CN104156522B - A kind of mode identification method based on UFIR moment invariants - Google Patents
A kind of mode identification method based on UFIR moment invariants Download PDFInfo
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Abstract
The present invention relates to a kind of digital image processing fields, and in particular to a kind of mode identification method based on UFIR moment invariants.The present invention includes：Original image is converted, each pixel is multiplied by transformation factor respectively；Calculate the UFIR moment functions of image after converting；UFIR moment functions after calculating are expressed as to the form of the linear sum of geometric moment；Geometric moment in expression formula is replaced with into geometry moment invariants, obtains the UFIR moment invariants of original image；The identical object of 5 width shapes is chosen as standard picture, calculates separately the UFIR moment invariants of standard picture；Result is handled, absolute mean is calculated and single measurements subtracts the sum of the absolute value after mean value；Piece image is chosen as standard picture, translated, scaled and rotation transformation respectively, the UFIR moment invariants of image after converting are calculated.The UFIR moment invariants of the present invention have better invariance for image transformation.
Description
Technical field
The present invention relates to a kind of digital image processing fields, and in particular to a kind of pattern based on UFIR moment invariants
Recognition methods.
Background technology
Since HuShi squares and its invariant are found, moment characteristics are always to be examined at pattern-recognition, image analysis, edge
Survey the research hotspot with fields such as texture analysis.Compared to other features, moment characteristics have the following advantages that：(1) moment characteristics can be anti-
The gray distribution features in whole image region are reflected, can reflect target information origin feature；(2) and target location, placing direction without
It closes, not obtained conditions and environment by target image is influenced；(3) invariant features that construction has a variety of invariant features concurrently are easy.
The substrate of orthogonal moment is a series of mutually orthogonal multinomials, so will produce minimum using orthogonal moment expression image
Information redundancy.Teague has found that image can be reconstructed by a series of orthogonal moments, and uses corresponding polynomial construction square
Function, such as Legendre squares and Zernike squares.Orthogonal moment is compared with geometric moment, in addition to smaller information redundancy, going back
There is certain robustness to noise.However, since both orthogonal moments are continuous in domain, it is caused actually to answer
With when will appear some apparent problems.The continuity being primarily due in domain, need before application by image with
Multinomial establishes coordinate mapping relations, will appear error when coordinate is converted.It followed by needs to integrate continuous orthogonal moment
Operation, this will also result in calculating error.
In recent years, series of discrete orthogonal moment, for example, Tchebichef squares, Krawtchouk squares, Hahn squares and dual
Hahn squares, are applied in image analysis.Discrete orthogonal moments are using series of discrete orthogonal polynomial as substrate so that they
It can completely avoid and establish coordinate mapping relations, while also not needing integral operation, to eliminate continuous orthogonal moment in image
Error caused by analysis.This makes quadrature discrete multinomial be better than continuous orthogonal moment in terms of image analysis.
In addition, moment invariants are also the much-talked-about topic of area of pattern recognition.Researcher is obtained by the method for Image normalization
Obtained translation and the rotational invariants of Zernike and Legendre squares.In document [1], author is by Krawtchouk moment preservings
Amount is converted to the form of the linear sum of geometric invariant moment, and orthogonally-persistent square is constructed with nonopiate not bending moment.Then, same side
Method is also applied in some documents.
UFIR moment invariants are constructed, and have been carried out the experiment of pattern-recognition.The results show UFIR moment invariants
With good invariance.
Invention content
The purpose of the present invention is to provide a kind of mode identification methods based on UFIR moment invariants.
The object of the present invention is achieved like this：
(1) original image is converted, each pixel is multiplied by transformation factor respectively；
(2) the UFIR moment functions of image after converting are calculated；
(3) the UFIR moment functions after calculating are expressed as to the form of the linear sum of geometric moment；
(4) geometric moment in expression formula is replaced with into geometry moment invariants, obtains the UFIR moment invariants of original image；
(5) the identical object of 5 width shapes is chosen as standard picture, calculates separately the UFIR moment invariants of standard picture；
(6) result is handled, calculates absolute mean | μ | and single measurements subtract the sum of the absolute value after mean value
δ, using δ and | μ | ratio as measurement standard, wherein
(7) piece image is chosen as standard picture, is translated, is scaled and rotation transformation respectively, calculated and scheme after converting
The UFIR moment invariants and δ of picture/| μ | value.
