[[alternative]]An Efficient Shape-Representation Method for Content Based Image Retrieval

計畫編號：NSC93-2213-E032-006研究期間：200408~200507研究經費：593,000[[abstract]]以內容為基礎之影像查詢(CBIR)的研究可分為特徵選取、物件表示以及結果比 對。假如以物件的外形輪廓表示物件的特徵，那麼邊緣點偵測就是抽取這類特徵的第 一個步驟。當找完了邊緣點後，一個好的物件表示法必須能夠克服物件在影像中的移 位、旋轉、以及放大或縮小等問題。甚至對於物件外形在一定程度內的損毀下也必須 能夠有好的比對結果。這些問題都是在利用物件外形特徵來表示物件時以及比對過程 中相當重要的議題。 因此本計畫將提出一個有效率及強健的以物件外形特徵為基礎的影像查詢系統。 我們使用一快速的邊緣點偵測演算法來偵測出影像中所有可能的邊緣點，並提出一新 的物件表示法—爬山式序列表示法(Mountain Climbing Sequence (MCS))。此表示法 對於前面所提之影像中的移位、旋轉、以及放大或縮小等問題都可以達到不變的效果。 另外，由於邊緣點的偵測就目前的研究經驗上並無法保証能夠找一物件的完整外形， 因此我們也將嘗試在現有的外形特徵表示法下，克服物件外形不完整抽取的情況，甚 至於在物件少部份被遮蔽的狀況也能得到好的比對結果。[[sponsorship]]行政院國家科學委員

Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape

We present a full pipeline for computing the medial axis transform of an arbitrary 2D shape. The instability of the medial axis transform is overcome by a pruning algorithm guided by a user-defined Hausdorff distance threshold. The stable medial axis transform is then approximated by spline curves in 3D to produce a smooth and compact representation. These spline curves are computed by minimizing the approximation error between the input shape and the shape represented by the medial axis transform. Our results on various 2D shapes suggest that our method is practical and effective, and yields faithful and compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing

A unified Pythagorean hodograph approach to the medial axis transform and offset approximation

AbstractAlgorithms based on Pythagorean hodographs (PH) in the Euclidean plane and in Minkowski space share common goals, the main one being rationality of offsets of planar domains. However, only separate interpolation techniques based on these curves can be found in the literature. It was recently revealed that rational PH curves in the Euclidean plane and in Minkowski space are very closely related. In this paper, we continue the discussion of the interplay between spatial MPH curves and their associated planar PH curves from the point of view of Hermite interpolation. On the basis of this approach we design a new, simple interpolation algorithm. The main advantage of the unifying method presented lies in the fact that it uses, after only some simple additional computations, an arbitrary algorithm for interpolation using planar PH curves also for interpolation using spatial MPH curves. We present the functionality of our method for G1 Hermite data; however, one could also obtain higher order algorithms

Nouvelle approche de calcul de l'axe de médiane d'objets basée sur le clustering

Le squelette et l'axe de la médiane sont des outils nés du besoin de décrire les propriétés globales d'un objet, en particulier leur forme. La plupart des algorithmes proposés calculent l'axe de médiane à partir du contour. Ceci rend ces algorithmes sensibles au bruit. Dans ce mémoire nous présentons deux nouvelles approches de calcul de la médiane. La première approche s'applique aux objets simples sans bifurcation et la deuxième traite des objets plus complexes avec plusieurs branches et des épaisseurs variables. Les deux méthodes sont basées sur le"clustering" afin de calculer l'axe de médiane à partir de tout l'objet

Proper shape representation of single figure and multi-figure anatomical objects

Extracting anatomic objects from medical images is an important process in various medical applications. This extraction, called image segmentation, is often realized by deformable models. Among deformable model methods, medial deformable models have the unique advantage of representing not only the object boundary surfaces but also the object interior volume. Based on one medial deformable model called the m-rep, the main goal of this dissertation is to provide proper shape representations of simple anatomical objects of one part and complex anatomical objects of multiple parts in a population. This dissertation focuses on several challenges in the existing medially based deformable model method: 1. how to derive a proper continuous form by interpolating a discrete medial shape representation; 2. how to represent complex objects with several parts and do statistical analysis on them; 3. how to avoid local shape defects, such as folding or creasing, in shapes represented by the deformable model. The proposed methods in this dissertation address these challenges in more detail: 1. An interpolation method for a discrete medial shape model is proposed to guarantee the legality of the interpolated shape. This method is based on the integration of medial shape operators. 2. A medially based representation with hierarchy is proposed to represent complex objects with multiple parts by explicitly modeling interrelations between object parts and modeling smooth transitions between each pair of connected parts. A hierarchical statistical analysis is also proposed for these complex objects. 3. A method to fit a medial model to binary images is proposed to use an explicit legality penalty derived from the medial shape operators. Probability distributions learned from the fitted shape models by the proposed fitting method have proven to yield better image segmentation results

