Huazhong Shu

Color Image Analysis by Quaternion-Type Moments

In this paper, by using the quaternion algebra, the conventional complex-type moments (CTMs) for gray-scale images are generalized to color images as quaternion-type moments (QTMs) in a holistic manner. We first provide a general formula of QTMs from which we derive a set of quaternion-valued QTM invariants (QTMIs) to image rotation, scale and translation transformations by eliminating the influence of transformation parameters. An efficient computation algorithm is also proposed so as to reduce computational complexity. The performance of the proposed QTMs and QTMIs are evaluated considering several application frameworks ranging from color image reconstruction, face recognition to image registration. We show they achieve better performance than CTMs and CTM invariants (CTMIs). We also discuss the choice of the unit pure quaternion influence with the help of experiments.

Artifact Suppressed Dictionary Learning for Low-Dose CT Image Processing

(i-j-k)/\sqrt{3}

Affine Legendre Moment Invariants for Image Watermarking Robust to Geometric Distortions

(i-j-k)/3 appears to be an optimal choice.

Translation and scale invariants of Tchebichef moments

In this paper, we introduce a set of discrete orthogonal functions known as dual Hahn polynomials. The Tchebichef and Krawtchouk polynomials are special cases of dual Hahn polynomials. The dual Hahn polynomials are scaled to ensure the numerical stability, thus creating a set of weighted orthonormal dual Hahn polynomials. They are allowed to define a new type of discrete orthogonal moments. The discrete orthogonality of the proposed dual Hahn moments not only ensures the minimal information redundancy, but also eliminates the need for numerical approximations. The paper also discusses the computational aspects of dual Hahn moments, including the recurrence relation and symmetry properties. Experimental results show that the dual Hahn moments perform better than the Legendre moments, Tchebichef moments, and Krawtchouk moments in terms of image reconstruction capability in both noise-free and noisy conditions. The dual Hahn moment invariants are derived using a linear combination of geometric moments. An example of using the dual Hahn moment invariants as pattern features for a pattern classification application is given.

A novel algorithm for fast computation of Zernike moments

Low-dose computed tomography (LDCT) images are often severely degraded by amplified mottle noise and streak artifacts. These artifacts are often hard to suppress without introducing tissue blurring effects. In this paper, we propose to process LDCT images using a novel image-domain algorithm called “artifact suppressed dictionary learning (ASDL).” In this ASDL method, orientation and scale information on artifacts is exploited to train artifact atoms, which are then combined with tissue feature atoms to build three discriminative dictionaries. The streak artifacts are cancelled via a discriminative sparse representation operation based on these dictionaries. Then, a general dictionary learning processing is applied to further reduce the noise and residual artifacts. Qualitative and quantitative evaluations on a large set of abdominal and mediastinum CT images are carried out and the results show that the proposed method can be efficiently applied in most current CT systems.

Improving abdomen tumor low-dose CT images using a fast dictionary learning based processing

Moments and moment invariants have become a powerful tool in pattern recognition and image analysis. Conventional methods to deal with color images are based on RGB decomposition or graying, which may lose some significant color information. In this paper, by using the algebra of quaternions, we introduce the quaternion Zernike moments (QZMs) to deal with the color images in a holistic manner. It is shown that the QZMs can be obtained from the conventional Zernike moments of each channel. We also provide the theoretical framework to construct a set of combined invariants with respect to rotation, scaling and translation (RST) transformation. Experimental results are provided to illustrate the efficiency of the proposed descriptors.

Blurred Image Recognition by Legendre Moment Invariants

Geometric distortions are generally simple and effective attacks for many watermarking methods. They can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark. In this paper, we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks. The novelty of our approach stands on a set of affine invariants we derived from Legendre moments. Watermark embedding and detection are directly performed on this set of invariants. We also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction. Experimental results show that the proposed watermarking scheme is robust to a wide range of attacks: geometric distortion, filtering, compression, and additive noise.

Full 4-D quaternion discrete Fourier transform based watermarking for color images

Discrete orthogonal moments such as Tchebichef moments have been successfully used in the field of image analysis. However, the invariance property of these moments has not been studied mainly due to the complexity of the problem. Conventionally, the translation and scale invariant functions of Tchebichef moments can be obtained either by normalizing the image or by expressing them as a linear combination of the corresponding invariants of geometric moments. In this paper, we present a new approach that is directly based on Tchebichef polynomials to derive the translation and scale invariants of Tchebichef moments. Both derived invariants are unchanged under image translation and scale transformation. The performance of the proposed descriptors is evaluated using a set of binary characters. Examples of using the Tchebichef moments invariants as pattern features for pattern classification are also provided.