Active Contour Models for Manifold Valued Image Segmentation

Image segmentation is the process of partitioning a image into different regions or groups based on some characteristics like color, texture, motion or shape etc. Active contours is a popular variational method for object segmentation in images, in which the user initializes a contour which evolves in order to optimize an objective function designed such that the desired object boundary is the optimal solution. Recently, imaging modalities that produce Manifold valued images have come up, for example, DT-MRI images, vector fields. The traditional active contour model does not work on such images. In this paper, we generalize the active contour model to work on Manifold valued images. As expected, our algorithm detects regions with similar Manifold values in the image. Our algorithm also produces expected results on usual gray-scale images, since these are nothing but trivial examples of Manifold valued images. As another application of our general active contour model, we perform texture segmentation on gray-scale images by first creating an appropriate Manifold valued image. We demonstrate segmentation results for manifold valued images and texture images

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

Exploration of Balanced Metrics on Symmetric Positive Definite Matrices

International audienceSymmetric Positive Definite (SPD) matrices have been usedin many fields of medical data analysis. Many Riemannian metrics havebeen defined on this manifold but the choice of the Riemannianstructurelacks a set of principles that could lead one to choose properly the met-ric. This drives us to introduce the principle of balanced metrics that re-late the affine-invariant metric with the Euclidean and inverse-Euclideanmetric, or the Bogoliubov-Kubo-Mori metric with the Euclidean and log-Euclidean metrics. We introduce two new families of balanced metrics,the mixed-power-Euclidean and the mixed-power-affine metrics and wediscuss the relation between this new principle of balanced metrics and the concept of dual connection in information geometry

Surface-Based Analysis on Shape and Fractional Anisotropy of White Matter Tracts in Alzheimer's Disease

10.1371/journal.pone.0009811PLoS ONE53

Nonnegative Definite EAP and ODF Estimation via a Unified Multi-Shell HARDI Reconstruction

International audienceIn High Angular Resolution Diffusion Imaging (HARDI), Orientation Distribution Function (ODF) and Ensemble Average Propagator (EAP) are two important Probability Density Functions (PDFs) which reflect the water diffusion and fiber orientations. Spherical Polar Fourier Imaging (SPFI) is a recent model-free multi-shell HARDI method which estimates both EAP and ODF from the diffusion signals with multiple b values. As physical PDFs, ODFs and EAPs are nonnegative definite respectively in their domains S^2 and R^3 . However, existing ODF / EAP estimation methods like SPFI seldom consider this natural constraint. Although some works considered the nonnegative constraint on the given discrete samples of ODF / EAP, the estimated ODF/EAP is not guaranteed to be nonnegative definite in the whole continuous domain. The Riemannian framework for ODFs and EAPs has been proposed via the square root parameterization based on pre-estimated ODFs and EAPs by other methods like SPFI. However, there is no work on how to estimate the square root of ODF / EAP called as the wavefuntion directly from diffusion signals. In this paper, based on the Riemannian framework for ODFs / EAPs and Spherical Polar Fourier (SPF) basis representation, we propose a unified model-free multi-shell HARDI method, named as Square Root Parameterized Estimation (SRPE), to simultaneously estimate both the wavefunction of EAPs and the nonnegative definite ODFs and EAPs from diffusion signals. The experiments on synthetic data and real data showed SRPE is more robust to noise and has better EAP reconstruction than SPFI, especially for EAP profiles at large radius