Radon–Fourier descriptor for invariant pattern recognition

2019 ◽  
Vol 17 (02) ◽  
pp. 1940004 ◽  
Author(s):  
Jianwei Yang ◽  
Liang Zhang ◽  
Peiyao Li
Keyword(s):  
Pattern Recognition ◽  
Radon Transform ◽  
Mellin Transform ◽  
Closed Curve ◽  
Fourier Descriptor ◽  
Binary Images ◽  
Invariant Features ◽  
Special Cases ◽  
Robust To Noise

Radon transform is not only robust to noise, but also independent on the calculation of pattern centroid. In this paper, Radon–Mellin transform (RMT), which is a combination of Radon transform and Mellin transform, is proposed to extract invariant features. RMT converts any object into a closed curve. Radon–Fourier descriptor (RFD) is derived by applying Fourier descriptor to the obtained closed curve. The obtained RFD is invariant to scaling and rotation. (Generic) R-transform and some other Radon-based methods can be viewed as special cases of the proposed method. Experiments are conducted on some binary images and gray images.

scholarly journals METHOD FOR ASSESSING THE SYMMETRY OF OBJECTS ON DIGITAL BINARY IMAGES BASED ON FOURIER DESCRIPTOR

2019 ◽  
Vol XLII-2/W12 ◽  
pp. 143-148
Author(s):  
L. Mestetskiy ◽  
A. Zhuravskaya
Keyword(s):  
Symmetry Axis ◽  
Fourier Descriptor ◽  
Earth Remote Sensing ◽  
Discrete Object ◽  
Binary Images ◽  
Special Cases ◽  
Exact Symmetry ◽  
Measure Of Asymmetry ◽  
Axis Of Symmetry ◽  
High Computational Complexity

<p><strong>Abstract.</strong> In this paper we solve the problem of finding the symmetry axis of the object in a digital binary image. A new axial symmetry criterion is formulated for a connected discrete object. The problem of determining the symmetry measure and finding the symmetry axes arises in a variety of applications. In discrete images, exact symmetry is possible only in special cases. The disadvantage of the existing methods solving this problem is the high computational complexity. To improve computational efficiency, it is proposed to use the so-called Fourier descriptor. A new method for estimating the asymmetry of a discrete silhouette is proposed. The described algorithm for calculating the measure of asymmetry and determining the axis of symmetry is quadratic by the number of contour points. Methods for reducing the volume of calculations using a convex hull and taking into account the values of the modules of Fourier coefficients are proposed. Computational experiments are conducted with silhouettes of aircraft extracted from earth remote sensing images. The reliability of the described solution is established.</p>

THE MELLIN CENTRAL PROJECTION TRANSFORM

2017 ◽  
Vol 58 (3-4) ◽  
pp. 256-264
Author(s):  
JIANWEI YANG ◽  
LIANG ZHANG ◽  
ZHENGDA LU
Keyword(s):  
Radial Direction ◽  
Mellin Transform ◽  
Closed Curve ◽  
Chinese Characters ◽  
Central Projection ◽  
Affine Invariant ◽  
Closed Curves ◽  
Affine Invariants ◽  
Invariant Features ◽  
Special Case

The central projection transform can be employed to extract invariant features by combining contour-based and region-based methods. However, the central projection transform only considers the accumulation of the pixels along the radial direction. Consequently, information along the radial direction is inevitably lost. In this paper, we propose the Mellin central projection transform to extract affine invariant features. The radial factor introduced by the Mellin transform, makes up for the loss of information along the radial direction by the central projection transform. The Mellin central projection transform can convert any object into a closed curve as a central projection transform, so the central projection transform is only a special case of the Mellin central projection transform. We prove that closed curves extracted from the original image and the affine transformed image by the Mellin central projection transform satisfy the same affine transform relationship. A method is provided for the extraction of affine invariants by employing the area of closed curves derived by the Mellin central projection transform. Experiments have been conducted on some printed Chinese characters and the results establish the invariance and robustness of the extracted features.

