Combined invariants to similarity transformation and to blur using orthogonal Zernike moments

Copy Move Forgery Image Detection via Discrete Radon and Polar Complex Exponential Transform-Based Moment Invariant Features

Copy move forgery with geometric distortions such as the rotational operation, the scaling operation, the mirror operation and the additive noise operation became more common. Existing methods are not competent for the detection of the copy move forgery with these distortions. In fact, the most critical issue for the detection of the forgery is the determination of the geometric features. This paper proposes an efficient Discrete Radon Polar Complex Exponential Transform (DRPCET)-based method for the extraction of the rotational and the scaling invariant features for the copy move forgery detection. First, the features obtained by the Radon transform (RT) and the Polar Complex Exponential Transform (PCET) are fused together. Then, these features are normalized. In order to achieve the scaling invariant property, an auxiliary circular template is introduced. With the auxiliary circular template, the translational moment invariant features, the rotational moment invariant features and the scaling moment invariant features are constructed for the extraction of the planar geometrical features. By further extracting some useful features for the representation of the image background, the interference of the background information can be reduced. After extracting the geometrical features, the lexicographic sorting is applied. Then, a correlation between the same part or similar parts of the image which are copied and moved to another image is computed. Based on the obtained correlations, these forgery parts can be identified and their composed positions can be located. Finally, these images are denoted as the forgery image. Extensive computer numerical simulations have been performed. The obtained results show that the proposed method can detect the copy move region in the forgery image precisely even though the forgery regions are suffered from the mixed geometric distortions.

Recognition of Images Degraded by Gaussian Blur

In this paper, we propose a new theory of invariants to Gaussian blur. We introduce a notion of a primordial image as a canonical form of all Gaussian blur-equivalent images. The primordial image is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to Gaussian blur and we derive recursive formulas for their direct computation without actually constructing the primordial image itself. We show how to extend their invariance also to image rotation. The application of these invariants is in blur-invariant image comparison and recognition. In the experimental part, we perform an exhaustive comparison with two main competitors: 1) the Zhang distance and 2) the local phase quantization.

Projection Operators and Moment Invariants to Image Blurring

In this paper we introduce a new theory of blur invariants. Blur invariants are image features which preserve their values if the image is convolved by a point-spread function (PSF) of a certain class. We present the invariants to convolution with an arbitrary N-fold symmetric PSF, both in Fourier and image domain. We introduce a notion of a primordial image as a canonical form of all blur-equivalent images. It is defined in spectral domain by means of projection operators. We prove that the moments of the primordial image are invariant to blur and we derive recursive formulae for their direct computation without actually constructing the primordial image. We further prove they form a complete set of invariants and show how to extent their invariance also to translation, rotation and scaling. We illustrate by simulated and real-data experiments their invariance and recognition power. Potential applications of this method are wherever one wants to recognize objects on blurred images.

Registration of images with N -fold dihedral blur

In this paper, we extend our recent registration method designed specifically for registering blurred images. The original method works for unknown blurs, assuming the blurring point-spread function (PSF) exhibits an N -fold rotational symmetry. Here, we also generalize the theory to the case of dihedrally symmetric blurs, which are produced by the PSFs having both rotational and axial symmetries. Such kind of blurs are often found in unfocused images acquired by digital cameras, as in out-of-focus shots the PSF typically mimics the shape of the shutter aperture. This makes our registration algorithm particularly well-suited in applications where blurred image registration must be used as a preprocess step of an image fusion algorithm, and where common registration methods fail, due to the amount of blur. We demonstrate that the proposed method leads to an improvement of the registration performance, and we show its applicability to real images by providing successful examples of blurred image registration followed by depth-of-field extension and multichannel blind deconvolution.

