CN110728653A - Composite image tampering detection method based on discrete polarity complex exponential transformation - Google Patents
Composite image tampering detection method based on discrete polarity complex exponential transformation Download PDFInfo
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Abstract
The invention discloses a composite image tampering detection method based on discrete polarity complex exponential transformation, which comprises the following steps: constructing a frame with a polarity complex exponential transformation of a rotation invariant moment; discretizing under a frame of polarity compound exponential transformation with rotation invariant moment to construct discrete rotation invariant moment of polarity compound exponential transformation; converting the detected image into a gray image, and defining the detected image in a discrete space domain; constructing a 9 x 9 pixel template, and approximately mapping the rotation invariant moment realizing discrete polarity compound index transformation in the pixel template from a polar coordinate space to a Cartesian space; extracting the characteristics of the detected image by using the rotation invariant moment of discrete polarity compound index transformation to obtain effective image characteristics; and obtaining a matching feature pair through consistency sensitive hash operation, and displaying the matching feature pair in a sectional manner. The invention aims at the copying-pasting tampered images of translation and rotation deformation, has higher detection success rate and eliminates background interference.
Description
Technical Field
The invention relates to the field of image tampering detection, in particular to a composite image tampering detection method based on discrete polarity complex exponential transformation.
Background
In recent years, with the increasing functionality of digital image editing software, digital images are widely used in various industries in society, such as news reports, scientific research, law, and the like. A potential problem with such digital images is that they can be easily modified by using these powerful image editing tools. Some users misuse picture editing software for various purposes to produce some images that are contrary to reality. Today, those tampering behaviors that are not allowed by the author become so severe that our social lives are deeply influenced by them. Therefore, digital image tamper detection has become increasingly important in the field of information security.
Tampering with a "copy-and-paste" image is the copying of a portion of the image content one or more times to cover an important image feature for the purpose of hiding the associated content. During the last decade, many research institutes, researchers, have conducted intensive research into methods of detecting copy-paste tampered images.
Among them, Fridrich, J., Soukal, D. & Luk' as, J. [2003] "Detection of copy-motion formation in Digital images," Digital imaging Research works, pp.55-61, proposes a method of dividing an image into 8 × 8 overlapping blocks and extracting DCT coefficients for these blocks. Popescu, a.c. [2005] "explicit dimensions for generations by detecting tracks of reconstruction," ieee trans. signal.process.53, 758-767, proposes a method of Principal Component Analysis (PCA) to extract and compactly represent feature vectors from overlapping blocks, one advantage of the PCA method is to reduce the dimensionality of the feature vectors. Chakraborty, S. [2013] "Copy mobile image for detection using the technical information," 4th int. Conf. computing, Communications and Networking Technologies (ICCCNT), pp.1-4, propose to use information common in different regions of an image to detect Copy-paste tampered images.
The detection method can achieve good effect on detecting common tampered images without post-processing. However, these cases do not all approach the real case. In image tampering operations, post-processing is quite common, such as geometric deformation, blur deformation, additive noise, and so forth. Since forgers have created new images using various morphing forgery operations, conventional image verification methods have been unable to detect and identify images that include scaling, rotation, translation, and other geometric operations.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a composite image tampering detection method based on discrete polarity complex exponential transformation. The technical scheme of the invention is realized in such a way that the method for detecting the falsification of the synthetic image based on the discrete polarity complex exponential transformation comprises the following steps
Step 1: constructing a frame with a polarity complex exponential transformation of a rotation invariant moment;
step 2: discretizing under the frame of the polar compound exponential transformation with the rotation invariant moment to construct a discrete polar compound exponential transformation rotation invariant moment;
and step 3: converting the detected image from an RGB digital image into a gray image, and defining the detected image in a discrete space domain;
and 4, step 4: constructing a 9 x 9 pixel template, and approximately mapping the rotation invariant moment realizing discrete polarity compound index transformation in the pixel template from a polar coordinate space to a Cartesian space;
and 5: extracting the characteristics of the detected image by using the rotation invariant moment of the discrete polarity compound index transformation to obtain effective image characteristics;
step 6: and obtaining a matching feature pair through consistency sensitive hash operation, and displaying the matching feature pair in a sectional manner.
Further, the extraction of the pixel features of the detected image in step 4 is performed by MATLAB software.
Compared with the prior art, the method has the advantages that the detection success rate is higher for the copying-pasting tampered images of translation and rotation deformation; meanwhile, the invention also eliminates background interference, such as similar colors of a large area, such as sky, ocean, wall and the like.