The beneficial effects of the present invention are：
The UFIR moment invariants of the present invention have better invariance for image transformation.
Description of the drawings
Fig. 1 is to choose 5 width hammers without loss of generality as normal pictures.
Fig. 2 be 5 class hammer images UFIR moment invariants and δ/| μ | value
Fig. 3 be UFIR moment invariants and δ after hammer (d) translation transformation/| μ | value
Fig. 4 be UFIR moment invariants and δ after hammer (d) scale transformation/| μ | value
Fig. 5 be UFIR moment invariants and δ after hammer (d) rotation transformation/| μ | value
Fig. 6 be hammer (d) be carried out at the same time translation, scale and choose to install UFIR moment invariants and δ after transformation/| μ | value
Specific implementation mode
The present invention is described further below in conjunction with the accompanying drawings：
Concrete methods of realizing of the present invention is as follows：
(1) original image is converted, each pixel is multiplied by transformation factor；
(2) the UFIR moment functions of image after converting are calculated；
(3) the UFIR moment functions of the image after converting can be expressed as a series of form of the linear sum of geometric moments；
(4) geometric moment obtained in expression formula is replaced with corresponding geometry moment invariants by us, to obtain artwork
The UFIR moment invariants of picture；
(5) in the experiment of pattern-recognition, we have chosen the similar different objects of 5 width shapes as standard picture, divide
Its UFIR moment invariants is not calculated；
(6) we handle result, calculate it | μ | and δ, using δ and | μ | ratio as measurement standard；
(7) we arbitrarily choose piece image therein as standard picture, are translated, scaled and are rotated to it respectively
Transformation, calculate transformation after image UFIR moment invariants and δ/| μ |；
(8) comparison becomes the measurement standard changed from same object without the measurement standard of object different, we demonstrate that
UFIR moment invariants are translated in image, scale and rotation transformation after there is good invariance.
(1) UFIR multinomials hn(x, N) is defined as shown in (1) formula
Wherein x is independent variable, and n is polynomial exponent number, and N is signal length, coefficient ajn(N) it is defined as follows
| D (N) | it is Hankel matrixesDeterminant value, M(j+1)1(N) it is Hankel matrixes
Complementary minor,
Each element c in matrixk(N) by Bernoulle polynomial Bn(x) it defines, it is as follows
We list the UFIR multinomials of preceding 4 rank, as follows
It is previously mentioned the multinomial that UFIR multinomials are orthogonal, orthogonality relation meets
Weighting functionIt is equal to
Wherein (a)0=1, (a)k=a (a+1) ... (a+k-1), another non-negative weighting function ρ (x, N) meet
We are by hn(x, N) is normalized, and obtains normalized UFIR multinomials
We convert pending image f (x, y), each pixel is multiplied by transformation factor
F'(x, y)=[ρ (x, N) ρ (y, N)]-1/2f(x,y) (13)
(2) the UFIR moment functions of image after converting are calculated
(3) the UFIR moment functions of the image after transformation are expressed as to a series of form of the linear sum of geometric moments, wherein several
How the discrete form of square is
So (11) formula can be expressed as the linear of geometric moment and
(4) the geometric moment GM that we will obtain in expression formulamnReplace with corresponding geometry moment invariants Vij, to obtain
The UFIR moment invariants of original image.The wherein translation of geometric moment, rotation, scales the form of invariant
Wherein
μmnIt is geometric center square, the definition in document [1] is
In order to obtain within the scope of 0 ° to 360 ° θ value, need to modify to the computational methods of θ, concrete modification method can
With bibliography [1].Geometry moment invariants VijIt is as follows
Then we have obtained UFIR moment invariants HMImn
(5) we choose 5 width hammer images as standard picture, such as Fig. 1 without loss of generality；
(6) we handle result, calculate UFIR moment invariants HMImn, | μ | with δ, using δ/| μ | marked as weighing
Standard, as a result such as Fig. 2；
(7) we arbitrarily choose piece image therein as standard picture, are translated, scaled and are rotated to it respectively
Transformation, calculate transformation after image UFIR moment invariants with δ/| μ |, result of calculation such as Fig. 3-Fig. 6；
(8) δ that comparison is changed without measurement standard and the same hammer of hammer in different changes/| μ |, it has been found that for same
One UFIR moment invariants, the error of different hammers are at least 100 times of same hammer error.Then we can prove UFIR
Moment invariants are translated in image, scale and rotation transformation after there is good invariance.
