scholarly journals Construction of Affine Invariant Functions in Spatial Domain

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Jianwei Yang ◽  
Yunjie Chen ◽  
Massimo Scalia
Keyword(s):  
Object Classification ◽  
Invariant Function ◽  
Spatial Domain ◽  
Closed Curve ◽  
Experimental Results ◽  
Transform Domain ◽  
Affine Invariant ◽  
Invariant Functions ◽  
Object Contour

Affine invariant functions are constructed in spatial domain. Unlike the previous affine representation functions in transform domain, these functions are constructed directly on the object contour without any transformation. To eliminate the effect of the choice of points on the contour, an affine invariant function using seven points on the contour is constructed. For objects with several separable components, a closed curve is derived to construct the affine invariant functions. Several experiments have been conducted to evaluate the performance of the proposed method. Experimental results show that the constructed affine invariant functions can be used for object classification.

scholarly journals Cutting Affine Moment Invariants

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Jianwei Yang ◽  
Ming Li ◽  
Zirun Chen ◽  
Yunjie Chen
Keyword(s):  
Image Processing ◽  
Closed Curve ◽  
Experimental Results ◽  
Moment Invariants ◽  
Affine Invariant ◽  
Original Image ◽  
Invariant Features ◽  
General Contour ◽  
Classification Tasks ◽  
Affine Moment Invariants

The extraction of affine invariant features plays an important role in many fields of image processing. In this paper, the original image is transformed into new images to extract more affine invariant features. To construct new images, the original image is cut in two areas by a closed curve, which is called general contour (GC). GC is obtained by performing projections along lines with different polar angles. New image is obtained by changing gray value of pixels in inside area. The traditional affine moment invariants (AMIs) method is applied to the new image. Consequently, cutting affine moment invariants (CAMIs) are derived. Several experiments have been conducted to evaluate the proposed method. Experimental results show that CAMIs can be used in object classification tasks.

RADIAL CENTROID CURVE FOR AFFINE INVARIANT FEATURES EXTRACTION

2012 ◽  
Vol 10 (04) ◽  
pp. 1250035 ◽  
Author(s):  
JIANWEI YANG ◽  
RUSHI LAN ◽  
YUAN YAN TANG ◽  
YUNJIE CHEN
Keyword(s):  
Computer Vision ◽  
Wavelet Transform ◽  
Line Segment ◽  
Invariant Function ◽  
Closed Curve ◽  
Affine Invariant ◽  
Stationary Wavelet Transform ◽  
Radial Line ◽  
Invariant Features ◽  
Wavelet Methods

The extraction of affine invariant features plays an important role in many fields of computer vision. Contour-based wavelet methods are unapplicable to objects with several separable components. In this paper, a method is proposed by converting the object into a closed curve, which is called radial centroid curve (RCC). Point on this curve is the centroid of radial line segment from centroid of the object. It is shown that the RCC derived from the affine transformed object is the same affine transformed version as that of the original object. An affine invariant function (AIF) is constructed by applying stationary wavelet transform (SWT) to the derived RCC. This scheme is applicable to objects with several separable components. Several experiments have been conducted to evaluate the performance of the proposed method.

scholarly journals Random Fiber Grating Characterization Based on OFDR and Transfer Matrix Method

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6071
Author(s):  
Zichao Zhou ◽  
Chen Chen ◽  
Ping Lu ◽  
Stephen Mihailov ◽  
Liang Chen ◽  
...  
Keyword(s):  
Fiber Lasers ◽  
Spectral Response ◽  
Quantitative Relationship ◽  
Spatial Domain ◽  
Experimental Results ◽  
Period Variation ◽  
Peak Wavelength ◽  
Variation Range ◽  
Wavelength Variation ◽  
Simulation Results

