Efficient Distance Transformation for Path-based Metrics

In many applications, separable algorithms have demonstrated their efficiency to perform high performance volumetric processing of shape, such as distance transformation or medial axis extraction. In the literature, several authors have discussed about conditions on the metric to be considered in a separable approach. In this article, we present generic separable algorithms to efficiently compute Voronoi maps and distance transformations for a large class of metrics. Focusing on path-based norms (chamfer masks, neighborhood sequences...), we propose efficient algorithms to compute such volumetric transformation in dimension $n$. We describe a new $O(n\cdot N^n\cdot\log{N}\cdot(n+\log f))$ algorithm for shapes in a $N^n$ domain for chamfer norms with a rational ball of $f$ facets (compared to $O(f^{\lfloor\frac{n}{2}\rfloor}\cdot N^n)$ with previous approaches). Last we further investigate an even more elaborate algorithm with the same worst-case complexity, but reaching a complexity of $O(n\cdot N^n\cdot\log{f}\cdot(n+\log f))$ experimentally, under assumption of regularity distribution of the mask vectors

Systematized calculation of optimal coefficients of 3-D chamfer norms

International audienceChamfer distances are widely used in image analysis, and many ways have been investigated to compute optimal chamfer mask coefficients. Unfortunately, these methods are not systematized: they have to be conducted manually for every mask size or image anisotropy. Since image acquisition (e.g. medical imaging) can lead to anisotropic discrete grids with unpredictable anisotropy value, automated calculation of chamfer mask coefficients becomes mandatory for efficient distance map computation. This article presents a systematized calculation of these coefficients based on the automatic construction of chamfer masks of any size associated with a triangulation that allows to derive analytically the relative error with respect to the Euclidean distance, in any 3-D anisotropic lattice

MEASUREMENT OF THE SHORTEST PATH LENGTH; DISTANCE ESTIMATION WITHIN THE 3D BORDERS OF A TISSUE OF INTEREST

Volume data, such as 3D reconstructions from histological sections orMRI and CT data, are commonly used in studies in biology and medicine. The quantification of morphological parameters and changes within a region of interest is a key concern in such studies. Specifically, it is often required to measure the distance between two points. These distance measurements have to follow a track through the tissue when measuring in sheetlike or contorted organs like the developing heart. A tool was developed that enables this kind of distance measurements. Three existing neighborhood estimators were compared; two of Verwer and one of Kiryati, all originally designed to compute chamfer distances in data sets with isotropic, cubic voxels. The estimators were therefore adjusted to handle non-isotropic data sets. Moreover, the shortest path along a track within a given tissue was calculated. The measurement of known distances, through a simplified model of an early heart tube, with anisotropic voxels was used decide which of the three estimators should be implemented. The observed Root Mean Square (RMS) errors were similar to the ones reported in literature in the unrestrained isotropic case. The adjusted Verwer estimator measuring in a 53 neighborhood performed best by far with the lowest mean and RMS errors

Three Dimensional Fast Exact Euclidean Distance (3D-FEED) Maps

In image and video analysis, distance maps are frequently used. They provide the (Euclidean) distance (ED) of background pixels to the nearest object pixel. Recently, the Fast Exact Euclidean Distance (FEED) transformation was launched. In this paper, we present the three dimensional (3D) version of FEED. 3D-FEED is compared with four other methods for a wide range of 3D test images. 3D-FEED proved to be twice as fast as the fastest algorithm available. Moreover, it provides true exact EDs, where other algorithms only approximate the ED. This unique algorithm makes the difference, especially there where time and precision are of importance

Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension

In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and the reversible medial axis extraction problems for $d$-dimensional images. We also present a $d$-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

Projections et distances discrètes

Le travail se situe dans le domaine de la géométrie discrète. La tomographie discrète sera abordée sous l'angle de ses liens avec la théorie de l'information, illustrés par l'application de la transformation Mojette et de la "Finite Radon Transform" au codage redondant d'information pour la transmission et le stockage distribué. Les distances discrètes seront exposées selon les points de vue théorique (avec une nouvelle classe de distances construites par des chemins à poids variables) et algorithmique (transformation en distance, axe médian, granulométrie) en particulier par des méthodes en un balayage d'image (en "streaming"). Le lien avec les séquences d'entiers non-décroissantes et l'inverse de Lambek-Moser sera mis en avant

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Facility Location Problems: Models, Techniques, and Applications in Waste Management

This paper presents a brief description of some existing models of facility location problems (FLPs) in solid waste management. The study provides salient information on commonly used distance functions in location models along with their corresponding mathematical formulation. Some of the optimization techniques that have been applied to location problems are also presented along with an appropriate pseudocode algorithm for their implementation. Concerning the models and solution techniques, the survey concludes by summarizing some recent studies on the applications of FLPs to waste collection and disposal. It is expected that this paper will contribute in no small measure to an integrated solid waste management system with specific emphasis on issues associated with waste collection, thereby boosting the drive for e�ective and e�cient waste collection systems. The content will also provide early career researchers with some necessary starting information required to formulate and solve problems relating to FLP

Tensor-cut: A tensor-based graph-cut blood vessel segmentation method and its application to renal artery segmentation

Blood vessel segmentation plays a fundamental role in many computer-aided diagnosis (CAD) systems, such as coronary artery stenosis quantification, cerebral aneurysm quantification, and retinal vascular tree analysis. Fine blood vessel segmentation can help build a more accurate computer-aided diagnosis system and help physicians gain a better understanding of vascular structures. The purpose of this article is to develop a blood vessel segmentation method that can improve segmentation accuracy in tiny blood vessels. In this work, we propose a tensor-based graph-cut method for blood vessel segmentation. With our method, each voxel can be modeled by a second-order tensor, allowing the capture of the intensity information and the geometric information for building a more accurate model for blood vessel segmentation. We compared our proposed method’s accuracy to several state-of-the-art blood vessel segmentation algorithms and performed experiments on both simulated and clinical CT datasets. Both experiments showed that our method achieved better state-of-the-art results than the competing techniques. The mean centerline overlap ratio of our proposed method is 84% on clinical CT data. Our proposed blood vessel segmentation method outperformed other state-of-the-art methods by 10% on clinical CT data. Tiny blood vessels in clinical CT data with a 1-mm radius can be extracted using the proposed technique. The experiments on a clinical dataset showed that the proposed method significantly improved the segmentation accuracy in tiny blood vessels