The present invention provides a kind of mode identification methods based on UFIR moment invariants.We construct the UFIR of image first
Square translation, scaling and rotational invariants then use the UFIR moment invariants of construction to carry out pattern-recognition reality as feature descriptor
It tests.Image is converted first, calculate transformation after image UFIR squares, and be expressed as a series of the linear of geometric moments and
Form.Geometric moment in expression formula is replaced with corresponding geometry moment invariants by us, has then obtained the UFIR squares of image not
Variable.In the experiment of pattern-recognition, we have carried out standard picture translation, scaling and rotation transformation respectively, calculate transformation
The UFIR moment invariants of image and the UFIR moment invariants of standard picture are compared afterwards, the results show UFIR moment invariants
Translated in image, scale and rotation transformation after there is good invariance.And classical discrete orthogonal polynomials are join more
Several, so need to choose optimized parameter in application, and UFIR multinomials are not multi-parameters, avoid the problem, it is more suitable
Close processing in real time.
Claims (1)
1. a kind of mode identification method based on UFIR moment invariants, it is characterised in that：
(1) original image is converted, each pixel is multiplied by transformation factor respectively；
UFIR multinomials hn(x, N) is：
Wherein x is independent variable, and n is polynomial exponent number, and N is signal length, coefficient ajn(N) it is defined as follows
| D (N) | it is Hankel matrixesDeterminant value, M(j+1)1(N) be Hankel matrixes minor
Formula,
Each element c in matrixk(N) by Bernoulle polynomial Bn(x) it defines, it is as follows
The UFIR multinomials of preceding 4 rank, it is as follows
UFIR multinomials are orthogonal multinomials, and orthogonality relation meets
Weighting function
Wherein (a)0=1, (a)k=a (a+1) ... (a+k-1), another non-negative weighting function ρ (x, N) meet
By hn(x, N) is normalized, and obtains normalized UFIR multinomials
Pending image f (x, y) is converted, each pixel is multiplied by transformation factor；
F'(x, y)=[ρ (x, N) ρ (y, N)]-1/2f(x,y)；
(2) the UFIR moment functions of image after converting are calculated；
(3) the UFIR moment functions after calculating are expressed as to the form of the linear sum of geometric moment；
(4) by the geometric moment GM in expression formulamnReplace with corresponding geometry moment invariants Vij, obtain the UFIR moment preservings of original image
Amount；
The wherein translation of geometric moment, rotation, scales the form of invariant
Wherein
μmnIt is geometric center square,
(5) the identical object of 5 width shapes is chosen as standard picture, calculates separately the UFIR moment invariants of standard picture；
UFIR moment invariants HMImn
(6) result is handled, calculates absolute mean | μ | and single measurements subtract the absolute value after mean value and δ, with
δ and | μ | ratio as measurement standard, wherein
(7) piece image is chosen as standard picture, translated, scaled and rotation transformation respectively, and image after converting is calculated
UFIR moment invariants and δ/| μ | value.
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| CN103500455A (en) * | 2013-10-15 | 2014-01-08 | 北京航空航天大学 | Improved maneuvering target tracking method based on unbiased finite impulse response (UFIR) filter |
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| CN103500455A (en) * | 2013-10-15 | 2014-01-08 | 北京航空航天大学 | Improved maneuvering target tracking method based on unbiased finite impulse response (UFIR) filter |
Non-Patent Citations (3)
| Title |
|---|
| A new class of discrete orthogonal polynomials for blind fitting of finite data;Luis J.Morales-Mendoza et al;《Signal Processing》;20131231;摘要，正文第1786-1787页 * |
| Image analysis by Krawtchouk moments;Pew-Thian Yap.etc;《IEEE Transactions on Image Processing》;20031211;第12卷;正文第1371页第2栏-第1372页第1栏 * |
| 基于Krawtchouk矩的运动目标分类;王晓静等;《计算机工程与设计》;20120516(第5期);第1890-1893、1982页 * |
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