Random fiber gratings (RFGs) have shown great potential applications in fiber sensing and random fiber lasers. However, a quantitative relationship between the degree of randomness of the RFG and its spectral response has never been analyzed. In this paper, two RFGs with different degrees of randomness are first characterized experimentally by optical frequency domain reflectometry (OFDR). Experimental results show that the high degree of randomness leads to low backscattering strength of the grating and strong strength fluctuations in the spatial domain. The local spectral response of the grating exhibits multiple peaks and a large peak wavelength variation range when its degree of randomness is high. The linewidth of its fine spectrum structures shows scaling behavior with the grating length. In order to find a quantitative relationship between the degree of randomness and spectrum property of RFG, entropy was introduced to describe the degree of randomness induced by period variation of the sub-grating. Simulation results showed that the average reflectivity of the RFG in dB scale decreased linearly with increased sub-grating entropy, when the measured wavelength range was smaller than the peak wavelength variation range of the sub-grating. The peak reflectivity of the RFG was determined by κ2LΔP (where κ is the coupling coefficient, L is the grating length, ΔP is period variation range of the sub-grating) rather than κL when ΔP is larger than 8 nm in the spatial domain. The experimental results agree well with the simulation results, which helps to optimize the RFG manufacturing processes for future applications in random fiber lasers and sensors.

scholarly journals Towards Stochasticity through Joint Invariant Functions of Two Isomorphic Lie Algebras of SL(2R) Type

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 226
Author(s):  
Maricel Agop ◽  
Mitică Craus
Keyword(s):  
Complex System ◽  
Fractal Theory ◽  
Invariant Function ◽  
Hydrodynamic Type ◽  
Simultaneous Action ◽  
Systems Dynamics ◽  
Invariant Functions ◽  
Scale Relativity ◽  
The One ◽  
Joint Invariant

In the motion fractal theory, the scale relativity dynamics of any complex system are described through various Schrödinger or hydrodynamic type fractal “regimes”. In the one dimensional stationary case of Schrödinger type fractal “regimes”, synchronizations of complex system entities implies a joint invariant function with the simultaneous action of two isomorphic groups of the S L ( 2 R ) type as solutions of Stoka type equations. Among these joint invariant functions, Gaussians become in the Jeans’s sense, probability density (i.e., stochasticity) whenever the information on the complex system analyzed is fragmentary. In the two-dimensional case of hydrodynamic type fractal “regimes” at a non-differentiable scale, the soliton and soliton-kink of fractal type of the velocity field generate the minimal vortex of fractal type that becomes the source of all turbulences in the complex systems dynamics. Some correlations of our model to experimental data were also achieved.

scholarly journals Extraction of Affine Invariant Features Using Fractal

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jianwei Yang ◽  
Guosheng Cheng ◽  
Ming Li
Keyword(s):  
Pattern Recognition ◽  
Feature Vector ◽  
Fractal Dimensions ◽  
Input Pattern ◽  
Experimental Results ◽  
Central Projection ◽  
Affine Invariant ◽  
Invariant Features ◽  
General Contour ◽  
New Feature

An approach based on fractal is presented for extracting affine invariant features. Central projection transformation is employed to reduce the dimensionality of the original input pattern, and general contour (GC) of the pattern is derived. Affine invariant features cannot be extracted from GC directly due to shearing. To address this problem, a group of curves (which are called shift curves) are constructed from the obtained GC. Fractal dimensions of these curves can readily be computed and constitute a new feature vector for the original pattern. The derived feature vector is used in question for pattern recognition. Several experiments have been conducted to evaluate the performance of the proposed method. Experimental results show that the proposed method can be used for object classification.

