Jean-Louis Coatrieux

Image analysis by discrete orthogonal Racah moments

Discrete orthogonal moments are powerful tools for characterizing image shape features for applications in pattern recognition and image analysis. In this paper, a new set of discrete orthogonal moments is proposed, based on the discrete Racah polynomials. In order to ensure numerical stability, the Racah polynomials are normalized, thus creating a set of weighted orthonormal Racah polynomials, to define the so-called Racah moments. This new type of discrete orthogonal moments eliminates the need for numerical approximations. The paper also discusses the properties of Racah polynomials such as recurrence relations and permutability property that can be used to reduce the computational complexity in the calculation of Racah polynomials. Finally, we demonstrate Racah moments feature representation capability by means of image reconstruction and compression. Comparison with other discrete orthogonal transforms is performed, and the results show that the Racah moments are potentially useful in the field of image analysis.

Image analysis by discrete orthogonal dual Hahn 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.

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.

3D Reconstruction of Cerebral Blood Vessels

A new technique that uses photogrammetry and computer graphics for the 3D display of cerebral blood vessels provides anatomic images for diagnosis and treatment planning.

Vectorial tracking and directed contour finder for vascular network in digital subtraction angiography

Abstract Emphasis has been recently given to automatic segmentation of vascular network observed by means of Digital Subtraction Angiography. This paper details a new algorithm which determines the medial axes and the contours of the vessesl in the whole vascular tree.

Reconstruction of tomographic images from limited range projections using discrete Radon transform and Tchebichef moments

This paper presents an image reconstruction method for X-ray tomography from limited range projections. It makes use of the discrete Radon transform and a set of discrete orthogonal Tchebichef polynomials to define the projection moments and the image moments. By establishing the relationship between these two sets of moments, we show how to estimate the unknown projections from known projections in order to improve the image reconstruction. Simulation results are provided in order to validate the method and to compare its performance with some existing algorithms.

Three-dimensional motion and reconstruction of coronary arteries from biplane cineangiography

Abstract A new approach is described for reconstructing coronary arteries from two sequences of projection images. The estimation of motion is performed on three-dimensional line segments (or centrelines), and is based on a ‘predictionprojection-optimization’ loop. The method copes with time varying properties, deformations and superpositions of vessels. Experiments using simulated and real data have been carried out. and the results found to be robust over a full cycle of a human heart. Local and global kinetic features can then be derived to obtain a greater insight on the cardiac functional state

Moment-Based Approaches in Imaging. 1. Basic Features [A Look At ...]

This first article was aimed at providing the basic formulations of moments, a classification, and an introductory bibliography. This first part presents a classification of moments, and, rather than entering into theoretical details, it sketches their different expressions. The companion articles will review their properties and the potential contributions they already bring to imaging.

Quaternion Bessel-Fourier moments and their invariant descriptors for object reconstruction and recognition

In this paper, the quaternion Bessel-Fourier moments are introduced. The significance of phase information in quaternion Bessel-Fourier moments is investigated and an accurate estimation method for rotation angle is described. Furthermore, a new set of invariant descriptors based on the magnitude and the phase information of quaternion Bessel-Fourier moments is derived. Experimental results show that quaternion Bessel-Fourier moments lead to better performance for color image reconstruction than the other quaternion orthogonal moments such as quaternion Zernike moments, quaternion pseudo-Zernike moments and quaternion orthogonal Fourier-Mellin moments. In addition, the angles estimated by the proposed moments are more accurate than those obtained by using other quaternion orthogonal moments. The proposed invariant descriptors show also better robustness to geometric and photometric transformations. Quaternion Bessel-Fourier moments for color image reconstruction and recognition.An accurate estimation method for rotation angle throughout quaternion moments.The invariant descriptor using the moment magnitudes and phase coefficients.

Image reconstruction from limited range projections using orthogonal moments

A set of orthonormal polynomials is proposed for image reconstruction from projection data. The relationship between the projection moments and image moments is discussed in detail, and some interesting properties are demonstrated. Simulation results are provided to validate the method and to compare its performance with previous works.