Image deconvolution by means of frequency blur invariant concept

Different blur invariant descriptors have been proposed so far, which are either in the spatial domain or based on the properties available in the moment domain. In this paper, a frequency framework is proposed to develop blur invariant features that are used to deconvolve a degraded image caused by a Gaussian blur. These descriptors are obtained by establishing an equivalent relationship between the normalized Fourier transforms of the blurred and original images, both normalized by their respective fixed frequencies set to one. Advantage of using the proposed invariant descriptors is that it is possible to estimate both the point spread function (PSF) and the original image. The performance of frequency invariants will be demonstrated through experiments. An image deconvolution is done as an additional application to verify the proposed blur invariant features.

A Unified Methodology for Computing Accurate Quaternion Color Moments and Moment Invariants

In this paper, a general framework for computing accurate quaternion color moments and their corresponding invariants is proposed. The proposed unified scheme arose by studying the characteristics of different orthogonal polynomials. These polynomials are used as kernels in order to form moments, the invariants of which can easily be derived. The resulted scheme permits the usage of any polynomial-like kernel in a unified and consistent way. The resulted moments and moment invariants demonstrate robustness to noisy conditions and high discriminative power. Additionally, in the case of continuous moments, accurate computations take place to avoid approximation errors. Based on this general methodology, the quaternion Tchebichef, Krawtchouk, Dual Hahn, Legendre, orthogonal Fourier-Mellin, pseudo Zernike and Zernike color moments, and their corresponding invariants are introduced. A selected paradigm presents the reconstruction capability of each moment family, whereas proper classification scenarios evaluate the performance of color moment invariants.

Region and boundary feature estimation on ultrasound images using moment invariants

In ultrasound images, tissues are characterized by their speckle texture. Moment-based techniques have proven their ability to capture texture features. However, in ultrasound images, the speckle size increases with the distance from the probe and in some cases the speckle has a concentric texture arrangement. We propose to use moment invariants with respect to image scale and rotation to capture the texture in such cases. Results on synthetic data show that moment invariants are able to characterize the texture but also that some moment orders are sensitive to regions and, moreover, some are sensitive to the boundaries between two different textures. This behavior seems to be very interesting to be used within some segmentation scheme dealing with a combination of regional and boundary information. In this paper we will try to prove the usability of this complementary information in a min-cut/max-flow graph cut scheme.

Blur invariant translational image registration for N-fold symmetric blurs

In this paper, we propose a new registration method designed particularly for registering differently blurred images. Such a task cannot be successfully resolved by traditional approaches. Our method is inspired by traditional phase correlation, which is now applied to certain blur-invariant descriptors instead of the original images. This method works for unknown blurs assuming the blurring PSF exhibits an N-fold rotational symmetry. It does not require any landmarks. We have experimentally proven its good performance, which is not dependent on the amount of blur. In this paper, we explicitly address only registration with respect to translation, but the method can be readily generalized to rotation and scaling.

Gaussian blurring-invariant comparison of signals and images

We present a Riemannian framework for analyzing signals and images in a manner that is invariant to their level of blurriness, under Gaussian blurring. Using a well known relation between Gaussian blurring and the heat equation, we establish an action of the blurring group on image space and define an orthogonal section of this action to represent and compare images at the same blur level. This comparison is based on geodesic distances on the section manifold which, in turn, are computed using a path-straightening algorithm. The actual implementations use coefficients of images under a truncated orthonormal basis and the blurring action corresponds to exponential decays of these coefficients. We demonstrate this framework using a number of experimental results, involving 1D signals and 2D images. As a specific application, we study the effect of blurring on the recognition performance when 2D facial images are used for recognizing people.

Blur invariants constructed from arbitrary moments

This paper deals with moment invariants with respect to image blurring. It is mainly a reaction to the works of Zhang and Chen , recently published in these Transactions. We present a general method on how to construct blur invariants from arbitrary moments and show that it is no longer necessary to separately derive the invariants for each polynomial basis. We show how to discard dependent terms in blur invariants definition and discuss a proper implementation of the invariants in orthogonal bases using recurrent relations. An example for Legendre moments is given.