Generalizations of Ripley's K-function with Application to Space Curves

The intensity function and Ripley's K-function have been used extensively in the literature to describe the first and second moment structure of spatial point sets. This has many applications including describing the statistical structure of synaptic vesicles. Some attempts have been made to extend Ripley's K-function to curve pieces. Such an extension can be used to describe the statistical structure of muscle fibers and brain fiber tracks. In this paper, we take a computational perspective and construct new and very general variants of Ripley's K-function for curves pieces, surface patches etc. We discuss the method from [Chiu, Stoyan, Kendall, & Mecke 2013] and compare it with our generalizations theoretically, and we give examples demonstrating the difference in their ability to separate sets of curve pieces.Comment: 9 pages & 8 figure

Topology preserving atlas construction from shape data without correspondence using sparse parameters

pre-printStatistical analysis of shapes, performed by constructing an atlas composed of an average model of shapes within a population and associated deformation maps, is a fundamental aspect of medical imaging studies. Usual methods for constructing a shape atlas require point correspondences across subjects, which are difficult in practice. By contrast, methods based on currents do not require correspondence. However, existing atlas construction methods using currents suffer from two limitations. First, the template current is not in the form of a topologically correct mesh, which makes direct analysis on shapes difficult. Second, the deformations are parametrized by vectors at the same location as the normals of the template current which often provides a parametrization that is more dense than required. In this paper, we propose a novel method for constructing shape atlases using currents where topology of the template is preserved and deformation parameters are optimized independently of the shape parameters. We use an L1-type prior that enables us to adaptively compute sparse and low dimensional parameterization of deformations.We show an application of our method for comparing anatomical shapes of patients with Down's syndrome and healthy controls, where the sparse parametrization of diffeomorphisms decreases the parameter dimension by one order of magnitude

Learning Myelin Content in Multiple Sclerosis from Multimodal MRI through Adversarial Training

Multiple sclerosis (MS) is a demyelinating disease of the central nervous system (CNS). A reliable measure of the tissue myelin content is therefore essential for the understanding of the physiopathology of MS, tracking progression and assessing treatment efficacy. Positron emission tomography (PET) with [^{11} \mbox{C}] \mbox{PIB} has been proposed as a promising biomarker for measuring myelin content changes in-vivo in MS. However, PET imaging is expensive and invasive due to the injection of a radioactive tracer. On the contrary, magnetic resonance imaging (MRI) is a non-invasive, widely available technique, but existing MRI sequences do not provide, to date, a reliable, specific, or direct marker of either demyelination or remyelination. In this work, we therefore propose Sketcher-Refiner Generative Adversarial Networks (GANs) with specifically designed adversarial loss functions to predict the PET-derived myelin content map from a combination of MRI modalities. The prediction problem is solved by a sketch-refinement process in which the sketcher generates the preliminary anatomical and physiological information and the refiner refines and generates images reflecting the tissue myelin content in the human brain. We evaluated the ability of our method to predict myelin content at both global and voxel-wise levels. The evaluation results show that the demyelination in lesion regions and myelin content in normal-appearing white matter (NAWM) can be well predicted by our method. The method has the potential to become a useful tool for clinical management of patients with MS.Comment: Accepted by MICCAI201

Sparse Adaptive Parameterization of Variability in Image Ensembles

International audienceThis paper introduces a new parameterization of diffeomorphic deformations for the characterization of the variability in image ensembles. Dense diffeomorphic deformations are built by interpolating the motion of a finite set of control points that forms a Hamiltonian flow of self-interacting particles. The proposed approach estimates a template image representative of a given image set, an optimal set of control points that focuses on the most variable parts of the image, and template-to-image registrations that quantify the variability within the image set. The method automatically selects the most relevant control points for the characterization of the image variability and estimates their optimal positions in the template domain. The optimization in position is done during the estimation of the deformations without adding any computational cost at each step of the gradient descent. The selection of the control points is done by adding a L 1 prior to the objective function, which is optimized using the FISTA algorithm

Syntactic complexity in the comprehension of wh-questions and relative clauses in typical language development and autism

This study investigates effects of syntactic complexity operationalised in terms of movement, intervention and (NP) feature similarity in the development of A’ dependencies in 4-, 6-, and 8-year old typically developing (TD) French children and children with Autism Spectrum Disorders (ASD). Children completed an off-line comprehension task testing eight syntactic structures classified in four levels of complexity: Level 0: No Movement; Level 1: Movement without (configurational) Intervention; Level 2: Movement with Intervention from an element which is maximally different or featurally ‘disjoint’ (mismatched in both lexical NP restriction and number); Level 3: Movement with Intervention from an element similar in one feature or featurally ‘intersecting’ (matched in lexical NP restriction, mismatched in number). The results show that syntactic complexity affects TD children across the three age groups, but also indicate developmental differences between these groups. Movement affected all three groups in a similar way, but intervention effects in intersection cases were stronger in younger than older children, with NP feature similarity affecting only 4-year olds. Complexity effects created by the similarity in lexical restriction of an intervener thus appear to be overcome early in development, arguably thanks to other differences of this intervener (which was mismatched in number). Children with ASD performed less well than the TD children although they were matched on non-verbal reasoning. Overall, syntactic complexity affected their performance in a similar way as in their TD controls, but their performance correlated with non-verbal abilities rather than age, suggesting that their grammatical development does not follow the smooth relation to age that is found in TD children

