Geometric Moment Invariants Research Articles

Palmprint authentication using modified legendre moments

Abstract The resolution of the acquired biometric image is considered as one of the primary factors affecting the performance of a biometric authentication system. For low quality images, a powerful feature extraction method is very essential. Orthogonal Legendre moments are used in several pattern recognition and image processing applications for feature extraction. Translation and scale invariant Legendre moments are achieved directly by using the Legendre polynomial. However, this method does not yield a rotational invariant form. In this paper we propose a palmprint verification system in which the 2D Legendre moments are represented as a linear combination of geometric moment invariants. Geometric moments are invariant to translation, non-uniform scaling and rotation. The modified Legendre moments are used for feature extraction and a weighted fusion technique is used to fuse the matching scores of the sub-images. The results obtained using a Baye’s classifier indicate an impressive prediction accuracy of 98%, validating the choice of low order Legendre moment for effective palmprint verification.

Estimating myocardial motion by 4D image warping

A method for spatio-temporally smooth and consistent estimation of cardiac motion from MR cine sequences is proposed. Myocardial motion is estimated within a four-dimensional (4D) registration framework, in which all three-dimensional (3D) images obtained at different cardiac phases are simultaneously registered. This facilitates spatio-temporally consistent estimation of motion as opposed to other registration-based algorithms which estimate the motion by sequentially registering one frame to another. To facilitate image matching, an attribute vector (AV) is constructed for each point in the image, and is intended to serve as a “morphological signature” of that point. The AV includes intensity, boundary, and geometric moment invariants (GMIs). Hierarchical registration of two image sequences is achieved by using the most distinctive points for initial registration of two sequences and gradually adding less-distinctive points to refine the registration. Experimental results on real data demonstrate good performance of the proposed method for cardiac image registration and motion estimation. The motion estimation is validated via comparisons with motion estimates obtained from MR images with myocardial tagging.

Morphological Characterization of Intracranial Aneurysms Using 3-D Moment Invariants

Rupture of intracranial saccular aneurysms is the most common cause of spontaneous subarachnoid hemorrhage, which has significant morbidity and mortality. Although there is still controversy regarding the decision on which unruptured aneurysms should be treated, this is based primarily on their size. Nonetheless, many large lesions do not rupture whereas some small ones do. It is commonly accepted that hemodynamical factors are important to better understand the natural history of cerebral aneurysms. However, it might not always be practical to carry out a detailed computational analysis of such factors if a prompt assessment is required. Since shape is likely to be dependent on the balance between hemodynamic forces and the aneurysmal surrounding environment, an appropriate morphological 3-D characterization is likely to provide a practical surrogate to quickly evaluate the risk of rupture. In this paper, an efficient and novel methodology for 3-D shape characterization of cerebral aneurysms is described. The aneurysms are isolated by taking into account a portion of their adjacent vessels. Two methods to characterize the morphology of the aneurysms models using moment invariants have been considered: geometrical moment invariants (GMI) and Zernike moment invariants (ZMI). The results have been validated in a database containing 53 patients with a total of 31 ruptured aneurysms and 24 unruptured aneurysms. It has been found that ZMI indices are more robust than GMI, and seem to provide a reliable way to discriminate between ruptured and unruptured aneurysms. Correct rupture prediction rates of approximately equal to 80% were achieved in contrast to 66% that is found when the aspect ratio index is considered.

Translation and scale invariants of Tchebichef moments

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.

The scale invariants of pseudo-Zernike moments

The definition of pseudo-Zernike moments has a form of projection of the image intensity function onto the pseudo-Zernike polynomials, and they are defined using a polar coordinate representation of the image space. Hence, they are commonly used in recognition tasks requiring rotation invariance. However, this coordinate representation does not easily yield a scale invariant function because it is difficult to extract a common scale factor from the radial polynomials. As a result, vision applications generally resort to image normalisation method or using a combination of scale invariants of geometric orradial moments to achieve the corresponding invariants of pseudo-Zernike moments. In this paper, we present a mathematical framework to derive a new set of scale invariants of pseudo-Zernike moments based on pseudo-Zernike polynomials. They are algebraically obtained by eliminating the scale factor contained in the scaled pseudo-Zernike moments. They remain unchanged under equal-shape expansion, contraction and reflection of theoriginal image. They can be directly computed from any scaled image without prior knowledge of the normalisation parameters, or assistance of geometric or radial moments. Their performance is experimentally verified using a set of Chinese and Latin characters. In addition, a comparison of computational speed between the proposed descriptors and the present methods is also presented.

