios becomes stronger. Such objects are only represented by relatively small coverage of pixels, and the features are degraded severely after being extracted by a deep convolutional neural network, which is detrimental to the detection performance for small objects. Therefore, an intuitive solution is to increase the resolution of small objects by cropping the original image. In this paper, we propose a simple but effective object density map guided region localization module (DMGRL) to locate and crop the regions of interest where small objects may exist. Firstly, the density map of the objects is estimated by object density map estimation network, and then the coordinates of the small object regions are calculated;Secondly, the continuous differentiable affine transformation is utilized to crop these regions so that the detector with DMGRL can be trained end-to-end instead of two-stage training. Finally, the all prediction results of input image and cropped region images are merged together to output the final detection results by non maximum suppression (NMS). Extensive experiments demonstrate the superior performance of the detector incorporated DMGRL.

Point pattern Matching Using Irreducible Matrixand Relative Invariant

Point pattern matchingisanimportantproblem inthefieldsofcomputervision and patternrecognition.In this paper,new algorithms based onirreducible matrix andrelativeinvariantfor matchingtwosets ofpoints withthe same cardinality are proposed.Theirfundamentalideaistransformingthetwo dimensionalpointsets with n points intothe vectorsin n dimensional space. Considering these vectors as one dimensional point patterns,these new algorithms aim atreducingthe point matching problem to thatofsorting vectorsin n dimensionalspace aslong asthe sensornoise does notalterthe order ofthe elementsinthe vectors.Theoreticalanalysis and simulationresults show thatthe new algorithms are effective .

Color image encryption scheme based on chaotic systems

To improve the security of the color image encryption scheme,a color image encryption scheme based on chaotic systems is proposed. Firstly, the proposed scheme sets the color image as a three-dimensional matrix which is scrambled by affine transformation. Second, the Logistic chaotic sequence applied to generate the control parameter and auxiliary key is used to encrypt the three-dimensionaL matrix. Here, we mainly focus on two methods for encryption processes. One is to generate a chaotic sequence by Logistic map and Henon map, which is used to perform XOR operation with the scrambled components R＇, G＇, B＇ respectively. The other one is to adopt a binary Logistic sequence to select the pixel position for the scrambled components R＇, G＇, B＇ image, and then applying the Henon map and Logistic map with the auxiliary key to perform the replacement encryption. Based on this, an encrypted image is synthesized. Simulation results show that the proposed image encryption scheme can implement better encryption and achieve higher security performance.

Tracking and recognition algorithm for a robot harvesting oscillating apples

Apple fruits on trees tend to swing because of wind or other natural causes,therefore reducing the accuracy of apple picking by robots.To increase the accuracy and to speed up the apple tracking and identifying process,tracking and recognition method combined with an affine transformation was proposed.The method can be divided into three steps.First,the initial image was segmented by Otsu’s thresholding method based on the two times Red minus Green minus Blue(2R-G-B)color feature;after improving the binary image,the apples were recognized with a local parameter adaptive Hough circle transformation method,thus improving the accuracy of recognition and avoiding the long,time-consuming process and excessive fitted circles in traditional Hough circle transformation.The process and results were verified experimentally.Second,the Shi-Tomasi corners detected and extracted from the first frame image were tracked,and the corners with large positive and negative optical flow errors were removed.The affine transformation matrix between the two frames was calculated based on the Random Sampling Consistency algorithm(RANSAC)to correct the scale of the template image and predict the apple positions.Third,the best positions of the target apples within 1.2 times of the prediction area were searched with a de-mean normalized cross-correlation template matching algorithm.The test results showed that the running time of each frame was 25 ms and 130 ms and the tracking error was more than 8%and 20%in the absence of template correction and apple position prediction,respectively.In comparison,the running time of our algorithm was 25 ms,and the tracking error was less than 4%.Therefore,test results indicate that speed and efficiency can be greatly improved by using our method,and this strategy can also provide a reference for tracking and recognizing other oscillatory fruits.