Learning distributions of shape trajectories from longitudinal datasets: a hierarchical model on a manifold of diffeomorphisms

We propose a method to learn a distribution of shape trajectories from longitudinal data, i.e. the collection of individual objects repeatedly observed at multiple time-points. The method allows to compute an average spatiotemporal trajectory of shape changes at the group level, and the individual variations of this trajectory both in terms of geometry and time dynamics. First, we formulate a non-linear mixed-effects statistical model as the combination of a generic statistical model for manifold-valued longitudinal data, a deformation model defining shape trajectories via the action of a finite-dimensional set of diffeomorphisms with a manifold structure, and an efficient numerical scheme to compute parallel transport on this manifold. Second, we introduce a MCMC-SAEM algorithm with a specific approach to shape sampling, an adaptive scheme for proposal variances, and a log-likelihood tempering strategy to estimate our model. Third, we validate our algorithm on 2D simulated data, and then estimate a scenario of alteration of the shape of the hippocampus 3D brain structure during the course of Alzheimer's disease. The method shows for instance that hippocampal atrophy progresses more quickly in female subjects, and occurs earlier in APOE4 mutation carriers. We finally illustrate the potential of our method for classifying pathological trajectories versus normal ageing

Learning the clustering of longitudinal shape data sets into a mixture of independent or branching trajectories

Given repeated observations of several subjects over time, i.e. a longitudinal data set, this paper introduces a new model to learn a classification of the shapes progression in an unsupervised setting: we automatically cluster a longitudinal data set in different classes without labels. Our method learns for each cluster an average shape trajectory (or representative curve) and its variance in space and time. Representative trajectories are built as the combination of pieces of curves. This mixture model is flexible enough to handle independent trajectories for each cluster as well as fork and merge scenarios. The estimation of such non linear mixture models in high dimension is known to be difficult because of the trapping states effect that hampers the optimisation of cluster assignments during training. We address this issue by using a tempered version of the stochastic EM algorithm. Finally, we apply our algorithm on different data sets. First, synthetic data are used to show that a tempered scheme achieves better convergence. We then apply our method to different real data sets: 1D RECIST score used to monitor tumors growth, 3D facial expressions and meshes of the hippocampus. In particular, we show how the method can be used to test different scenarios of hip-pocampus atrophy in ageing by using an heteregenous population of normal ageing individuals and mild cog-nitive impaired subjects

Bilingualism and creativity across development: Evidence from divergent thinking and convergent thinking.

Numerous studies have demonstrated the benefits of creativity from bilingualism. Divergent thinking and convergent thinking are considered the two most important components of creativity. Various (although not all) studies have concluded that bilingual children outperform monolingual children in divergent thinking, however, no study on children or adolescents so far has explored the relation between bilingualism and convergent thinking, or the brain structural basis of interaction between bilingualism and creativity. This study aimed to explore the impact of bilingualism on both convergent and divergent thinking in children and adolescents based on neuropsychological assessments, and the possible structural basis of the effect of bilingualism on creativity by a whole-brain analysis of regional gray matter volume (rGMV) and cortical thickness in children and adolescents. 92 healthy children and adolescents of age 4-18 were recruited from public or private schools in the French-speaking side of Switzerland. Demographic data of the participants were collected, including gender, age, pedagogy, usage of language, and parents' socioeconomic status. Most of the participants underwent the neuropsychological assessments of divergent thinking, convergent thinking, and fluid intelligence. Structural image data of 75 participants were analyzed. Both voxel-based morphometry (VBM) and surface-based morphometry (SBM) were processed, to perform the analyses of rGMV and cortical thickness respectively. The outcomes indicated that convergent thinking, but not divergent thinking benefits from bilingualism in children and adolescents. However, this bilingual advantage appears to weaken across development. Unexpectedly, no significant correlation between morphometry and bilingualism was found. Neither divergent thinking scores nor convergent thinking scores showed any significant correlation with rGMV. However, the whole brain SBM showed that the cortical thickness in the right supplementary motor area (SMA) was negatively correlated with convergent thinking scores, which suggested that the children and adolescents with higher convergent thinking abilities may have thinner, more mature, and more activated cortex in the right SMA. Bilingualism and cortical thinness in the right SMA might facilitate convergent thinking independently, by enhancing this selective ability