EVOLUTIONS OF PLANAR POLYGONS

1995 ◽  
Vol 09 (06) ◽  
pp. 991-1014 ◽  
Author(s):  
ALFRED M. BRUCKSTEIN ◽  
GUILLERMO SAPIRO ◽  
DORON SHAKED
Keyword(s):  
General Theory ◽  
Experimental Results ◽  
Curve Evolution ◽  
Affine Invariant ◽  
Polygonal Approximation ◽  
Curve Shortening Flow ◽  
Planar Curves ◽  
Cyclic Pursuit ◽  
Invariant Differential ◽  
Curve Shortening

Evolutions of closed planar polygons are studied in this work. In the first part of the paper, the general theory of linear polygon evolutions is presented, and two specific problems are analyzed. The first one is a polygonal analog of a novel affine-invariant differential curve evolution, for which the convergence of planar curves to ellipses was proved. In the polygon case, convergence to polygonal approximation of ellipses, polygo nal ellipses, is proven. The second one is related to cyclic pursuit problems, and convergence, either to polygonal ellipses or to polygonal circles, is proven. In the second part, two possible polygonal analogues of the well-known Euclidean curve shortening flow are presented. The models follow from geometric considerations. Experimental results show that an arbitrary initial polygon converges to either regular or irregular polygonal approximations of circles when evolving according to the proposed Euclidean flows.

A PUBLIC MESH WATERMARKING ALGORITHM BASED ON ADDITION PROPERTY OF FOURIER TRANSFORM

2006 ◽  
Vol 06 (01) ◽  
pp. 35-43 ◽  
Author(s):  
LI LI ◽  
ZHIGENG PAN ◽  
DAVID ZHANG
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Spatial Domain ◽  
Experimental Results ◽  
Original Image ◽  
The Fourier Transform

This paper presents a public mesh watermarking algorithm whereby the resultant watermarked image minus the original image is the watermark information. According to the addition property of the Fourier transform, a change of spatial domain will cause a change in the frequency domain. The watermark information is then scaled down and embedded in one part of the x-coordinate of the original mesh. Finally, the x-coordinate of the test mesh is amplified before extraction. Experimental results prove that our algorithm is resistant to a variety of attacks without the need for any preprocessing.

scholarly journals Image Denoising Based on Dilated Singularity Prior

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Shaoxiang Hu ◽  
Zhiwu Liao ◽  
Wufan Chen
Keyword(s):  
Em Algorithm ◽  
Image Denoising ◽  
Mathematical Morphology ◽  
Visual Quality ◽  
Spatial Domain ◽  
Experimental Results ◽  
Canny Operator ◽  
Nonlocal Means ◽  
Spatial Image ◽  
Noisy Images

In order to preserve singularities in denoising, we propose a new scheme by adding dilated singularity prior to noisy images. The singularities are detected by canny operator firstly and then dilated using mathematical morphology for finding pixels “near” singularities instead of “on” singularities. The denoising results for pixels near singularities are obtained by nonlocal means in spatial domain to preserve singularities while the denoising results for pixels in smooth regions are obtained by EM algorithm constrained by a mask formed by downsampled spatial image with dilated singularity prior to suiting the sizes of the subbands of wavelets. The final denoised results are got by combining the above two results. Experimental results show that the scheme can preserve singularity well with relatively high PSNR and good visual quality.

scholarly journals COMPUTER AIDED ANALYSIS OF LUNG CT BASED ON TRANSFORM DOMAIN FEATURES

2014 ◽  
pp. 244-249
Author(s):  
V. MINNAL
Keyword(s):  
Wavelet Transforms ◽  
Spatial Domain ◽  
Classification Performance ◽  
Transform Domain ◽  
Pixel Intensity ◽  
Second Stage ◽  
Contour Segmentation ◽  
Spatial Features ◽  
Computer Aided Analysis ◽  
Combined Feature

As Many CADx systems have been developed to detect lung cancer based on spatial domain features that process only the pixel intensity values, the proposed scheme applies frequency transform to the lung images to extract frequency domain features and they are combined with spatial features so that the features that are not revealed in spatial domain will be extracted and the classification performance can be tuned up. The proposed CADx comprises of four stages. In the first stage, lung region is segmented using Convexity based active contour segmentation. At second stage ROIs are extracted using spatially constrained KFCM clustering. Followed by standard wavelet transforms is applied on ROI so that transform domain features are extracted with shape and haralick histogram features. Finally neural network is trained by combined feature set to identify the cancerous nodules. Our proposed scheme has shown sensitivity of 95% and specificity of 96%.

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