Locally adaptive density estimation on Riemannian manifolds

In this paper, we consider kernel type estimator with variable bandwidth when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also considered to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyse two real examples where two different manifolds are considered

Cải tiến tiêu chuẩn khoảng cách trong xây dựng chùm các phần tử rời rạc

Nghiên cứu này đề nghị một độ đo mới để đánh giá sự tương tự chùm của các phần tử rời rạc được gọi là chỉ số tương tự chùm (CSI). CSI được sử dụng làm tiêu chuẩn để xây dựng các thuật toán phân tích chùm mờ, không mờ và xác định số chùm thích hợp. CSI cũng được sử dụng để đánh giá chất lượng của các chùm được thiết lập cũng như so sánh chúng với nhau. Các thuật toán được thiết lập có thể thực hiện nhanh chóng bởi những chương trình được viết trên phần mềm Matlab. Những ví dụ số minh họa các thuật toán đề nghị và cho thấy thuận lợi của chúng so với các thuật toán khác. Phân tích chùm các hình ảnh từ thuật toán đề nghị cho thấy tiềm năng trong áp dụng thực tế của vấn đề được nghiên cứu

Segmenting Fiber Bundles in Diffusion Tensor Images

Abstract. We consider the problem of segmenting fiber bundles in diffusion tensor images. We cast this problem as a manifold clustering problem in which different fiber bundles correspond to different submanifolds of the space of diffu-sion tensors. We first learn a local representation of the diffusion tensor data using a generalization of the locally linear embedding (LLE) algorithm from Euclidean to diffusion tensor data. Such a generalization exploits geometric properties of the space of symmetric positive semi-definite matrices, particularly its Riemannian metric. Then, under the assumption that different fiber bundles are physically distinct, we show that the null space of a matrix built from the local representation gives the segmentation of the fiber bundles. Our method is computationally simple, can handle large deformations of the principal direction along the fiber tracts, and performs automatic segmentation without requiring previous fiber tracking. Results on synthetic and real diffusion tensor images are also presented.

Bayesian network modeling of the consensus between experts: an application to neuron classification

Neuronal morphology is hugely variable across brain regions and species, and their classification strategies are a matter of intense debate in neuroscience. GABAergic cortical interneurons have been a challenge because it is difficult to find a set of morphological properties which clearly define neuronal types. A group of 48 neuroscience experts around the world were asked to classify a set of 320 cortical GABAergic interneurons according to the main features of their three-dimensional morphological reconstructions. A methodology for building a model which captures the opinions of all the experts was proposed. First, one Bayesian network was learned for each expert, and we proposed an algorithm for clustering Bayesian networks corresponding to experts with similar behaviors. Then, a Bayesian network which represents the opinions of each group of experts was induced. Finally, a consensus Bayesian multinet which models the opinions of the whole group of experts was built. A thorough analysis of the consensus model identified different behaviors between the experts when classifying the interneurons in the experiment. A set of characterizing morphological traits for the neuronal types was defined by performing inference in the Bayesian multinet. These findings were used to validate the model and to gain some insights into neuron morphology

Re-identification by Covariance Descriptors

International audienceThis chapter addresses the problem of appearance matching, while employing the covariance descriptor. We tackle the extremely challenging case in which the same non-rigid object has to be matched across disjoint camera views. Covariance statistics averaged over a Riemannian manifold are fundamental for designing appearance models invariant to camera changes. We discuss different ways of extracting an object appearance by incorporating various training strategies. Appearance matching is enhanced either by discriminative analysis using images from a single camera or by selecting distinctive features in a covariance metric space employing data from two cameras. By selecting only essential features for a specific class of objects (\textit{e.g.} humans) without defining \textit{a priori} feature vector for extracting covariance, we remove redundancy from the covariance descriptor and ensure low computational cost. Using a feature selection technique instead of learning on a manifold, we avoid the over-fitting problem. The proposed models have been successfully applied to the person re-identification task in which a human appearance has to be matched across non-overlapping cameras. We carry out detailed experiments of the suggested strategies, demonstrating their pros and cons \textit{w.r.t.} recognition rate and suitability to video analytics systems