Image analysis by krawtchouk moments

In this paper, a new set of orthogonal moments based on the discrete classical Krawtchouk polynomials is introduced. The Krawtchouk polynomials are scaled to ensure numerical stability, thus creating a set of weighted Krawtchouk polynomials. The set of proposed Krawtchouk moments is then derived from the weighted Krawtchouk polynomials. The orthogonality of the proposed moments ensures minimal information redundancy. No numerical approximation is involved in deriving the moments, since the weighted Krawtchouk polynomials are discrete. These properties make the Krawtchouk moments well suited as pattern features in the analysis of two-dimensional images. It is shown that the Krawtchouk moments can be employed to extract local features of an image, unlike other orthogonal moments, which generally capture the global features. The computational aspects of the moments using the recursive and symmetry properties are discussed. The theoretical framework is validated by an experiment on image reconstruction using Krawtchouk moments and the results are compared to that of Zernike, pseudo-Zernike, Legendre, and Tchebyscheff moments. Krawtchouk moment invariants are constructed using a linear combination of geometric moment invariants; an object recognition experiment shows Krawtchouk moment invariants perform significantly better than Hu's moment invariants in both noise-free and noisy conditions.

Translation and scale invariants of Legendre moments

By convention, the translation and scale invariant functions of Legendre moments are achieved by using a combination of the corresponding invariants of geometric moments. They can also be accomplished by normalizing the translated and/or scaled images using complex or geometric moments. However, the derivation of these functions is not based on Legendre polynomials. This is mainly due to the fact that it is difficult to extract a common displacement or scale factor from Legendre polynomials. In this paper, we introduce a new set of translation and scale invariants of Legendre moments based on Legendre polynomials. The descriptors remain unchanged for translated, elongated, contracted and reflected non-symmetrical as well as symmetrical images. The problems associated with the vanishing of odd-order Legendre moments of symmetrical images are resolved. The performance of the proposed descriptors is experimentally confirmed using a set of binary English, Chinese and Latin characters. In addition to this, a comparison of computational speed between the proposed descriptors and the aforesaid geometric moments-based method is also presented.

Feature extraction with an improved scale-invariants for deformation digits

This paper presents an alternative formulation on improved scaled-invariants using higher order centralized moments for digits with deformations. We claim that deformation digits would be digits with improper shapes, unconstrained styles of writing and different orientations. A detail experimental evaluation of the utilizing various moments order as pattern features in recognition of handprinted and handwritten digits have been carried out using the proposed invariants. We use scale-invariants of centralized moments of order 2 for the numerator and order 4 for the denominator while preserving the scale factor of the same order. Unconstrained digits are rotated clockwise and counter clockwise of 45 degree. As a comparison, we generate geometric moment invariants on these digits. We train these invariants using standard back-propagation and modified backpropagation in the classifications phase. We found that the results are promising with an improved scaled-invariants of higher order, and the classifications of the digits are successfully recognized.

Improved Scale-Invariant Moments for Deformation Digits

This paper presents improved scaled-invariant moments for digits with deformations. We claim that deformation digits would be digits with improper shapes, unconstrained styles of writing and different orientations. An experimental evaluation of utilizing various moments order as pattern features in recognition of handprinted and handwritten digits have been carried out using improved scaled-invariant moments. We use scale-invariant moments of order 2 for the numerator and order 4 for the denominator while preserving the scale factor of the same order. These moments have been used as feature extraction for digits with various orientations. Digits are rotated clockwise and counter clockwise of 45 degree, and using unequal scaling in x and y directions. As a comparison, we generate geometric moment invariants on handwritten digits. We train improved scaled-invariant moments using a standard backpropagation model and modified backpropagation model for classifications. We found that the results are promising with improved scaled-invariant moments of higher order, and the classifications of digits are successfully recognized.