The recent definition of fractional Brownian motions on surfaces has raised the statistical issue of estimating the Hurst index characterizing these models. To deal with this open issue, we propose a method which is based on a spectral representation of surfaces built upon their Laplace-Beltrami operator. This method includes a first step where the surface supporting the motion is recovered using a mean curvature flow, and a second one where the Hurst index is estimated by linear regression on the motion spectrum. The method is evaluated on synthetic surfaces. The interest of the method is further illustrated on some fetal cortical surfaces extracted from magnetic resonance images as a means to quantify the brain complexity during the gestational age.

Gyrification index (GI) is an appropriate measure to quantify the complexity of the cerebral cortex. There is, however, no universal agreement on the notion of surface complexity and there are various methods in literature that evaluate different aspects of cortical folding. In this paper, we give two intuitive interpretations on folding quantification based on the magnitude and variation of the mean curvature of the cortical surface. We then present a local spectral analysis of the mean curvature to introduce two local gyrification indices that satisfy our interpretations. For this purpose, the graph windowed Fourier transform is extended to the framework of surfaces discretized with triangular meshes. An adaptive window function is also proposed to deal with the intersubject cortical size variability. The intrinsic nature of the method allows us to compute the degree of folding at different spatial scales. Our experiments show that while more classical surface area-based GIs may fail at differentiating deep folds from very convoluted ones, our spectral GIs overcome this issue. The method is applied to the cortical surfaces of 124 healthy adult subjects of OASIS database and average gyrification maps are computed and compared with other GI definitions. In order to illustrate the capacity of our method to capture and quantify important aspects of gyrification, we study the relationship between brain volume and cortical complexity, and design a scaling analysis with a power law model. Results indicate an allometric relation and confirm the well-known observations that larger brains are more folded. We also perform the scaling analysis at the vertex level to investigate how the degree of folding varies locally with the brain volume. Results reveal that in our healthy adult brain database, cortical regions which are the least folded on average show an increased folding complexity when brain size increases.

In this paper, we address a complex image registration issue arising while the dependencies between intensities of images to be registered are not spatially homogeneous. Such a situation is frequently encountered in medical imaging when a pathology present in one of the images modifies locally intensity dependencies observed on normal tissues. Usual image registration models, which are based on a single global intensity similarity criterion, fail to register such images, as they are blind to local deviations of intensity dependencies. Such a limitation is also encountered in contrast-enhanced images where there exist multiple pixel classes having different properties of contrast agent absorption. In this paper, we propose a new model in which the similarity criterion is adapted locally to images by classification of image intensity dependencies. Defined in a Bayesian framework, the similarity criterion is a mixture of probability distributions describing dependencies on two classes. The model also includes a class map which locates pixels of the two classes and weighs the two mixture components. The registration problem is formulated both as an energy minimization problem and as a maximum a posteriori estimation problem. It is solved using a gradient descent algorithm. In the problem formulation and resolution, the image deformation and the class map are estimated simultaneously, leading to an original combination of registration and classification that we call image classifying registration. Whenever sufficient information about class location is available in applications, the registration can also be performed on its own by fixing a given class map. Finally, we illustrate the interest of our model on two real applications from medical imaging: template-based segmentation of contrast-enhanced images and lesion detection in mammograms. We also conduct an evaluation of our model on simulated medical data and show its ability to take into account spatial variations of intensity dependencies while keeping a good registration accuracy.

In this paper, we focus on the design of Markov Chain Monte Carlo techniques in a statistical registration framework based on finite element basis (FE). Due to the use of FE basis, this framework has specific features. The main feature is that displacement random fields are Markovian. We construct two hybrid Gibbs/Metropolis-Hasting algorithms which take fully advantage of this Markovian property. The second technique is defined in a coarse-to-fine way by introducing a penalization on the sampled posterior distribution. We present some promising results suggesting that both techniques can accurately register images. Experiments also show that the penalized technique is more robust to local maxima of the posterior distribution than the first technique. This study is a preliminary step towards the estimation of model parameters in complex image registration problems.

The temporal comparison of mammograms is complex; a wide variety of factors can cause changes in image appearance. Mammogram registration is proposed as a method to reduce the effects of these changes and potentially to emphasize genuine alterations in breast tissue. Evaluation of such registration techniques is difficult since ground truth regarding breast deformations is not available in clinical mammograms. In this paper, we propose a systematic approach to evaluate sensitivity of registration methods to various types of changes in mammograms using synthetic breast images with known deformations. As a first step, images of the same simulated breasts with various amounts of simulated physical compression have been used to evaluate a previously described nonrigid mammogram registration technique. Registration performance is measured by calculating the average displacement error over a set of evaluation points identified in mammogram pairs. Applying appropriate thickness compensation and using a preferred order of the registered images, we obtained an average displacement error of 1.6 mm for mammograms with compression differences of 1-3 cm. The proposed methodology is applicable to analysis of other sources of mammogram differences and can be extended to the registration of multimodality breast data.