A WAVE APPROACH TO PATTERN RECOGNITION (WITH APPLICATION TO OPTICAL CHARACTER RECOGNITION)

1994 ◽  
Vol 04 (01) ◽  
pp. 193-207 ◽  
Author(s):  
VADIM BIKTASHEV ◽  
VALENTIN KRINSKY ◽  
HERMANN HAKEN
Keyword(s):  
Pattern Recognition ◽  
Character Recognition ◽  
Optical Character Recognition ◽  
Dissipative Structures ◽  
Binary Images ◽  
Optical Character ◽  
Nonlinear Version ◽  
Medium Quality ◽  
Scalar Products ◽  
Machine Reading

The possibility of using nonlinear media as a highly parallel computation tool is discussed, specifically for image classification and recognition. Some approaches of this type are known, that are based on stationary dissipative structures which can “measure” scalar products of images. In this paper, we exploit the analogy between binary images and point sets, and use the Hausdorff metrics for comparing the images. It does not require the measure at all, and is based only on the metrics of the space whose subsets we consider. In addition to Hausdorff distance, we suggest a new “nonlinear” version of this distance for comparison of images, called “autowave” distance. This distance can be calculated very easily and yields some additional advantages for pattern recognition (e.g. noise tolerance). The method was illustrated for the problem of machine reading (Optical Character Recognition). It was compared with some famous OCR programs for PC. On a medium quality xerocopy of a journal page, in the same conditions of learning and recognition, the autowave approach resulted in much fewer mistakes. The method can be realized using only one chip with simple uniform connection of the elements. In this case, it yields an increase in computation speed of several orders of magnitude.

scholarly journals Robust Image Hashing Using Radon Transform and Invariant Features

2016 ◽  
Vol 25 (3) ◽  
pp. 556-564 ◽  
Author(s):  
Y. L. Liu ◽  
G. J. Xin ◽  
Y. Xiao
Keyword(s):  
Radon Transform ◽  
Image Hashing ◽  
Invariant Features ◽  
Robust Image ◽  
Robust Image Hashing

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.

A THEORY AND A MODEL FOR PATTERN GENERATION IN PLANTS

1993 ◽  
Vol 01 (02) ◽  
pp. 159-186 ◽  
Author(s):  
ROGER V. JEAN
Keyword(s):  
Mathematical Model ◽  
Pattern Recognition ◽  
Optimal Design ◽  
Pattern Generation ◽  
Growth Functions ◽  
Systemic Theory ◽  
Functional Aspects ◽  
Special Cases ◽  
L Systems ◽  
By Products

This article introduces a systemic theory of phyllotaxis (study of primordial patterns on plants) and updates a mathematical model which is central in the theory. The theory deals with the descriptive and the functional aspects of phyllotaxis, and studies the origins of patterns as well. The article concentrates on the formal aspects of the model and on its explanatory values. The model possesses biological foundations which will not be recalled here. It supposes a principle of optimal design and the representation of phyllotactic patterns with control hierarchies. These hierarchies can be generated with irreducible matrices and L-systems. In the hierarchies, parameters can be identified representing important characteristics of growth that is complexity, stability and rhythm. A formula linking those parameters allows us to calculate the numerical cost of each one of the phyllotactic patterns and to order the costs. The various types of patterns come out, including whorled patterns which are seen as special cases of spiral patterns. The model proposes predictions which can be compared to observations. It predicts the existence of improbable patterns which have been later identified and it possesses explanatory values which have been interestingly put to contribution in difficult problems of pattern recognition in botany. It also possesses mathematical by-products in the theory of growth functions of L-systems, thus related to Perron-Frobenius spectral theory.

Memory-based reasoning approach for pattern recognition of binary images

1989 ◽  
Vol 22 (5) ◽  
pp. 505-518 ◽  
Author(s):  
Wu Wang ◽  
S Sitharama Iyengar ◽  
L.M Patnaik
Keyword(s):  
Pattern Recognition ◽  
Binary Images

Derivation of Green-type, transitional, and uniform asymptotic expansions from differential equations II. Whittaker functions W k,m for large k , and for large | K 2 – m 2 |

1964 ◽  
Vol 281 (1384) ◽  
pp. 111-129 ◽  
Keyword(s):  
Differential Equations ◽  
Asymptotic Expansions ◽  
Mellin Transform ◽  
Bessel Functions ◽  
Parabolic Cylinder ◽  
Whittaker Functions ◽  
Transform Method ◽  
Special Cases ◽  
Uniform Expansions ◽  
Uniform Asymptotic Expansions

The method for deriving Green-type asymptotic expansions from differential equations, introduced in I and illustrated therein by detailed calculations on modified Bessel functions, is applied to Whittaker functions W k,m , first for large k , and then for large |k 2 —m 2 |. Following the general theory of I, combination of this procedure with the Mellin transform method yields asymptotic expansions valid in transitional regions, and general uniform expansions. Weber parabolic cylinder and Poiseuille functions are examined as important special cases.

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