Drawings
FIG. 1 is a flow chart of a composite image tamper detection method based on discrete polarity complex exponential transformation according to the present invention;
FIG. 2 is a schematic diagram of the pixel coordinates of an inspected image in MATLAB space in accordance with one embodiment of the present invention;
FIG. 3 is a schematic representation of pixel coordinates of FIG. 2 after mapping to Cartesian space;
FIG. 4 is a schematic diagram of a matching analysis of MATLAB space and Cartesian space pixel coordinate systems;
FIG. 5 is a diagram illustrating the transformation of MATLAB space and Cartesian space pixel coordinates in accordance with an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, the method for detecting tampering of a composite image based on discrete polarity complex exponential transformation of the present invention includes
Step 1: constructing a frame with a polarity complex exponential transformation of a rotation invariant moment;
step 2: discretizing under the frame of the polar compound exponential transformation with the rotation invariant moment to construct a discrete polar compound exponential transformation rotation invariant moment;
and step 3: converting the detected image from an RGB digital image into a gray image, and defining the detected image in a discrete space domain;
step 4: constructing a 9 x 9 pixel template, and approximately mapping the rotation invariant moment realizing discrete polarity compound index transformation in the pixel template from a polar coordinate space to a Cartesian space;
and 5: extracting the characteristics of the detected image by using the rotation invariant moment of the discrete polarity compound index transformation to obtain effective image characteristics;
step 6: and obtaining a matching feature pair through consistency sensitive hash operation, and displaying the matching feature pair in a sectional manner.
The polar harmonic transformation consists of Polar Complex Exponential Transformation (PCET), Polar Cosine Transformation (PCT) and Polar Sine Transformation (PST). PCET has proven to be highly robust in detecting, identifying and locating duplicate or similar regions in images, particularly in terms of resistance to rotational deformation and gaussian noise. In step 1, for the image function f (r, θ), PCET is defined as:
wherein M isklIs a PCET expression having a function f (r, θ) of k-order ordinal numbers and l-order repetition coefficients, and | k |, | l |, 0,1Representing a basis function HklComplex conjugation of (r, θ). In the case of a PCET,consisting of a circular harmonic component and a radial component. Definition of
Is composed of
Wherein R isk(r) is the radial nucleus of the nucleus,
theta denotes the degree of rotation and r denotes the radius of the unit circle. By extracting the rotation features, post-processed copy regions, e.g., rotated and additive noise tampered, can be detected and located. From equations (1) and (2), we assume α ═ θ + β and derive the derivative d θ ═ d α. We assume simultaneously that a region pixel fR(r, α) is obtained by rotating f (r, θ) clockwise by an angle β. Thus, equation (1) can be redefined as:
wherein [ fR]A rotary expression is represented. From(3) In the formula, we can construct a rotation invariant moment with polarity complex exponential transformation, as shown in formula (4):
|Mkl(R)|＝|Mkle-ilβ|＝|Mkl| (4)
in step 2, a two-dimensional signal function f (x, y) is given, and the Polar Complex Exponential Transform (PCET) of this function is defined in cartesian coordinates as:
wherein
Hkl(x,y)＝Hkl(rcosθ,rsinθ)＝Hkl(r,θ)。
From equation (5), the framework of Polar Compound Exponential Transformation (PCET) with rotation invariant moment proposed in step 1 is still confined to a continuous spatial region. Furthermore, the PCET function describes the area where an image or pixels of a sub-image are mapped to the unit circle, which requires a suitable normalization. The above functions are suitable for transformation in a continuous space, and cannot be effectively applied to digital images. Digital images are made up of a number of discrete pixels, each arranged in a two-dimensional or N-dimensional matrix. Therefore, we will use the discretization of equation (3) in continuous space. In addition, equation (3) is a polar equation, which is not conducive to direct discretization. In the discretization process of the polar compound exponential transformation, the pixel position representation of the digital image is converted into a rectangular coordinate system, so that the method is more suitable and convenient. In step 2, the invention discretizes a polar complex exponential transformation defined in a cartesian coordinate system. Assuming that the size of an image is M × N (M is 0, 1.. t.m, N is 0, 1.. t.n), discretization of equation (5) defined in a continuous space is expressed as equation (6):
wherein
Equation (6) can be redefined as the following equation:
wherein,
and step 3: when detecting the detected image, the digital image of RGB needs to be converted into a grayscale image. Equation (7) is a normalization equation by which the detected image can be defined in a discrete spatial domain.
And 4, step 4: in computer processing a digital image is composed and represented by pixels. We assume that the distance between adjacent pixels in the same row or column is equal to 1. In one embodiment of the present invention, to detect a suspect image using MATLAB software, we define a 9 × 9 pixel template, with the 9 × 9 pixels arranged as in FIG. 2. The original pixel coordinates (1, 1) are in the upper left corner of the MATLAB operating space.
