ناحيه بندی فانتوم بيولوژيکی رشته اعصاب نخاع موش از روی تصاوير تشديد مغناطِيسی تانسور انتشار با روش نمو جبهه آماری غيرپارامتريک

زمينه و هدف مد لسازی آمارگان تانسور در ناحيه مورد علاقه می باشد سفيد را ب هصورت صحيح مدل نم يکند : مشکل عمده در اکثر کارهای پيشين ناحيه بندی تصاوير تانسور انتشار، استفاده از رويه پارامتريک جهت. اين نوع مد لسازی، آمارگان تانسورها در کلا فهای فيبری ماده. روش بررسی تصوير تانسور انتشار استفاده م يشود ناحيه بندی فانتوم بيولوژيکی رشته اعصاب نخاع موش استفاده می شود : در مطالعه حاضر از تخمين چگالی پارزن با هسته گوسی ب همنظور تعريف آمارگان در يک ناحيه مورد نظر از. اين تخمين در چارچوب الگوريتم ناحی هبندی نمو جبهه آماری غيرپارامتريک به منظور. يافت هها بالاتری از روش پارامتريک می انجامد م يباشد : آزمای شهای عددی نشان داد نمو سطح آماری غيرپارامتريک با متريک اقليدسی به نتايج ناحی هبندی با کيفيت. در ضمن مشخص شد علاوه بر متريک، مدل سازی آماری ناحيه نيز در کيفيت. s ناحی هبندی مؤثر م ی باشد. در ادامه، نتايج ما نشان داد مهم ترين بخش تخمين چگالی هسته، انتخاب پهنای باند نتيجه گيری عل يرغم هزينه محاسباتی بالای روش غيرپارامتريک، اين روش انتخاب مناسبی می باشد : درصورت يکه استفاده از مد لسازی پارامتريک به نتايج بخ شبندی مورد نظر در کاربرد خاص منجر نشود

PDEs for tensor image processing

Methods based on partial differential equations (PDEs) belong to those image processing techniques that can be extended in a particularly elegant way to tensor fields. In this survey paper the most important PDEs for discontinuity-preserving denoising of tensor fields are reviewed such that the underlying design principles becomes evident. We consider isotropic and anisotropic diffusion filters and their corresponding variational methods, mean curvature motion, and selfsnakes. These filters preserve positive semidefiniteness of any positive semidefinite initial tensor field. Finally we discuss geodesic active contours for segmenting tensor fields. Experiments are presented that illustrate the behaviour of all these methods

Second-order Democratic Aggregation

Aggregated second-order features extracted from deep convolutional networks have been shown to be effective for texture generation, fine-grained recognition, material classification, and scene understanding. In this paper, we study a class of orderless aggregation functions designed to minimize interference or equalize contributions in the context of second-order features and we show that they can be computed just as efficiently as their first-order counterparts and they have favorable properties over aggregation by summation. Another line of work has shown that matrix power normalization after aggregation can significantly improve the generalization of second-order representations. We show that matrix power normalization implicitly equalizes contributions during aggregation thus establishing a connection between matrix normalization techniques and prior work on minimizing interference. Based on the analysis we present {\gamma}-democratic aggregators that interpolate between sum ({\gamma}=1) and democratic pooling ({\gamma}=0) outperforming both on several classification tasks. Moreover, unlike power normalization, the {\gamma}-democratic aggregations can be computed in a low dimensional space by sketching that allows the use of very high-dimensional second-order features. This results in a state-of-the-art performance on several datasets

A Generic Framework for Tracking Using Particle Filter With Dynamic Shape Prior

©2007 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or distribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.DOI: 10.1109/TIP.2007.894244Tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time. Tracking algorithms using Kalman filters or particle filters (PFs) have been proposed for tracking such objects, but these have limitations due to the lack of dynamic shape information. In this paper, we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter. The PF also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and backgroun

Curvature-driven PDE methods for matrix-valued images

Matrix-valued data sets arise in a number of applications including diffusion tensor magnetic resonance imaging (DT-MRI) and physical measurements of anisotropic behaviour. Consequently, there arises the need to filter and segment such tensor fields. In order to detect edgelike structures in tensor fields, we first generalise Di Zenzo\u27s concept of a structure tensor for vector-valued images to tensor-valued data. This structure tensor allows us to extend scalar-valued mean curvature motion and self-snakes to the tensor setting. We present both two-dimensional and three-dimensional formulations, and we prove that these filters maintain positive semidefiniteness if the initial matrix data are positive semidefinite. We give an interpretation of tensorial mean curvature motion as a process for which the corresponding curve evolution of each generalised level line is the gradient descent of its total length. Moreover, we propose a geodesic active contour model for segmenting tensor fields and interpret it as a minimiser of a suitable energy functional with a metric induced by the tensor image. Since tensorial active contours incorporate information from all channels, they give a contour representation that is highly robust under noise. Experiments on three-dimensional DT-MRI data and an indefinite tensor field from fluid dynamics show that the proposed methods inherit the essential properties of their scalar-valued counterparts

Bregman Divergences for Infinite Dimensional Covariance Matrices

Abstract We introduce an approach to computing and comparing Covariance Descriptors (CovDs

Efficient Clustering on Riemannian Manifolds: A Kernelised Random Projection Approach

Reformulating computer vision problems over Riemannian manifolds has demonstrated superior performance in various computer vision applications. This is because visual data often forms a special structure lying on a lower dimensional space embedded in a higher dimensional space. However, since these manifolds belong to non-Euclidean topological spaces, exploiting their structures is computationally expensive, especially when one considers the clustering analysis of massive amounts of data. To this end, we propose an efficient framework to address the clustering problem on Riemannian manifolds. This framework implements random projections for manifold points via kernel space, which can preserve the geometric structure of the original space, but is computationally efficient. Here, we introduce three methods that follow our framework. We then validate our framework on several computer vision applications by comparing against popular clustering methods on Riemannian manifolds. Experimental results demonstrate that our framework maintains the performance of the clustering whilst massively reducing computational complexity by over two orders of magnitude in some cases