Estimation of probability distribution on multiple anatomical objects and evaluation of statistical shape models

The estimation of shape probability distributions of anatomic structures is a major research area in medical image analysis. The statistical shape descriptions estimated from training samples provide means and the geometric shape variations of such structures. These are key components in many applications. This dissertation presents two approaches to the estimation of a shape probability distribution of a multi-object complex. Both approaches are applied to objects in the male pelvis, and show improvement in the estimated shape distributions of the objects. The first approach is to estimate the shape variation of each object in the complex in terms of two components: the object's variation independent of the effect of its neighboring objects; and the neighbors' effect on the object. The neighbors' effect on the target object is interpreted using the idea on which linear mixed models are based. The second approach is to estimate a conditional shape probability distribution of a target object given its neighboring objects. The estimation of the conditional probability is based on principal component regression. This dissertation also presents a measure to evaluate the estimated shape probability distribution regarding its predictive power, that is, the ability of a statistical shape model to describe unseen members of the population. This aspect of statistical shape models is of key importance to any application that uses shape models. The measure can be applied to PCA-based shape models and can be interpreted as a ratio of the variation of new data explained by the retained principal directions estimated from training data. This measure was applied to shape models of synthetic warped ellipsoids and right hippocampi. According to two surface distance measures and a volume overlap measure it was empirically verified that the predictive measure reflects what happens in the ambient space where the model lies

Continuous Medial Models in Two-Sample Statistics of Shape

In questions of statistical shape analysis, the foremost is how such shapes should be represented. The number of parameters required for a given accuracy and the types of deformation they can express directly influence the quality and type of statistical inferences one can make. One example is a medial model, which represents a solid object using a skeleton of a lower dimension and naturally expresses intuitive changes such as "bending", "twisting", and "thickening". In this dissertation I develop a new three-dimensional medial model that allows continuous interpolation of the medial surface and provides a map back and forth between the boundary and its medial axis. It is the first such model to support branching, allowing the representation of a much wider class of objects than previously possible using continuous medial methods. A measure defined on the medial surface then allows one to write integrals over the boundary and the object interior in medial coordinates, enabling the expression of important object properties in an object-relative coordinate system. I show how these properties can be used to optimize correspondence during model construction. This improved correspondence reduces variability due to how the model is parameterized which could potentially mask a true shape change effect. Finally, I develop a method for performing global and local hypothesis testing between two groups of shapes. This method is capable of handling the nonlinear spaces the shapes live in and is well defined even in the high-dimension, low-sample size case. It naturally reduces to several well-known statistical tests in the linear and univariate cases

Proceedings of the First International Workshop on Mathematical Foundations of Computational Anatomy (MFCA'06) - Geometrical and Statistical Methods for Modelling Biological Shape Variability

International audienceNon-linear registration and shape analysis are well developed research topic in the medical image analysis community. There is nowadays a growing number of methods that can faithfully deal with the underlying biomechanical behaviour of intra-subject shape deformations. However, it is more difficult to relate the anatomical shape of different subjects. The goal of computational anatomy is to analyse and to statistically model this specific type of geometrical information. In the absence of any justified physical model, a natural attitude is to explore very general mathematical methods, for instance diffeomorphisms. However, working with such infinite dimensional space raises some deep computational and mathematical problems. In particular, one of the key problem is to do statistics. Likewise, modelling the variability of surfaces leads to rely on shape spaces that are much more complex than for curves. To cope with these, different methodological and computational frameworks have been proposed. The goal of the workshop was to foster interactions between researchers investigating the combination of geometry and statistics for modelling biological shape variability from image and surfaces. A special emphasis was put on theoretical developments, applications and results being welcomed as illustrations. Contributions were solicited in the following areas: * Riemannian and group theoretical methods on non-linear transformation spaces * Advanced statistics on deformations and shapes * Metrics for computational anatomy * Geometry and statistics of surfaces 26 submissions of very high quality were recieved and were reviewed by two members of the programm committee. 12 papers were finally selected for oral presentations and 8 for poster presentations. 16 of these papers are published in these proceedings, and 4 papers are published in the proceedings of MICCAI'06 (for copyright reasons, only extended abstracts are provided here)