L. Luo

A moment-based three-dimensional edge operator

A three-dimensional edge operator for detecting anatomical structures in medical imaging is presented. It uses the spatial moments of the gray-level surface, and operates in three dimensions with any window size. It allows the location and the contrast surface, as well as the surface orientation, to be estimated. The computation of the discrete version is reported. Bias and errors due to the spatial sampling and noise are analyzed at both a theoretical and experimental level. The moment-based operator is compared with other well-known edge operators using simple shaped primitives for which the analytical solution is known. The 3-D rendering of real data is then provided by merging the operator in a ray-tracing framework. >

Efficient Legendre moment computation for grey level images

Legendre orthogonal moments have been widely used in the field of image analysis. Because their computation by a direct method is very time expensive, recent efforts have been devoted to the reduction of computational complexity. Nevertheless, the existing algorithms are mainly focused on binary images. We propose here a new fast method for computing the Legendre moments, which is not only suitable for binary images but also for grey level images. We first establish a recurrence formula of one-dimensional (1D) Legendre moments by using the recursive property of Legendre polynomials. As a result, the 1D Legendre moments of order p, Lp=Lp(0), can be expressed as a linear combination of Lp-1(1) and Lp-2(0). Based on this relationship, the 1D Legendre moments Lp(0) can thus be obtained from the arrays of L1(a) and L0(a), where a is an integer number less than p. To further decrease the computation complexity, an algorithm, in which no multiplication is required, is used to compute these quantities. The method is then extended to the calculation of the two-dimensional Legendre moments Lpq. We show that the proposed method is more efficient than the direct method.

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.

Treatment planning optimization by quasi-Newton and simulated annealing methods for gamma unit treatment system

The gamma unit is used to irradiate a target within the brain. During such a treatment many parameters, including the number of shots, the coordinates, the collimator size and the weight associated with each shot, affect the amount of dose delivered to the target volume and to the surrounding normal tissues. Hence it is not easy to determine an appropriate set of these parameters by a trial and error method. For this reason, we present here an optimization method to determine mathematically those parameters. This method is composed of two steps: firstly, a quasi-Newton method is used to deal with the continuous variables such as position and weight of shots; the result obtained at the end of this step then serves as the initial configuration for the next step, in which a simulated annealing method is applied to optimize all the aforementioned parameters. Application of the proposed methods to two examples shows that our optimization algorithm runs in a satisfactory way.

Medical image integrity control and forensics based on watermarking — Approximating local modifications and identifying global image alterations

In this paper we present a medical image integrity verification system that not only allows detecting and approximating malevolent local image alterations (e.g. removal or addition of findings) but is also capable to identify the nature of global image processing applied to the image (e.g. lossy compression, filtering …). For that purpose, we propose an image signature derived from the geometric moments of pixel blocks. Such a signature is computed over regions of interest of the image and then watermarked in regions of non interest. Image integrity analysis is conducted by comparing embedded and recomputed signatures. If any, local modifications are approximated through the determination of the parameters of the nearest generalized 2D Gaussian. Image moments are taken as image features and serve as inputs to one classifier we learned to discriminate the type of global image processing. Experimental results with both local and global modifications illustrate the overall performances of our approach.

Medical image integrity control seeking into the detail of the tampering

In this paper, we propose a system which aims at verifying integrity of medical images. It not only detects and localizes alterations, but also seeks into the details of the image modification to understand what occurred. For that latter purpose, we developed an image signature which allows our system to approximate modifications by a simple model, a door function of similar dimensions. This signature is partly based on a linear combination of the DCT coefficients of pixel blocks. Protection data is attached to the image by watermarking. Whence, image integrity verification is conducted by comparing this embedded data to the recomputed one from the observed image. Experimental results with malicious image modification illustrate the overall performances of our system.

An orthogonal moment-based method for automatic verification of radiation field shape.

The purpose of this paper is to develop a new method for automated on-line verification of the treatment field shape during radiotherapy. The treatment field boundary is extracted from the digital portal image and is then approximated by a polygon. The proposed procedure used one of the approved field shapes as the reference boundary for automated comparison with subsequent portal field boundaries. The orthogonal moment-based method was applied to align treatment field boundaries that include the translational shifts, scaling factor and rotation angle. Firstly, the moments of order up to one were used to adjust the magnification and translation of the test field boundary related to the reference one; this step created a common coordinate system for the two images. Then a quadratic least-square objective function based on the orthogonal moments (e.g. Legendre moments) of the two field shapes was employed to perform rotational correction. Since moment computation by a straightforward method required a large number of multiplication and addition operations, a fast method for computing Legendre moments was also developed to decrease the calculation time. Application of the method to some simulated cases showed that our alignment procedure has an accuracy of 0.5 mm in detecting translational shift, 0.004 in detecting magnification and less than 0.3 degrees in detecting rotation angle between the test shape and the reference shape. The alignment procedure using the proposed method can be done within 2 s on a Pentium II personal computer. Therefore, our method is potentially useful for automated real-time treatment field shape verification.

A vectorial image classification method based on neighborhood weighted Gaussian mixture model

The CT uroscan contains three to four time-spaced acquisitions of the same patient. Registration of these acquisitions forms a vectorial volume, which contains a more complete anatomical information. In order to outline the anatomical structures, multi-dimensional classification is necessary for analyzing this vectorial volume. Because of the partial volume effect (PVE), probability distributions are assigned to the different material types within this vectorial volume instead of a definite material distribution. Gaussian mixture model is often used in probability classification problems to model such distributions, but it relies only on the intensity distributions, which will lead a misclassification on the boundaries and inhomogeneous regions with noises. In order to solve this problem, a neighborhood weighted Gaussian mixture model is proposed in this paper. Expectation Maximization algorithm is used as optimization method. The experiments demonstrate that the proposed method can get a better classification result and less affected by the noise.

Estimation and Removal of Physiological Noise from Undersampled Multi-slice fMRI data in Image Space

The signal variations induced by respiration and cardiac motion decrease the statistical significance in functional MRI data analysis. Significant components of these fluctuations are aliased into the activation spectrum in standard multi-slice imaging protocols. A method of estimation and removal physiological noise in image space is reported. Based on reordering the data from slice ordering to time ordering, the aliased physiological information is available in multi-slice magnitude images. Then physiological noise can be estimated and removed adaptively using signal projecting technique with the actual functional signal preserved

A 3D Static Heart Model From a MSCT Data Set

Dynamic computed tomography (CT) imaging aims to access the kinetics of the moving organs. In cardiac imaging, the interest lies in the possibility of obtaining anatomic and functional information on the heart and the coronaries during the same examination. However, segmentation, reconstruction and registration algorithms need to be developed for diagnostic purposes. We propose thus to built a 3D heart model from multi-slice spiral computed tomography (MSCT) dynamic sequences to facilitate the evaluation of these algorithms. The model building relies on semi-automatic segmentation techniques based on deformable models such as fast marching and active contours. Shape-based interpolation and marching cube algorithms are then used for the 3D surface reconstruction