The MATLAB-space coordinate system of fig. 2 is neither convenient nor efficient when using MATLAB software to extract image features via the discretized PCET of equation (7). Therefore, we first transform the original pixels from the top left corner to the 9 × 9 pixel template center. The approximate mapping from the polar space of MATLAB to the cartesian space we define is shown in fig. 3.
In fig. 3, the new original coordinates (0, 0) are adjusted to the center of the 9 × 9 pixel template. Assume that the new coordinates of each pixel in the template are (x'm,y'n). The gray grid represents the polar region on the template. The pixels at the top left, top right, bottom left, and bottom right corners are not included in the polar coordinate region. This will result in an error in the conversion from polar to rectangular coordinates. Therefore, we propose a new transformation method between two coordinate systems. In FIG. 3, the transformation of a 9 × 9 pixel template from a polar coordinate system to a Cartesian coordinate system is shown. In fig. 4, equation (7) contains some unreasonable transformations, which may result in a relatively large conversion error. First, discrete pixels near the origin of the polar coordinate system are more strongly clustered near the origin, while discrete pixels of the polar coordinate system are more dispersed from the origin of coordinates. The pixels in the cartesian coordinate system should be stored in a vertically and horizontally equidistant matrix, i.e. all pixels are equally distributed around the origin. First, most pixels in a 9 × 9 template are not in the same position in both coordinate systems. Converting pixels from a polar coordinate system to a cartesian coordinate system using equation (7) will result in conversion errors, while some pixels in cartesian coordinates are not included in the polar coordinate system when the radius of the polar or radial coordinates is less than 1. The conversion system of the present invention is illustrated by an example. We set a pixel to the top left of the template, with the pixel having a pentagon as the marker. From FIG. 5 we find that the coordinates (x, y) are (-3, 2.) the distance from the origin of the coordinates (x, y) is
And r is more than 3 and less than 4. The pixel radial coordinate radius for a 9 x 9 template in a polar coordinate system is 3. In both coordinate systems, we match pixels by reducing the distance between pixels in cartesian coordinates or increasing the radius of the pixels in polar coordinates. The arrows as outlined in fig. 5 show the direction of the movement of the pixel, so that the pixel should be directed towards the outlined arrow, keeping the angle moving towards a circle of radius 3. By doing so, we obtain equation (8) as follows:
where [ f' ] represents the expression of the transformed coordinates and INT [ ] is an integer function.
We propose a method of converting a pixel feature from polar to rectangular coordinates and from continuous to discrete regions, redefining equation (7) to obtain equation (9):
where Δ x 'is 1 and Δ y' is 1.
Equation (9) has the feature that discrete rotation invariance moments can effectively extract a composite image.
And 5: and (3) extracting the block characteristics of all pixels of the detected image by using the formula (9) to obtain effective image characteristics.
Step 6: matching feature pairs are obtained and displayed in a scratch-map manner by Consistency Sensitive Hash (CSH) operations such as B.Fan, F.Wu, and Z.Hu, "aggregation distribution inter-importance descriptors: A novel local image descriptor," in Computer Vision and Pattern Recognition (CVPR),2011 IEEE Conference on,2011, pp.2377-2384, etc. Thus, it is possible to determine whether or not the detected image is a composite image.
While the foregoing is directed to the preferred embodiment of the present invention, it will be understood by those skilled in the art that various changes and modifications may be made without departing from the spirit and scope of the invention.
Claims (2)
1. A composite image tampering detection method based on discrete polarity complex exponential transformation is characterized by comprising
Step 1: constructing a frame with a polarity complex exponential transformation of a rotation invariant moment;
step 2: discretizing under the frame of the polar compound exponential transformation with the rotation invariant moment to construct a discrete polar compound exponential transformation rotation invariant moment;
and step 3: converting the detected image from an RGB digital image into a gray image, and defining the detected image in a discrete space domain;
and 4, step 4: constructing a 9 x 9 pixel template, and approximately mapping the rotation invariant moment realizing discrete polarity compound index transformation in the pixel template from a polar coordinate space to a Cartesian space;
and 5: extracting the characteristics of the detected image by using the rotation invariant moment of the discrete polarity compound index transformation to obtain effective image characteristics;
step 6: and obtaining a matching feature pair through consistency sensitive hash operation, and displaying the matching feature pair in a sectional manner.
2. The method for detecting falsification of a synthetic image based on discrete polarity complex exponential transformation according to claim 1, wherein the extraction of the pixel characteristics of the detected image in step 4 is performed by MATLAB software.
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